8.2 world_communicates

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PHYPRE43200 P0025949

PhysicsPreliminary CourseStage 6

The world communicates

Incorporating October 2002

AMENDMENTS

Number: 43200 Title: The World Communicates

All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.

This publication is copyright New South Wales Department of Education and Training (DET), however it may contain material from other sources which is not owned by DET. We would like to acknowledge the following people and organisations whose material has been used: Extracts from Physics Stage 6 Syllabus © Board of Studies, NSW 2002 Introduction p iv,

Part 1 pp 3, 4 Parts 2, 3 & 4 p 2 Part 5 pp 3, 4 Part 6 p 2

Photograph of cloud formation courtesy NASA Front Cover and Part Covers

Photographs Australian Photo Library Vols 1 & 2 Front Covers and Part Covers

Diagram of electromagnetic spectrum from Messel, H (1963) Science for High School Students, The Nuclear Foundation, University of Sydney

Part 4 p 9

COMMONWEALTH OF AUSTRALIA

Copyright Regulations 1969

WARNING

This material has been reproduced and communicated to you on behalf of the New South Wales Department of Education and Training

(Centre for Learning Innovation) pursuant to Part VB of the Copyright Act 1968 (the Act).

The material in this communication may be subject to copyright under the Act. Any further reproduction or communication of this material by you may be the

subject of copyright protection under the Act.

Published by Centre for Learning Innovation (CLI) 51 Wentworth Rd Strathfield NSW 2135 _______________________________________________________________________________________________

_ Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction or transmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited without the written authority of the Centre for Learning Innovation (CLI). © State of New South Wales, Department of Education and Training 2006.

Introduction i

Contents

Module overview ....................................................................... iii

Indicative time.......................................................................................v

Resources.............................................................................................v

Icons ................................................................................................... vii

Glossary............................................................................................. viii

Part 1: Waves......................................................................1–68

Part 2: Sound waves ...........................................................1–25

Part 3: Superposition...........................................................1–28

Part 4: Electromagnetic waves............................................1–34

Part 5: Reflection and refraction..........................................1–60

Part 6: Applications ............................................................1–28

Bibliography ............................................................................ 29

Student evaluation of the module

ii Th world communicates

Introduction iii

Module overview

There are many ways to look at events and features and the technologythat drives our society. The physicists view is one of the fundamentalviews that aims to explain the phenomena around us. Physics is ascience that makes use of mathematics, concepts, models, principles andideas to explain events in the world around you.

Through this Preliminary course in Physics you will gain anunderstanding of the basis of communication methods, electricity, motionin vehicles and the place of our Solar System in the universe. All thiswill be achieved by using the physicist’s view of the world.

In the Preliminary modules the Assumed Knowledge of the ScienceStage 4-5 Syllabus will be briefly revised. You may find some of thesesections of work easy as they could cover work that you already knowand understand.

The achievement of the outcomes - knowledge and understanding, skills,values and attitudes will be assessed by:

• you, when comparing your answers to questions with suggestedanswers

• your teacher, using your send-in exercises at the end of each part ofwork.

The best way to help your teacher to help you is by:

• attempting each of the questions and activities

• returning your send-in exercises regularly and on time.

Remember your teacher is there to help you!

If you have access to a computer and the Internet you may wish toparticipate in an online forum for students of Physics. One such forumcan be found on the Physics website page at

http://www.lmpc.edu.au/science

iv Th world communicates

Practical experiences are essential for the successful completion of thePhysics Stage 6 course. These practical experiences include:

• undertaking laboratory experiments, including the use of appropriatecomputer based and digital technologies

• fieldwork

• research using a wide range of sources, including print material, theInternet and digital technologies

• the use of computer simulations for modelling or manipulating data

• using and reorganising secondary data

• extracting and reorganising information in the form of flow charts,tables, graphs, diagrams, prose and keys

• the use of animation, video and film resources that can be used tocapture/obtain information not available in other forms.

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amendedOctober 2002.The original and most up-to-date version of this document can be found on theBoard’s website at http://www.boardofstudies.nsw.edu.au.

Introduction v

Indicative time

There are four modules in the Preliminary Stage 6 Physics course. Eachmodule has an indicative completion time of 30 hours. All modules inyour Physics course are made up of six parts. Each part needs about fivehours of your time for completion.

Resources

Materials and equipment that you need to complete all activities in thismodule are listed below. Remember that some of the activities will bebest conducted at your practical session with your teacher. If you do nothave access to some of the materials do not become concerned. Yourteacher may suggest alternative activities.

For one of the exercises in Part 6 you are required to collect and analysedata on the digital process of the Internet for a 200 word report. Thisdata could be collected from the computer lift-out section of thenewspaper, TV or the Internet itself. You should be aware of this andbegin collating information now in order that you will have the necessaryresources at hand when you need them.

Access to a computer, graphics calculator and the Internet are aids toassist you in achieving the outcomes of the course. Computer relatedactivities are indicated throughout the module. If you do not have accessto a computer this will not prevent you from achieving the courseoutcomes.

For Part 1 you will need access to:

• a scientific calculator

• a graphics calculator

• a pond or puddle of still water

• a broad sheet newspaper

• a slinky spring

• a length of rope.


• a slinky spring

vi Th world communicates

• a CRO (or digital oscilloscope/CRO computer program)

• a microphone or alternative.


• a portable cassette player capable of recording sound

• a portable source of sound such as a cassette player and tape orportable CD

• a CRO (or digital oscilloscope/CRO computer program)

• a microphone or alternative.


• a light meter

• a balloon

• a ruler

• an AM/FM radio with a clearly marked tuning dial

• two cups or mugs.


• a torch (preferably a Mag® light type)

• a mirror

• a magnifying glass

• pins

• a dessert spoon

• a glass slab or perspex slab

• a protractor.


• 2 sheets of Polaroid® plastic or the lenses from polarising sunglassesor two polarising camera filters

• sticky tape.

Introduction vii

Icons

The following icons are used within this module. The meaning of eachicon is written beside it.

The hand icon means there is an activity for you to do.It may be an experiment or you may make something.

You need to use a computer for this activity.

Discuss ideas with someone else. You could speak withfamily or friends or anyone else who is available. Perhapsyou could telephone someone?

There is a safety issue that you need to consider.

There are suggested answers for the following questionsat the end of the part.

There is an exercise at the end of the part for you tocomplete.

viii Th world communicates

Glossary

This list of words and meanings is provided so that as you work throughthe module you will be able to look up the words that are unfamiliar toyou. The glossary for the entire six parts of work making up this moduleis supplied with Part 1. You will need to refer back to this glossary asyou progress through the module.

The following words, listed here with their meanings, are found in thelearning material in this module. They appear bolded the first time theyoccur in the learning material.

acceleration rate of change in velocity.

amplitude maximum displacement of a vibrating particlefrom its equilibrium position.

analyser the uppermost polaroid sheet in a petrologicalmicroscope with a polarisation direction at90∞ to the polariser.

anisotropic has variable optical properties particularlyrefractive index or colour absorption alongdifferent crystal axes.

annulment complete cancellation of wave amplitude.

antinode point of maximum displacement from theequilibrium point.

bandwidth range of frequencies.

constructiveinterference

superposition where wave displacements addto give a larger wave displacement in theresultant wave.

crest maximum positive amplitude position on atransverse wave.

decode convert a signal to a form able to beunderstood.

density mass of material in a unit volume.

destructive interference superposition of wave displacements add togive a smaller displacements.

displacement movement of the particle or field from theposition or equilibrium.

elastic ability to return to an undisturbed state whena stress is removed.

elasticity ability of a medium to return to itsundisturbed state after being deformed orstressed.

Introduction ix

electromagneticspectrum

the full range of electromagneticfrequencies/wavelengths.

electromagnetic wave an electric field and a magnetic field vibratingat right angles to each other and also to thedirection of propagation. Produced byoscillating (accelerated) charges.

emission release of energy, particle or radiation.

encode convert message into a signal for ease oftransmission.

forced (forcing)frequency

frequency of an applied vibration that isdifferent to the natural frequency.

kinetic energy energy a mass possesses due to its movement.

isotropic medium waves travel in such a medium with the samevelocity in all directions.

inversely proportional one variable is directly proportional to thereciprocal of the other.

laser acronym for light amplification by stimulatedemission of radiation.

longitudinal wave particles of the medium vibrate back and forthalong the direction of propagation.

maxima maximum amplitudes.

mechanical wave waves that travel through a medium able to bedeformed that is an elastic medium.

medium substance through which the wave istravelling.

minima amplitude of the signal is low.

monochromatic single wavelength or frequency.

nodes points of zero amplitude.

periodic repeating over time, that is, a repeated motionor a repeated waveform.

phase points of a wave are said to be in phase if theamplitude and velocities at these points at anytime are exactly the same.

phase difference the amount one wave is behind anotherusually expressed in a fraction of awavelength.

phase velocity velocity of the wave through the medium.

plane flat surface such as a sheet of paper.

x Th world communicates

polariser the lowermost polaroid sheet in a petrologicalmicroscope closest to the light source with apolarisation direction at 90∞ to the analyser.

potential energy energy possessed by an object due to itsposition.

radiation anything propagated as a wave.

reciprocal the inverse of for example the reciprocal of x

is 1

x.

resolution ability to distinguish points that are closetogether.

simple harmonicmotion (SHM)

vibrating motion such that the acceleration isproportional to the distance from theequilibrium position and directed towards thatequilibrium position.

sine wave has a wave form the same as a sine functionwhen plotted. The shape of the curveproduced when y = sin x is plotted.

superposition adding the displacements of two or morewaves in the same medium to produce aresultant waveform.

telecommunications a system or method of transferringinformation by means of any electromagneticsystem such as radios waves or copper cable.

transmitter the device or apparatus that sends the signalto the receiving parts of a telecommunicationssystem.

transverse wave vibrate in a plane that is perpendicular to thedirection of propagation.

trough maximum negative amplitude position on atransverse wave.

velocity a speed in a certain direction.

vibrate move to-and-fro along a straight line or alongthe arc.

viscosity resistance to flow in a fluid.

wave transfer of energy from a point withoutaccompanying transfer of mass.

wavelength distance between two successive crests ortroughs of a simple sine wave.

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Part 1: Waves


AMENDMENTS








Part 4 p 9



WARNING







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Part 1: Waves 1

Contents

Introduction ............................................................................... 3

Communication outline.............................................................. 5

Developments in communication........................................................6

What do you know now?.....................................................................8

Communication devices....................................................................10

What is a wave anyway?......................................................... 12

Describing a wave.............................................................................12

What is the source of waves?...........................................................13

What is the wave model?..................................................................16

Waves are carriers of energy .................................................. 17

Examples of waves ...........................................................................17

Do waves carry energy? ...................................................................19

Wave detectors .................................................................................20

Evidence of energy transfer..............................................................21

Waves in one dimension...................................................................21

Waves in two dimensions .................................................................23

Drawing waves, rays and wavefronts...............................................25

Experimenting with water waves ......................................................27

Waves in three dimensions...............................................................28

The features of waves ............................................................. 31

2 The world communicates

Frequency and wavelength ..............................................................32

How can waves be classified?................................................. 36

Can you make a longitudinal wave? ................................................37

Making a transverse wave................................................................39

Electromagnetic waves.....................................................................41

Wave motion............................................................................ 43

Simple harmonic motion ...................................................................43

Amplitude of a wave..........................................................................45

What does frequency mean? ...........................................................46

Frequency, wavelength and velocity................................................48

Wave velocity, v ................................................................................49

Using the wave equation ......................................................... 51

Can you use the wave equation?.....................................................52

Communication devices and waves......................................... 54

Summary ................................................................................. 57

Suggested answers ................................................................. 59

Exercises – Part 1.................................................................... 65

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Part 1: Waves 3

Introduction

This part introduces the topic ‘The world communicates’. Some of thematerial in Part 1 may seem familiar to you. This is material you shouldrecall from the Science Stage 4 or 5 course.

In Part 1, you will be given opportunities to learn to:

• analyse information to identify the waves involved in the transfer ofenergy that occurs during the use of one of the followingtransformations required in one of the following:

– mobile telephone

– television

– radar

• describe waves as a transfer of energy disturbance that may occur inone, two or three dimensions, depending on the nature of the wavemedium

• identify that mechanical waves require a medium for propagationwhile electromagnetic waves do not

• describe electromagnetic waves in terms of their speed in space andtheir lack of requirement of a medium for propagation

• define and apply the following terms to the wave model: ‘medium’,‘displacement’, ‘annulment’, ‘period’, ‘compression’,‘rarefaction’, ‘crest’, ‘trough’, ‘transverse waves’, ‘longitudinalwaves’, ‘frequency’, ‘wavelength’, ‘velocity’

• describe the relationship between particle motion and the directionof energy propagation in transverse and longitudinal waves

• quantify the relationship between velocity, frequency andwavelength for a wave:

rv f= l

In this part you will be given opportunities to:

• perform a first–hand investigation to observe and gather informationabout the transmission of waves in:

– slinky springs


– water waves

– ropes

or use appropriate computer simulations

• present diagrammatic information about transverse and longitudinalwaves, direction of particle movement and the direction ofpropagation

• solve problems and analyse information by applying themathematical model of

rv f= l to a range of situations

• present diagrammatic information showing the troughs and crests oftransverse waves and calculate the wavelength and amplitude

• perform a first–hand investigation to gather information about thefrequency, amplitude and velocity of waves using an oscilloscopeand electronic data–logging equipment

• present and analyse information from displacement–time graphs fortransverse wave motion.

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amendedOctober 2002. The original and most up - to - date version of this documentcan be found on the Board’s website athttp://www.boardofstudies.nsw.edu.au/syllabus_hsc/syllabus2000_listp.html#p

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Part 1: Waves 5

Communication outline

Humans are social animals. They need to communicate to maintain theirsocial structure. Humans may have first communicated with gesturesusing light waves. Then they developed speech or noises utilising soundwaves so they could warn others of impending danger.

These sound codings were then supplemented with symbols and writtencommunication. The use of a written message meant thatcommunications could be maintained over larger distances and throughtime. Storage of communications became possible.

The trend has been for faster and more efficient methods ofcommunication. It took several days or months to get information fromone side of the world to the other 150 years ago. The discovery ofelectricity and the use of the electromagnetic spectrum to carry signalshas led to changes to the way you communicate. Now our society is saidto be in the ‘information age’. The information modern society relies onis the result of messages carried as energy pulses by waves.

To speed communication of information you can use a broad range of thewaves in electromagnetic spectrum to transfer messages including lightand radio waves. It is now possible for you, speaking in a normal voice,to communicate a message around the world. In the late 19th centurythis communication would have made it only from one end of a room tothe other.

Now you can encode the spoken word through common devices such asthe telephone that converts the sound waves to a more suitable form fortransmission over a longer distance and send the message to another partof the world almost instantaneously. The phone you called re–assemblesor decodes the message into sound waves and you can communicate withthe user of that phone on the other side of the world.

Most of us now accept the transfer of ‘live’ sporting or cultural eventsbroadcast by television to our home as routine. The conversion andtransfer of the vision and sound of the event to our television on the otherside of the world from where the event is occurring is the result of energytransfer by waves. The light and sound of the event is not transferred.


The energy is transformed by an encoding device and forwarded to adecoding device. This occurs using the pulsed waveform most suitableto move that signal rapidly over vast distances.

This module will examine some wave properties and some of the waysyou are using waves to provide you with a better understanding of theimportance of different waves for communication in the modern world.

Developments in communication

You can see, after reading the outline for the module, that the history ofcommunication has followed a sequence of technological change that hasresulted in improvements in our capacity to communicate overincreasingly large distances.

You should now prepare your own time sequence that places theadvancements in methods of communication in an increasing time order.

This exercise will allow you to get a feel for the module. You shouldn’t feelyou need a comprehensive knowledge of the history of communication atthis stage.

Here are some of the events in communication system development youmight like to include in your time sequence:

• writing on clay tablets around six or seven thousand years ago

• the use of paper began 2000 years ago

• the printing press was invented around 600 years ago

• Morse code was invented around 150 years ago

• the radio was invented around 100 years ago

• the telephone was invented 80 years ago

• television was invented around 40–50 years ago

• the Internet revolution occurred in the past 10 years.

What other advances can you think of to add to your time sequence?

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Try to imagine how each of these advances has impacted on society.As well try to think of the developments in technology that permittedeach of the advances. Write these things down next to each developmenton your time sequence. Remember, technology is any change inknowledge or equipment that enabled a task to be completed.

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Part 1: Waves 7

Complete your time sequence in the space below. Use the sequenceabove and any other data you can source from elsewhere.

Time sequence

Years ago Advance incommunication

Impacts on society Development intechnology requiredfor the advance


What do you know now?

You have read the outline. It described some of the ways you use wavesto communicate. You already use some these technologies. Now it istime for you to take what you are already aware of a step further.You should now ask yourself ‘What do I know?’ and ‘How can I connectthe pieces of information I know already?’

One of the best ways to organise your ideas and realise the answer to thesekey questions is by drawing a concept map. This will help you to preparefor the learning in the module.

Concept maps are collections of main ideas that are interrelated. Writingdown all the main ideas in a topic and then connecting the related ideas withlines makes concept maps. On the connecting lines you write what youbelieve is the link between the concepts. As you progress through the topicyou can add links to your concept map. This means the concept map willform a summary for you at the end of the topic.

Concept maps:

• are rarely neat. Lines connecting concepts can and do go anywhereand everywhere

• are yours. No one else will make exactly the same map

• are drawn at the beginning of a module to help you to organise yourthoughts about what you already know and gives you some ideaabout possible connections that you might make as your learning inthe module continues

• should be added to as you go through the module

• drawn at the end of a module, can help your teacher to help you clearup any misunderstanding you have about the learning in a module orsection of a module.

As you progress through the module you may change your mind aboutsome of the things your map contained earlier. That means you arelearning more. Therefore, it is a good idea to do your map in pencil or byusing a computer so you can easily delete or add things later.

Drawing a concept map

There is an outline of a concept map on the next page. The mainconcepts you will need to connect and learn about in this module areshown in the bubbles. There may be more that you can add later as thetopic progresses.

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Part 1: Waves 9

Your task is to complete this concept map by joining interrelated concepts inthe bubbles with a line as the topic progresses. You should write on theconnecting lines you have drawn to show how these ideas and any othersyou can think of are connected. It may be better for you to copy these pointsto a large sheet of paper to ensure that you have enough room to add yourcomments and any other major points you think of while doing the module.

A concept map allows you to see what you know before beginning themodule. Don’t worry if you can’t make too many connections.Remember you haven’t done the learning activities in this module yet.At the end of the module you will submit your concept map to yourteacher to enable him/her to assess your understanding of the module.

communication

mechanicalwaves

theinformation

age

refraction waves reflection

light informationtechnology

the wavemodel

energytransformation

sound electromagneticwaves

Having completed as much of the concept map as you can, answer thefollowing questions.


• Do you understand the content of the module more clearly now?

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• What would you like to know more about from the topics shown inthe concept map for this module?

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• Where do you think you could find more information about thetopics in the bubbles of the concept map?

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• Can you locate this easily? Will this information help your study?

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The idea of communication is now synonymous with the use ofcommunication devices. There are large numbers of mediaadvertisements (using communication devices) for the latest and bestcommunication devices. The next section of this module looks at what acommunication device does.

Communication devices

What does a communication device need to work and what hascommunication got to do with waves? This is probably one of thequestions you have already thought about.

One of the best descriptions of the requirements of a communicationsdevice is that provided by Samuel Morse of Morse code fame.Morse was the first great pioneer of telecommunications.

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Part 1: Waves 11

Morse listed the essential parts of his telecommunication system as:

• a system of signs, by which numbers, and consequently words andsentences, are converted into a signal; this is equivalent to anencoding device. Encoding simply means converting the messageinto a form that can be used as a signal

• a set of type instructions or symbols adapted to regulate andcommunicate the signals, with rules in which to set up the type; thisis equivalent to a transmitter or sending device

• an apparatus called the port–rule, for regulating the movement of thetype–rules, that regulate the times and intervals of the passage ofelectricity; this is equivalent to a device to add information to thewave signal

• methods of laying conductors to preserve them from injury; this is amedium for the wave carrying the message to travel through

• a register, which records the signs permanently; this is equivalent toa receiver that detects the wave

• a dictionary, or vocabulary of words, numbered and adapted to thissystem of telegraph; this is equivalent to a decoding device.

Every modern device you can use for telecommunication must have thesebasic parts.

Drawing a communication flow chart

When you use a communication device such as a transistor radio it has all ofthese features. Draw a flow chart in the space below to identify all of theparts of the chain necessary to make up a radio transmission from yourfavourite radio station to you.


What is a wave anyway?

In a communication device the signal carrier is a wave. When you go outform the shore one or two kilometres over the ocean in an aeroplane orlook at the sea from a tall cliff, you often see swells rolling in towardshore. Swells are big waves. If you were able to look at the swells incross–section you would see they are in the shape of a sine wave.

A sine wave is the curve that you can produce if you plot y = sin x forvalues of x between 0 and 360°. The highest points of the waves arecrests (that would be 90° on your plot of y = sin x), and the lowest pointsare troughs (that would be 270° on your plot of y = sin x).

The distance, crest to crest between waves is called the wavelength. Ifyou were to cut a wavelength in halves, you would get two oppositeshapes, one down and the other up. If you were to count how many fullocean waves pass a fixed point per second you have the wave frequency.

Describing a wave1 On the diagram of a wave below label a trough and a crest.

The wave drawn above shows one complete wavelength.

2 Write a definition for a wavelength by describing the wave above.

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Part 1: Waves 13

3 Continue this wave on by drawing a wave shape pattern so that youdraw in another complete wavelength on this diagram.

Do you know a mathematical function that has a similar shape to thewave you have drawn? A sine curve has a similar shape to the wavesshown in the diagram.

What is the source of waves?

The source of all waves is a vibration.

To see how a wave is produced from a simple vibration, imagine youhave set up the apparatus in the figure below. The mass on a spring has apen attached to the mass, m. The pen is able to write on a strip of paper.

Now imagine what would happen if a simple chart recorder is attached tothe paper. A chart recorder is a motor–driven mechanism that pullspaper off a roll at a constant speed.

If you set the mass vibrating up and down by pulling on the spring thenreleasing it with the chart recorder switched off, then the pen (being incontact with the paper) will mark out a straight line on the paper asshown in the figure below. The number of vibrations of the pen up anddown per second is assumed to be constant in this example.

paper is stationarym

straight line

vibration direction

The pattern produced when the source is vibrating but not moving forward inthe medium is a straight line.

Adapted from OTEN, Physics for Electrical and Electronic Engineers.

When the chart recorder is switched on, the paper moves past thevibrating pen at a constant speed. The pen will then mark out the patternshown in the figure on the next page.


m

Paper moving atconstant speed

trace left by pencil in a sine wave shape

The wave pattern being produced by a constantly vibrating source on paperpropagating forward. In this case it is the paper medium moving forward whilethe source of disturbance stays stationary.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

In this case, the pattern produced is a simple waveform, a sine wave(sine curve). Notice how the combination of one body vibrating in anup–and–down motion (the pen) and the second body moving in a straightline at a constant speed (the paper) at 90° to the vibration produces awaveform.

Making a wave

You may like to try this experiment yourself by using one hand to move apen up and down on a sheet of paper while slowly pulling the paper awayfrom the pen with your other hand.

Alternatively, you may like to have someone else help you by pulling thepaper as you move the pen up and down.

The horizontal movement of the paper shows two features. They are:

• the time the wave has propagated forward

• the distance the wave has propagated forward in that time.

Note that the distance or length of paper rolled out depends upon thespeed at which the paper was pulled out. A certain distance of paper willalways be pulled out in a fixed time if the speed of paper being pulled outis constant.

If you translate this to a graph of the motion of the vibrating pen then youcan present these graphs as shown in the figure opposite.

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Part 1: Waves 15

1 2 3

time (s)

1

0

–1

disp

lace

men

t (m

)

2 4 6

distance (m)

1

0

–1

disp

lace

men

t (m

)

These two graphs represent the same motion of the vibrating pen and the paperbeing rolled out.Adapted from OTEN, Physics for Electrical and Electronic Engineers

The first graph allows you to determine that a complete wavelength takestwo seconds to pass a point. This means the wave’s period is twoseconds. The wave’s frequency or the number of wavelengths passing apoint is 0.5 per second or 0.5 Hertz (0.5 Hz). The second graph enablesyou to determine that a wavelength is 4 m.

The combined information from these two graphs enables you todetermine the speed of the wave as represented by the amount of paperpulled out in a fixed time from the equation:

wave speed = distance travelled/time taken.

1 Use the information from the two graphs of the same motion shownabove to calculate the wave speed. Make sure your answer has units(ms–1) as well as numbers.

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2 When you see a wave travelling as a ripple across a pond or otherbody of still water what do you think is vibrating?

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Check your answers.


What is the wave model?

When most people hear the term ‘wave’ they think about the surfaceappearance of water waves in a pond or the ocean. You do this becausethese are the waves you see in nature. You can visualise the way thesewaves move in space and time and you can relate to the motion fromyour experiences with water waves.

The behaviour of water waves is obvious to all. You can see the heightof the wave, the distance between wave crests and troughs. You caneasily measure the speed of the wave propagating forward. You arecomfortable with the concept of the wave.

The wave model is an idea that enables you to describe everydayphenomena such as light or sound in a way that you can understand.In using the wave model you take information you can see in the waterworld and relate that to the behaviour you interpret to be occurring inphenomena such light and sound.

Neither light nor sound is what you could describe as obviously wavelikein appearance. If you were asked to describe behaviour of sound anddidn’t apply a wave model you would have great difficulty. A similarproblem would happen if you tried to describe light. But by the end ofthis module you will be able to describe sound and light waves in termsof a wave model.

In summary, the wave model is simply a construction to describe thebehaviour of complex phenomena in terms of something you can relateto, visible waves. In using the model though you must also accept thatsound and light are actually waves!

Do Exercise 1.1 now.

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Part 1: Waves 17

Waves are carriers of energy

How do you know waves are carriers of energy? If you ever go to thebeach and stand in front of a wave coming in you will know that wavescarry energy and can transfer that energy to objects they encounter.

Consider what happens in the following situations:

• a pebble is dropped into a pool of still water

• a flag ripples in the breeze

• the free end of a rope tied to a post is given a jerk.

In each case a disturbance caused by a vibration travelled through amedium (the water, the cloth of the flag, the material of the rope).The medium moved up and down or back and forth but did not go alongwith the disturbance.

Disturbances that travel through materials are waves. A wave can gofrom one place to another (through a medium) carrying energy with it.Wave motion is one of the most important means of transferring energyin the universe.

Examples of waves

Some everyday examples of energy being transferred by waves include:

• light waves from the Sun that carry the energy required to sustainplant life, and ultimately all life, on our planet

• light waves required for us to read printed text and signs, and viewthe visual world

• infrared waves from the Sun or hot objects such as an open fireplaceor radiators that are absorbed and detected by our bodies, providingwarmth on a cold morning


• microwaves absorbed by the water molecules in food that heat ourleftovers, speed our cooking, and can prepare us a coffee or tea inaround a minute or two

• sound waves that carry the energy from person to person which is soimportant for communicating with the spoken word

• sound waves from a siren that can act as a warning of danger orsignify the end or beginning of some event.

In which direction does the energy carried by a wave travel? In wavesthe flow of energy is in the direction that the waves travel.

The wave moving forward has a ‘face’ of continuous crest. This face iscalled the wavefront. Energy moves in the same direction as thewavefronts and is carried by the wave.

If the source of the waves is a point acting as a source of vibration (calleda point source) then the wave will radiate out from that point. This willresult in either circular or spherical wavefronts depending whether thewave is propagating in two or three dimensions.

A wave propagating in two dimensions can be represented as in thefigure below. The further the wave is from the source the straighter thosewavefronts will appear. This is because the wavefront will represent asmaller and smaller arc of a circle that is ever expanding.

point source near source far from source

spherical wavefront plane wavefront

Wavefronts from a point source.

Waves in water

In this activity you will perform an investigation in which you observe andgather information about the transmission of waves in water.

1 Find a still pond or dam.

2 Throw a rock into the middle of the pond and watch the waves asthey spread out from the disturbance. The further the individualwavefronts are from the source of the disturbance the straighter

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Part 1: Waves 19

small lengths of the wavefront will appear. Did you see the patternsshown above appearing?

3 Throw in a bigger rock. Is there any difference in the pattern? If sodescribe the difference.

4 Try throwing in two rocks at once. Describe the pattern you see bydrawing a labelled diagram on your own paper.

Do waves carry energy?

This activity is designed to assist you to recall that waves are carriers ofenergy. Many forms of energy can be carried by waves. These includemovement energy known as kinetic energy and electromagnetic energy.

There is an important difference between these two. Transfer of kineticenergy requires particles to move so that the wave travels from place toplace. Electromagnetic energy requires no particles to move from oneplace to another.

1 Using this information you should complete the following table.The energy possibilities are: kinetic energy and electromagnetic energy.

Tick the waves you decided could pass through the vacuum of space.

Wave Type of energy carried or transferred

sound wave

water wave

earthquake

light wave

radio wave

microwaves in a microwave oven

infrared wave

ultraviolet wave


2 Identify the type of energy transferred by waves in each of thesecases below.

Case Type of energy transferred

a surfer riding a wave

the stars at night

the stereo playing music at top volume

an earthquake

3 Sometimes waves are described as a transfer of an energydisturbance. What does this mean?

______________________________________________________

______________________________________________________

Check your answers.

Wave detectors

Did you know our bodies detect waves? Our senses provide our bodieswith the interface to the brain. This enables us to detect the energytransferred by small sections of the spectrum (or range) of sound andelectromagnetic waves.

Our eyes detect light waves. Sound waves are detected by our ears.Infrared waves are detected by nerve endings in our skin. You are awave detector!

Write out a list of any other wave detectors that you can think of that youwould expect to come in contact with on a regular basis, for example atelevision.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

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Part 1: Waves 21

Evidence of energy transfer

What evidence can you see that waves are a transfer of energydisturbance?

When you strike a golf ball some of the kinetic energy from the head ofyour club is transferred to the ball. The ball then takes off at a highspeed. Originally the ball had no kinetic energy. The ball gained kineticenergy when the moving club struck it. Therefore, the energy transferhas taken place by direct contact. This transfer of energy from one objectto another is easy to understand. Waves transfer energy without directcontact being necessary.

Waves in one dimension

You can make a wave travel along a rope or spring if one end is held firmlyand the other end moved up and down as shown in the figure below.

direction ofinitialvibration

direction waveshape moves

rest position of rope

Waves in one dimension. Example one: a wave in a rope.

This wave transports energy through a material by the motion of a pulseor disturbance without a transfer of the material itself.

Consider a long stretched spiral spring (see the figure below).

Stretched spiral spring.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

If the hand moves down and up as indicated in the figure above a wavewill travel along the spring as shown in the figure on the next page.


Waves in one dimension. Example two: slinky spring.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Making waves in one dimension

If you, or someone else you know, has a slinky spring, borrow it and try theactivity described above. It is often better for you to stand to the side andwatch someone else creating the wave. You may like to videotape yourwave to make slow speed observations using the frame advance on a VCR.

The wave travels along a horizontal spring or rope because as it movesdownwards one part of the spring or rope pulls the next part of the springor rope down. In so doing it loses some, and ultimately all, of its ownmovement energy. Stretching the next part of the spring or ropetransmits the down–and–up motion. That part then starts to move itself.The down–and–up motion is transmitted along the spring or rope as awave with a definite speed.

(Do not confuse this speed of the wave motion with the continuallychanging speed of the spring or rope particles. They are probablymoving up and down, with a different speed. That means the speed ofmotion of a particle or small part of the spring or rope bears littlerelationship to how fast the wave travels through the spring or rope.)

A wave travelling along a spring or rope like this is propagating (ormoving) in one dimension.

1 Relate this motion of the wave along the spring or rope to the earlieractivity where the pen moves up and down and the paper is pulled alongunder the vibrating pen.

______________________________________________________

______________________________________________________

______________________________________________________

2 How is the situation described here with the stretched spiral springor rope similar to the paper and pen experiment described earlier inthe module?

______________________________________________________

______________________________________________________

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Part 1: Waves 23

3 How is the situation described with the spring or rope different to thepaper and pen experiment?

_____________________________________________________

_____________________________________________________

_____________________________________________________

Check your answers.

Waves in two dimensions

Movement energy from one body can also be transferred to anotherwithout the bodies coming into direct contact. For example, a cork orfishing float dropped into a pond will vibrate up and down. When thecork bobs up and down in the still water, waves will be set up on thewater surface and these waves will propagate out from the cork as shownin the figure below.

TOP VIEW

FRONT VIEW

cork dropped here

Wavefronts radiating out from a disturbance in water. These waves areradiating out from the disturbance across the water surface as a series ofconcentric circular wavefronts.


The disturbance, if viewed from the front, would show a set of wavessimilar to that you saw in one dimension where a rope was attached atone end and shaken up and down. This is shown in the line diagram inthe figure above. This front view is the same as the projected waveprofile in the line diagram.

Can you see what mathematical curve it looks like? A sine curve.

On the line diagram above, mark on the projected sine wave profile thedirection of the wave motion away from the central point using arrows.

If you dropped the cork into a pond with a similar cork one or two metresaway, that cork would start to move up and down as a result of theenergy transferred to it from waves produced by the first cork.The energy from the first cork would have travelled along the watersurface, yet the water molecules themselves have simply moved in themanner described in the diagram below.

The motion of the molecules is different to the direction in which theenergy contained in the wave was moving. With water waves themolecules tend to move in nearly circular orbits as the wave passes.If you have ever gone to the beach for a swim out just beyond thebreaking surf, you may have felt the circular motion as you are moved upand down by a passing wave.

wave direction

wave trough

wave cresta water wave

water molecules move in circular orbits when a wave disturbance passes by

The actual particle movement that occurs as a wave propagates forward.

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Part 1: Waves 25

flow of energy

wavefronts

Wavefronts and the direction of energy flow

If you were to repeat the activity above but place 50 corks in a circle in astill pond and drop another cork in the centre of them, then the wavegenerated from the original disturbance would cause all of the corks tobob up and down. This example shows clearly that the water waves inthis case are an energy disturbance travelling in two dimensions capableof doing work on the still corks to make them bob up and down.The tops of a radiating wave of one concentric circle representsa wavefront.

Look at the diagram showing the wavefronts and the direction of energyflow. What can you say about the angle between the direction ofpropagation of the wave and flow of energy as indicated by the arrows?

_________________________________________________________

_________________________________________________________

Check your answer.

Drawing waves, rays and wavefronts

A line drawn perpendicular to a wavefront is called a ray. The arrowsshown on the figure are rays. Rays are drawn as straight lines witharrowheads showing the direction of wave propagation and energy flow.

If you looked down from an aircraft onto an ocean with a reasonableswell you would see parallel wavefronts moving in a directionperpendicular to the wave propagation direction.


The figure below shows a commonly used representation of thewavefronts as lines perpendicular to the direction of wave travel. A rayrepresents the direction of wave travel and could be represented by thearrow drawn on this figure.

directionof wave

The wavefronts are straight lines and the arrow in the figure below shows theirdirection of travel. This arrow could represent a ray.

The wavefronts shown above are straight. If these wavefronts were producedfrom a point source would that source be close to, or at a large distance from,the wavefronts represented in this diagram? Explain your answer.

_________________________________________________________

_________________________________________________________

_________________________________________________________

Check your answer.

It is easier to study waves and the way they interact when you can seethem. What you see in water waves can be used to explain otherphenomena in waveforms such as sound and light that you cannot see.

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Part 1: Waves 27

Experimenting with water waves

When you go to a practical session with your teacher you may see waterwaves generated with a ripple tank and wave generator.

rubberband

water(5 mmdeep)

screen

lamp

electric motor

bar touching waterfor straight ripples

ball down forcircular ripples

Wave generator. This device can generate straight wavefronts or circularwavefronts depending on the set–up.

The equipment and set–up may look like the one in the figure opposite.This device enables you to observe wave patterns in a controlledenvironment and make observations of the properties of waves.

This device is useful for studying two–dimensional waves. By adjustingthe equipment so that the bar is touching the water you can producestraight wave fronts. To produce circular wavefronts you adjust theequipment so that the ball touches the water first.


Waves in three dimensions

Can you think of some examples of a wave that might occur in threedimensions? Write down a list of any you can think of in the space below.Hint: They may be waves in which you can’t see anything moving.

_________________________________________________________

_________________________________________________________

_________________________________________________________

One of the best examples of three–dimensional wave motion is the lightfrom a globe suspended from a wire to the centre of an empty room.The light comes from the filament of the light globe yet the lightilluminates the walls, floor and ceiling of the room. The sphere of lightemitted from a globe is shown in the figure below.

Light from a suspended globe is emitted in three dimensions.

Similarly, sound generated from a point source by an explosion or sirenwill spread out in three dimensions from its source. Sirens are oftenlocated on towers above the ground to warn people higher in buildings,and on the ground in all directions from the tower. In the past in manyEuropean villages church bells were located high in the church tower forexactly this purpose. Sound from the bell spreads out in all directions,even to people high in surrounding hills.

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Part 1: Waves 29

Similarities and differences

Waves propagating in one or two dimensions are different to wavespropagating in three dimensions.

1 What similarities do three–dimensional waves have to one andtwo–dimensional waves?

_____________________________________________________

_____________________________________________________

2 What differences do three–dimensional waves have from one andtwo–dimensional waves?

_____________________________________________________

_____________________________________________________

Check your answers.

Can you describe waves?

Describing waves is simple. You have already learned some of theterminology or words used to describe the features of waves. List theterms you are familiar with already and write down what they mean.Check your definition of the word with the one given in the glossary ordefined earlier in the text.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________


_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

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Part 1: Waves 31

The features of waves

All types of waves have features in common. When describe a wave youcan refer to these features. The features of waves are listed below.

• The wavelength of a wave is the distance between adjacent points oftwo waves that are ‘in phase’. In phase means these points haveexactly the same motion at the same time.

One wavelength is the distance between adjacent crests or tops ofwaves. The symbol given to the wavelength is l.

• The wave speed is the speed of the wavefront moving forward.Wave speed has the symbol v.

• The amplitude is the maximum distance a particle vibrates from thelevel of no disturbance. The symbol for amplitude is A.

v

= wavelength

crest

trough

A

A

A = amplitude

v

v = velocity

Waves can be described in terms of wavelength, amplitude and velocity.

• The frequency of a wave is the number of wavelengths or completewave cycles that pass a fixed point in a unit of time. This is usuallyone second.

Frequency is often expressed in the units hertz (Hz). One Hz meansone wavelength passing a point in one second. One millionwavelengths passing a point in one second is a frequency of1 000 000 Hz. Frequency has the symbol f.


• The period is the time taken for one complete vibration. That is, thetime from rest to the maximum distance from the undisturbed level,then to the lowest point and back again to undisturbed level.

The period is related to the frequency by the relationship that theperiod is equal to the reciprocal of the frequency. The period hasthe symbol, T.

Tf

= 1

f is measured in hertz (Hz)

T is in seconds (s)

The figure below shows the cycle a particle would have to go through forone period as represented by the letters a to i. This cycle from a to irepresents a single wavelength.

direction of wave ripple

undisturbed levela

b

c

d

e

fg

h

i

A

The cycle of movement a wave particle goes through in one wavelength.

There a many sites on the Internet that deal with wave terminology andthe description of that terminology. Look at some pages that relate towave terminology on the Physics website page. At these websites youcan see frequency, wavelength and amplitude demonstrated. Somewebsites enable you to vary the amplitude and frequency of waves.


Frequency and wavelength

The activity below requires you to recall the features of a wave includingfrequency, wavelength and speed.

You will need to work with someone else to complete this activity mosteffectively.

Part 1: Waves 33

You should plan, choose equipment for and do this activity to gatherinformation so you can identify the relationship between the frequencyand wavelength of a wave.

In this activity you will observe a case of the frequency or amplitudechanging in a wave motion and relate that to the motion of a particlevibrating and causing a wave motion.

You will need the following equipment to do this activity:

• a double sheet from a newspaper

• a coloured marking pen.

Step 1

Use a marker pen held in one hand to set up a vibration.

Move the pen up and down in a regular motion so that it draws a straightline of constant length on the edge of a double page from a newspaper.

Have another person slowly pull the paper out from under your pen at aconstant speed so that you are drawing on the newspaper. This willenable you to draw a wave motion as in the earlier described activity nearthe beginning of the module where the pen was attached to a massvibrating on the end of a spring or rope.

While the paper is being dragged at a constant speed increase the rate atwhich you move the pen up and down the page but try not to change thelength of the motion you are drawing up and down the page.

Draw and label the resulting wave shape in the space below.

1 What feature of this wave changes going across the page?

_____________________________________________________


Step 2

Repeat the set–up above but move the pen at a constant rate. Move thepen up and down a constant number of times each minute. Graduallyincrease the length of the line you would draw up and down as the pageis pulled out from under your pen at a constant slow rate.

Draw the resulting wave shape in the space below and label it.

2 What feature of this wave changes going across the page?

______________________________________________________

Step 3

Move a marker pen up and down in a regular motion to draw a straightline of constant length on the edge of a double page from a newspaper.

Have another person slowly pull the paper out from under your pen at aconstant speed so that you draw a wave motion as in the earlier activity.

This time have the person assisting you pull the paper across the table alittle faster. Try to keep the rate at which you move the pen up and downa constant and the length of the line you are drawing a constant. Thiswould give your two waves a constant amplitude and frequency.

Draw the resulting wave shapes in the space below.

3 What feature of these two waves you have drawn is different?

______________________________________________________

Check your answers.

Part 1: Waves 35

Frequency in water waves

You have already studied frequency in the previous activity. Now youshould measure the frequency of some water waves.

Measure the frequency of a water wave in a still pond by doing thefollowing.

1 Throw a cork in near the middle of the pond. When the pond is stillagain, throw a stone near the cork. The stone will start the watervibrating where it enters and create waves.

2 Measure the time it takes for the cork to bob up and down once.

_____________________________________________________

3 Measure the time it takes for the cork to bob up and down twice.

_____________________________________________________

4 Measure the time it takes for the cork to bob up and down five times.

_____________________________________________________

5 Which answer do you feel is the most accurate and why?

_____________________________________________________

6 Divide the time taken for the cork to bob up and down five times byfive.This is the period of the wave or the time taken for one wavelengthto pass a point.

_____________________________________________________

7 The frequency of the wave is the reciprocal of the period.

The wave frequency is __________________________________

Note that the frequency of a wave can be less than 1 Hz and often iswith water waves such as those you would see at the beach.

Why do you think you get a more accurate answer if you measure thetime for the cork to bob up and down five times instead of just once?

_____________________________________________________

_____________________________________________________

Check your answer.

You know that waves have some features in common. There are,however, differences between waves also. In the next section you will beinvestigating different types of waves.


How can waves be classified?

You have probably already recognised that all wave types are not thesame in terms of the direction of vibration and energy propagation. Inthis section you will learn to classify waves according to this feature.

You can already assign waves to one of two categories according to thetype of energy they consist of:

• mechanical (kinetic/potential)

• electromagnetic.

Waves

electromagnetic mechanical

do not require mediumfor transmission

do require mediumfor transmission

all transverse

alternatingelectric andmagnetic fieldsoperatingperpendicularlyto the directionof wave travel

transverse

particles vibrateperpendicularlyto the directionof the wavepropagation

longitudinal

particles vibratein the samedirection aswavepropagation

Different wave types can be classified according to the energy they consist of orthe source of the vibration or disturbance producing the wave.

Part 1: Waves 37

Another way to classify waves is according to their ‘geometry’. This islinked to the source of the vibration or disturbance producing the wave.

The vibration or disturbance producing the wave may occur:

• at right angles (90∞) to the direction of wave propagation.

These waves are called transverse waves

• in the same direction as the direction of wave propagation.These waves are called longitudinal waves.

Use the information on the chart above to indicate whether the followingstatements are true or false.

Electromagnetic waves can travel in a vacuum. (true/false)

Mechanical waves can travel in a vacuum. (true/false)

Transverse waves are only ever electromagnetic waves. (true/false)

Longitudinal waves can be electromagnetic waves. (true/false)

A longitudinal wave can travel in a vacuum. (true/false)

Check your answers.


Can you make a longitudinal wave?

A longitudinal wave is really a series of compressions and rarefactions.Compressions are set up and travel through a medium. Sometimes thecompressions can be felt, as with a loud, low pitched note from a largeorgan pipe. At a rock concert you may feel pulses of sound if you areclose to the speakers. This is because sound is an example of alongitudinal or compression wave.

You can’t see a sound wave pulse but you can hear and feel one. If youwant to see a longitudinal wave pulse one of the easiest ways is to use aslinky spring.

compression rarefaction

Compressions and rarefactions in a slinky spring.


Longitudinal waves in a spring

To do this activity you will need to use a slinky spring. You may alreadyhave one of these but if not then you may wait and do this activity at yourpractical session with your teacher. The figures drawn below describe theresults you will see.

How to do the activity

1 Tie one end of the slinky to a post or door handle.

2 Stretch the slinky out.

3 Collect five or six coils from the ends of the slinky and compressthem together with your fingers. By doing this you are storingenergy in the compressed spring coils.

4 Let the compressed coils go.

What do you see? You should see a pulse of compressed coils travelalong the length of the slinky.

The picture below shows a pulse travelling along the slinky. This pulseis a longitudinal wave produced by compressing the spring. In alongitudinal wave, the motion of the particles of the medium is back andforth in the plane of propagation.

Longitudinal wave travelling along the slinky spring.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Part 1: Waves 39

The individual coils vibrate back and forth in the direction in which thewave pulse travels along the spring. If the compression and release ofthe coils nearest your hand is repeated, a series of longitudinal pulses willtravel along the spring. Where the coils are bunched up you have acompression and where the coils are widely separated relative to theirundisturbed positions you have a rarefaction.

Remember: In a longitudinal wave the particles vibrate in the same planeas the direction of wave travel.

Look at a page that shows an animation of a pulse travelling along a slinkyspring on the Physics website page.


Making a transverse wave

The vibration component of a transverse wave involves particlesundergoing an up and down motion while the wave travels horizontally.

One of the best examples of a transverse wave pulse is the ‘Mexicanwave’ at a sporting event in a circular stadium. The wave is created bypeople sitting in one section radiating out from the centre of the stadium.To continue the waves they raise their arms above their head just afterthe person seated next to them. Lower their arms just after the people tothe left or right of them lower their arms, depending on the direction ofwave travel.

For the wave to work most efficiently you raise your arms immediatelyafter the person beside you and lower then immediately after they lowertheirs. If everyone does this, a wave pulses forward around the stadium.The only motion of the people is at 90° to the direction of wave travel.Besides looking great it’s fun to keep the wave going.

Transverse waves in slinky springs or ropes

Tie one end of the slinky to a post or door handle. See the figure below.

Stretched slinky spring.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Stretch the slinky or rope out by walking away from where it is tied.


Be careful not to stretch the slinky too far or let it go when stretched. It mayhurt you or a friend.

Move the end of the slinky or rope you are holding down and up withsingle sharp jerk of your hand. A wave should be generated in the springand move forward as a pulse.

What do you see? You should see a pulse of vertically displaced slinkycoils or rope travel along the length of the slinky or rope. Your resultscould appear similar to the figure below.

If you look at the motion of the coils as shown you will be able to seethat the coils simply move down and up about their rest position shownby the dashed line but the pulse moves forward.

The up-and-down motion of the coils in a stretched slinky after a sudden jerk.Adapted from OTEN, Physics for Electrical and Electronic Engineers

Remember: In a transverse wave the vibration of particles is at 90∞ to the

direction of travel of the wave. Mechanical waves require the presenceof some solid, liquid or gaseous matter to travel through. That matter isthe medium that the energy forming the wave travels through.Examples of mechanical transverse waves include earthquake waves,water waves.

Now that you have looked at a transverse and a longitudinal wave in aspring you should be able to describe the method of wave travel inwords. In your description, refer to how the wave energy travels alongthe spring and how the particles vibrate to allow that wave motion.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

Part 1: Waves 41

Electromagnetic waves

Electromagnetic waves include radio, light, x-rays and gamma rays.The figure below shows a simple diagram of the electromagneticspectrum.

10–11 10–9 10–7 10–5 10–2 100 103 106

0.01 nm 1 nm 0.1 mm 0.01 mm 1 cm 1 m 1 km 103 km

gammarays

x-rays ultraviolet infra-redmicrowaves

0.4–0.7mm

light TV radioradio waves electrical

power

Wavelength

Wavelength in metres

A simple electromagnetic spectrum.Adapted from OTEN, Physics for Electrical and Electronic Engineers

In this figure the wavelength of some typical electromagnetic waves fromeach part of the spectrum are indicated. The abbreviation m is the

micrometre or 10-6 m while nm is one nanometre or 10-9 m.

1 Look at the figure above. What can you say about the trend in thewavelength of electromagnetic waves going from gamma rays to radiowaves?

_____________________________________________________

_____________________________________________________

2 The velocity of all electromagnetic waves is the same at 3 108 1¥ -msin a vacuum. Use this fact to explain how the frequency of thewaves varies as the wavelength changes.

_____________________________________________________

_____________________________________________________

_____________________________________________________

Check your answers.

Electromagnetic waves do not require matter to travel through; in factthey travel fastest in a vacuum, such as space. Most of the 150 millionkilometres between the Sun and the Earth is a vacuum. Yet light,infrared radiation and some ultraviolet radiation waves from the Sunreach us easily. As well, light from distant stars travels to our worldthrough the vast distances of the universe.


Electromagnetic waves consist of a wave propagating forward that ismade up of alternating electric and magnetic fields at 90∞ to one another.

This is shown in the figure on the next page.

source ofE-M wave

E B

An electromagnetic (E - M) wave. The electric field is represented by the symbolE and the magnetic field by the symbol B. The arrows represent the direction ofthe fields. The rise and decline of the field strengths periodically produces thewavelike form for both the magnetic and electric fields.Adapted from OTEN, Physics for Electrical and Electronic Engineers

The source of the wave is a vibrating charged particle. Electromagneticwaves always travel at a constant velocity in any medium. That velocityis given the symbol c.

No matter is involved in the transmission of electromagnetic waves.The magnetic and electric field fields propagate together in phase,perpendicular to each other as shown as shown in the figure above.

Look at a web page that shows an electromagnetic wave pulse propagatingforward on the Physics website page.


Part 1: Waves 43

Wave motions

When you look at either longitudinal or transverse mechanical wavemotion you can see that the vibration component of the wave motioninvolves particles of the medium (or bits of the spring or rope)undergoing an up-and-down or back-and-forth motion. This motion iscalled simple harmonic motion (SHM).

Simple harmonic motion

This simple harmonic motion occurs because the disturbed particles arerestrained by the elasticity of the medium and made to move backtoward the level of no disturbance. The behaviour of particles followsthe pattern outlined in the table below.

Particle positionof the wave

Displacement of theparticle from the level ofno disturbance

Speed of the particle Magnitude of theacceleration of theparticle

crest maximum zero – the particle hasstopped

maximum – theparticle will increasespeed towards thelevel of no disturbance

level of nodisturbance

zero maximum zero

trough negative maximum zero – the particle hasstopped

maximum – theparticle will increasespeed towards thelevel of no disturbance

Note that the maximum acceleration experienced by the particle at thecrest and at the trough is in opposite directions.


One of the commonest examples of simple harmonic motion is a child ona swing. This pendulum motion is simple harmonic motion. Can yousee the similarity between what is described in the table to a child’smotion on a swing?

zero zerospeed maximum

maximum maximumacceleration zero

negativemaximum

positivemaximum

position zero

The pendulum motion of the swing is simple harmonic motion.

1 Transfer the information from the table to the diagram of a wave motionbelow. Remember: Any position on the wave actually represents theposition of a particle. The vibration of the particle for a longitudinalwave is simply rotated through 90°. Write in the correct words in thefigure below.

The particle’s speed is __________________The particle’s acceleration is _____________The particle’s distance from the rest point is _



1 2 3 4 5 6 7

time (s)

dist

ance

from

und

istu

rbed

leve

l (m

)

2 If each unit on the scale on the side of the figure above represents 2m what is the amplitude of this wave? ______________________

Check your answers.

Part 1: Waves 45

Amplitude of a wave

-5

5

5 10 15510-15

y = sin x

-5

5

5 10 15510-15

y = 0.5 sin x

-5

5

5 10 15510-15

y = 5 sin x

The three curves shown above all have the same __________ and the same

___________________________ . The curves differ in the way they look

because the _________________or distance from the zero level of particle

disturbance is larger or smaller. This is represented by the value of the

number multiplying the sin x. This number is the amplitude of the wave.

Check your answers.


What does frequency mean?

The three curves shown on the following page represent waves travellingat the same velocity. All have the same amplitude but have differentfrequencies and wavelengths.

2

9

y = sin x/0.2

1

2

-1

-2

87654321

2

9

y = sin x/0.9

1

2

-1

-2

87654321

2

9

y = sin x/0.5

1

2

-1

-2

87654321

1 Are the amplitudes of the waves shown above the same or different?Explain your answer by referring to the curves.

_____________________________________________________

_____________________________________________________

2 Are the wavelengths the same or different?

______________________________________________________

______________________________________________________

Part 1: Waves 47

3 The frequencies are different. What do you think frequency is?

_____________________________________________________

_____________________________________________________

4 Complete these sentences.

(a) As the frequency increases the wavelength__________________ if the wave has a constant velocity.

(b) As the wavelength decreases the frequency____________________ if the wave has a constant velocity.

Check your answers.

Plotting curves using a graphing calculator

On a graphing calculator you can plot the graph of y = n sin x for a numberof values of n, such as for n from 1 to 5. Note how the shape of the graphchanges.

If your graphing calculator is on a computer and has an animate functionplot y = n sin x for a range of n (say 1 to 5) and you will see the amplitude ofthe wave changing.

If you don’t have a graphing calculator but have access to a computer youcan download a graphing calculator at sites on the Internet. Look at thesesites on the Physics website page.


How do changes in the amplitude (the value of n) affect frequency andwavelength?

On a graphing calculator plot the graph of y = sin x

n for a number of

values of n, say from 1 to 5.

You can see that the frequency of the wave changes.

If your graphing calculator is on a computer and has an animate function

you can plot y = sin x

n for a range of n (say 1 to 5) and you will see the

frequency of the wave changing.


Frequency, wavelength and velocity

You have seen that there is a useful connection between frequency,wavelength and velocity that is true for all types of waves. You candetermine the relationship by means of a simple experiment using a ropetied off at one end.

The faster the end of a rope is waggled, the shorter the wavelength of thewave produced. That is, the higher the frequency of a wave the smallerits wavelength.

If you measure the speed of the wave as it travels forward you will notethat it does not depend upon the speed with which the rope is waggled upand down. You could check this with two identical ropes waggled atdifferent rates.

P Q

crest A

vibrator(3 Hz)

time = 0 second

time = 1 second

3

Waves produced by waggling ropes at different rates.

Suppose your shaking produces waves of wavelength l = 20 cm

travelling on a long rope and you find that three crests pass a certainpoint, P every second. Then frequency, f = 3 Hz.

If crest A is at P at a particular time then 1 s later it will be at Q, adistance 3 l from P. That is,

3 x 20 = 60 cm from P.

The speed of the wave, v = 60 cm1 s

= 60 cm s–1

Part 1: Waves 49

Therefore, the speed of wave = frequency ¥ wavelength

v = f ¥ l where v = velocity in ms–1

f = frequency in Hz

l = wavelength in m

The quantities v, l and f are mutually interdependent. This is one of the

basic characteristics of all sorts of waves, including light and sound.This relationship is called the wave equation.

Since the frequency is equal to the reciprocal of the period f1

T= ,

then it follows that v = T

l.

Wave velocity, v

Wave velocity, v, is taken to be that of any point on the waveform (forexample, a crest) and is measured in metres per second (ms–1). Thismeans that:

velocity of a wave = distance travelled by a point on the waveform

time taken to travel that distance

Although different kinds of waves may pass through the same materialtheir velocities are generally different because of the different physicalproperties of the material that are involved in propagating them.

You may be interested in comparing the velocities of longitudinal,transverse and electromagnetic waves through various media.(Remember that electromagnetic waves include light, x-rays, and so on.)

Does the velocity of waves differ in different materials? ___________

Check your answer.

The table on the next page shows you how the velocity of waves varies indifferent materials.


Material (medium) Velocity of longitudinalmechanical waves (ms–1)

Velocity of transversemechanical waves (ms–1)

Velocity of electromagnetic waves (ms–1)

vacuum (no matter) waves not transmitted waves not transmitted 3.00 ¥108

air (dry, 0°C) 331 waves not transmitted 3.00 ¥108

body of water 1 500 variable 2.25 ¥108

crown glass 5 100 2 840 2.00 ¥108

polystyrene 2 350 1 120 1.89 ¥108

rubber 1 550 no figure available 1.73 ¥108

steel 5 960 3 235 g rays can penetrate

brass 4 700 2 110 g rays can penetrate

lead 1 960 690 g rays can penetrate

concrete 4 500 no figure available g rays can penetrate

Use the information in the table above to answer the questions below.

1 Does the velocity of longitudinal mechanical waves vary in differentmediums? ____________________________________________

2 Does the velocity of transverse mechanical waves vary in differentmediums? ____________________________________________

3 Does the velocity of electromagnetic waves vary in differentmediums? ____________________________________________

4 Are longitudinal mechanical waves able to be transmitted in solidsand liquids? ___________________________________________

5 Are transverse mechanical waves able to be transmitted in solids andliquids? Explain your answer.

______________________________________________________

______________________________________________________

6 Do electromagnetic waves travel with the same velocity in allmediums? ____________________________________________

Check your answers.

Part 1: Waves 51

Using the wave equation

In this section you will practice using the wave equation v = f ¥ l.

Sample problems follow and act as models of what you need to do.

The velocity of propagation of any periodic wave is related to thefrequency of vibration and the wavelength. This is shown in the equationbelow.

wave velocity = frequency ¥ wavelength

v = f ¥ l

Follow this worked example problem through.

Problem one

A plucked G-note on a guitar vibrates at a frequency of 384 Hz. What isthe wavelength of the resultant wave at 0∞C? Sound travels at a speed of

about 331 ms–1 at 0∞C in air.

The wave equation enables us to calculate that the wavelength of thatnote must be:

l = v ∏ f

= 331/384

= 0.86 m

Complete this sentence by crossing out the incorrect term.

As the frequency of a wave increases the wavelength increases/decreases.

Check your answer.


Problem two

Calculate the frequency of a radio wave of wavelength 150 m. The

velocity of the radio wave (an electromagnetic wave) is 3 ¥ 108 ms–1.

The equation for the wave is c = f ¥ l where:

c = 3 ¥ 108 ms–1

f = ? Hz

l = 150 m

Substituting the values into the equation gives:

c =f ¥ l

3 ¥ 108 = f ¥ 150

\ f = 3 ¥ 108/150

= 2 ¥ 106 Hz

= 2 MHz

The frequency of the radio wave is two megahertz.

Can you use the wave equation?The problems that follow require you to use the wave equation todetermine the solution.

The wave equation says:

velocity = frequency ¥ wavelength

or

v = f ¥ l

or

v =Tl

Part 1: Waves 53

1 The frequency of a hand moving one end of a tied off rope is 4 Hz.That is, the hand does 4 up-and-down motions each second. If thewaves produced measure ten centimetres from one crest to the nextcrest, calculate the velocity of the waves along the rope.

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

2 The velocity of the tsunami, (a circular wave of water sent out fromthe surface due to an underwater earthquake) observed in the PacificOcean in 1946 after an earthquake was about 800 kmh–1. Thefrequency of oscillation of the surface due to these waves was aboutonce every 12 minutes. What was the wavelength of the tsunamiwaves?

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

3 The human ear can hear sound waves across the frequency range

a) 20 Hz and

b) 20 000 Hz.

What is the range of wavelengths the ear can detect if the speed ofsound is assumed to be 340 ms–1?

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

Check your answers.

Do Exercises 1.3 to 1.5 now.


Communication devices and waves

Consider the mobile telephone. Waves transfer a representation of thesound energy of our voices across great distances, even around the world.The figure below shows some of the energy transformations that occur ina call from a mobile phone to a mobile phone.

sound vibrationsproduced in thelarynx – mechanicalenergy

electrical signalconverted toradio wave

radio waveconverted to anelectrical signalat the antenna

mechanical energyconverted toelectrical energy

sound waves convertedto mechanical energy asvibrations of the ear drum

electrical signalconverted tosound waves

radio wave convertedto an electrical signalat the antenna

radio wave converted toelectrical energy thensent to switching centre

connectingwire

The radio waves used in mobile phones are short wavelength radio wavescalled microwaves.

Part 1: Waves 55

Identify the waves involved in the transfer of energy that occurs during theuse of the mobile phone to make a call to another mobile user.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________


In the next part you will apply what you have learned by looking at theproperties of waves using sound as the wave type example.

You have finished the learning from Part 1 of the module. You shouldnow return your completed exercises to your teacher if you are aDistance Education student. If you are an Open Learning Programstudent you should refer to assignment 1 in your learners guide. Bydoing these exercises you should learn whether or not you haveunderstood the main concepts and achieved the outcomes for this sectionof the course.

Part 1: Waves 57

Summary

Draw a concept map as a summary of the information you have learnedin this part on a separate sheet of paper. Try to connect ideas and factsyou have learned together with linking statements. Doing this will helpto consolidate the learning you have done in this part.

Complete the following statements.

1. Waves are carriers of ____________________________________

2 The motion of the particles or fields in a transverse wave are at___

degrees to the propagation direction.

3 The motion of the particles in a longitude wave are at __________

degrees to the propagation direction.

4 Define the following terms:

crest_____________________________________________________

_________________________________________________________

trough ___________________________________________________

_________________________________________________________

amplitude_________________________________________________

_________________________________________________________

wavelength _______________________________________________

_________________________________________________________

frequency_________________________________________________

_________________________________________________________

period ___________________________________________________

_________________________________________________________

Part 1: Waves 59

Suggested answers

Making a wave

1 Wave speed = 6 m ∏ 3 s

Wave speed = 2 ms–1

2 The water particles.

Examples of waves as carriers of energy

1 Wave Type of energy carried or transferred

sound wave kinetic energy

water wave kinetic energy

earthquake kinetic energy

light wave ✔ electromagnetic energy

radio wave ✔ electromagnetic energy

microwaves in a microwave oven ✔ electromagnetic energy

infrared wave ✔ electromagnetic energy

ultraviolet wave ✔ electromagnetic energy


2 Case Type of energy transferred

a surfer riding a wave kinetic energy

the stars at night electromagnetic energy

the stereo playing music at top volume sound energy (kinetic energy transferredto particles)

an earthquake kinetic energy

3 The wave propagating forward carries energy with it. Withoutenergy transfer there is no wave.

Making waves in one dimension1 Particles or segments of rope move up and down in a motion at 90°

to the direction of wave travel. This compares to the pen and paperwhere the pen moves at 90° to the direction of the paper travel. Thepaper travel direction shows the path or trace of the wave and wherethe wave has been.

2 The direction of vibration of individual particles is at 90° to thedirection of wave propagation in both cases. The shape of the waveform produced in both cases is similar.

3 You can only see the disturbance moving forward with the rope orthe spring whereas you see the trace of the disturbance with the penand paper.

Waves in two dimensions

The angle between the direction of propagation of the wave and flow ofenergy is always at 90° to the wavefronts.

Drawing waves, rays and wavefronts

A large distance from the source because the wavefront represents such asmall segment of arc that it appears as a straight line.

Similarities and differences1 All carry energy away from the wave source.

2 They travel out from the source in three dimensions. These wavesare multidirectional. Their wavefronts form a sphere

Part 1: Waves 61

Frequency and wavelength1 The feature that changes is the frequency.

2 The feature that changes is the amplitude of the wave.

3 The feature of the wave that changes is the wavelength.

Frequency in water wavesReduces the chance of error. Increases reliability.

How can waves be classified?

Electromagnetic waves can travel in a vacuum. true

Mechanical waves can travel in a vacuum. false

Transverse waves are only ever electromagneticwaves.

false

Longitudinal waves can be electromagnetic waves. false

A longitudinal wave can travel in a vacuum. false

Electromagnetic waves1 Wavelength increases going from gamma rays to radio waves.

2 Since the velocity is constant for electromagnetic waves in any onemedium then an increase in wavelength must result in a decrease infrequency and a decrease in wavelength must result in an increase infrequency.

Simple harmonic motion1 At the crest the particle’s speed is zero; acceleration is maximum;

and displacement from rest point is maximum.

At the level of no disturbance the particle’s speed is maximum;acceleration is zero; and displacement from the rest point is zero.

At the trough the particle’s speed is zero; acceleration is maximum;and displacement from rest point is negative maximum.

2 The amplitude is 3 m.


Amplitude of a wave

The three curves shown all have the same wavelength and the samefrequency. The curves differ in the way they look because the amplitudeor distance from the zero level of particle disturbance is larger or smaller.This is represented by the value of the number multiplying the sin x.This number is the amplitude of the wave.

What does frequency mean?1 Amplitudes are the same because the wave heights are the same.

2 Wavelengths are different.

3 Number of wavelengths to pass a point per second.

4 (a) As the frequency increases the wavelengthdecreases if the wave has a constant velocity.

(b) As the wavelength decreases the frequencyincreases if the wave has a constant velocity.

Wave velocity

Yes, velocity differs between materials.

1 Yes

2 Yes

3 Yes

4 Yes

5 No. Not in liquids and gases.

6 No

Using the wave equationAs the frequency of a wave increases the wavelength decreases.

Can you use the wave equation?

1 l

l

==== ¥= -

10

4

4 10

cm

f Hz

v f

v

v 40cms 1

Part 1: Waves 63

2 v f

vf

v kmh

f h

km

1

-1

= ¥

=

==

=

=

-

l

l

l

l

800

5

8005

160

3 a v = f

=vf

m

¥

=

=

l

l

l

l

34020

17

b v = f

=vf

m

¥

=

=

l

l

l

l

340200000 017.

Part 1: Waves 65

Exercises - Part 1

Exercises 1.1 to 1.6 Name: _________________________________

Exercise 1.1Refer to the figure below.

direction of wave

undisturbed

a

b

c

d

e

fg

h

i

A

a) What does the distance a to i represent on the wave?

_____________________________________________________

b) What does the length A represent?

_____________________________________________________

c) Draw second wave with a wavelength half as long as the one drawnabove.

d) Label a crest and trough on the wave you have drawn.


Exercise 1.2

Identify the following waves as either transverse or longitudinal.

a) Sound _____________________________________________________

b) Ripples on the surface of a pond ______________________________

c) Radio waves _______________________________________________

d) Light waves ________________________________________________

Exercise 1.3

a) If sound travels in air at 330 ms–1, and a tuning fork vibrates at256 Hz, calculate the wavelength of the sound.

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

b) Calculate the frequency of a 200 m radio wave given that its speedof propagation is 3.0 ¥ 108 ms–1.

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

Part 1: Waves 67

Exercise 1.4A single mechanical wave is represented by the following twographs. Read the axes carefully!

1 2 3

distance (m)

1

0

–1

disp

lace

men

t (m

)

4 6

time (s)

1

0

–1

disp

lace

men

t (m

)

2

Use the two graphs to calculate:

a) the amplitude of the wave ___________________________________

b) the wavelength _____________________________________________

c) the period _________________________________________________

Calculate the velocity ___________________________________________


Exercise 1.5

a) Name your favourite radio station. What is the frequency of yourfavourite radio station? [This will be in kHz or MHz]

______________________________________________________

b) Calculate the wavelength of these radio waves from your favouriteradio station knowing that its radio waves travel at the speed oflight? (Assume the speed of light to be 3 ¥ 108 ms–1.)

______________________________________________________

______________________________________________________

Exercise 1.6

In the syllabus you are required to plan and choose equipment for andperform a first-hand investigation to gather information to identify therelationship between frequency and wavelength of a wave.

After looking back through the activities in the module you should:

• Write down how you would do this.

• Do the investigation you have planned.

• Write down your conclusions.

• Submit your results, conclusions and observations with these returnsheets to your teacher.

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

______________________________________________________

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Part 2: Sound waves


AMENDMENTS








Part 4 p 9



WARNING







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Part 2: Sound waves 1

Contents

Introduction ............................................................................... 2

Sound wave properties.............................................................. 3

What are sound waves? ......................................................................3

Sound generation...................................................................... 5

How does sound travel? ......................................................................5

Does sound need a medium?..............................................................7

Comparing waves...................................................................... 9

Compression and transverse waves .................................................10

Can you see sound waves? .................................................... 11

Sound waves and frequency .............................................................12

Volume and amplitude .......................................................................13

Summary................................................................................. 15

Suggested answers................................................................. 17

Exercises – Part 2 ................................................................... 19

Appendix ................................................................................. 25


Introduction

This part enables you to link observations of the properties of soundwaves to the properties possessed by other waves important incommunication.

In this part you will be given opportunities to learn to:

• identify that sound waves are vibrations or oscillations of particles ina medium

• relate compressions and rarefractions of sound waves to the crest andtroughs of transverse waves

• explain qualitatively that pitch is related to frequency and volume toamplitude of sound waves

In this part you will be given an opportunity to:

• perform a first–hand investigation to gather information about thefrequency and wavelength of waves using an oscilloscope orelectronic data–logging equipment

• plan, chose equipment for and perform a first–hand investigation togather information to identify the relationship between thefrequency and wavelength of a sound wave travelling at a constantvelocity

• perform a first–hand investigation and gather information to analysesound wave forms from a variety of sources using the cathode rayoscilloscope (CRO) or an alternative computer technology.

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amended October2002. The original and most up–to–date version of this document can be found on theBoard’s website athttp://www.boardofstudies.nsw.edu.au/syllabus_hsc/syllabus2000_listp.html#p

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Sound wave properties

Sound waves can be used to illustrate the properties of waves used incommunication.

In Part 1 you learned what waves are, how to describe waves and someof the properties that waves have. Now you will learn how waveproperties are able to be determined using sound waves as the example ofa wave type. Many of the properties of all waves can be shown withsound waves.

What are sound waves?

Sound waves are pressure changes or fluctuations that are produced by avibrating source. This source produces compressions (zones where theparticles are pushed together) and rarefactions (zones where the particlesare spread apart) in materials.

In an undisturbed medium the particles are randomly and evenlydistributed. Materials in which sound could propagate could include theparticles in a gas, liquid, solid or a composite material made up ofparticles in a number of states. Usually you think about sound travellingin a gaseous medium (such as air).

The figure below shows you a sound wave propagating forward as aseries of compressions (where the particles are closer together) andrarefactions (where the particles are further apart). The wavelength ofthese waves is shown.

A sound propagates forward as a series of compressions and rarefactions. Thewavelength is shown, l.


1 Is the vibration of the particle shown in the figure above representing asound wave in the same direction as the wave propagation or is it at 90∞to the propagation direction?

_____________________________________________________

2 Cross out the incorrect response in the sentence below:

Sound is therefore a longitudinal/transverse wave.

Check your answers

There are many sites on the Internet that deal with sound wavespropagating forward as a series of high pressure pulses.

For more information on how to search the internet see the Resourcebooklet.

Look at some information and animations that relate to sound wavepropagation on the Physics website page.


Hearing sound

You hear sound because when pressure fluctuations reach your ear drumthe compressions push the ear drum in (high pressure zone) and therarefactions allow the eardrum to flex out (low pressure zone).

This is more fully explained with an animated figure found on the Internet.Look at some information and animations that relate to sound waves andhearing on the Physics website page.


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Sound generation

You can feel sound being generated! Try the following activity.

• Turn a stereo volume up loud and feel the air in front of the speaker.You can feel the pressure of the moving air in front of the speaker cone.This sound wave can produce a feeling of motion or a push on yourhand in the same direction as the sound waves are moving, that is outfrom the speaker.

• Strike the prongs of a tuning fork and feel the prongs. Are theyvibrating in the same direction as the sound waves are moving?Find out by listening to a tuning fork held next to your ear andchanging its orientation by rotating it.

• Put your hand on your throat and talk or yell. You can feel yourvocal chords in your larynx (voice box) vibrating.

You can see a sound wave produced by a tuning fork travelling in the samedirection as the vibration of a tuning fork as an animation on the Physicswebsite. http://www.lmpc.edu.au/science

How does sound travel?

In sound waves, the molecules of any elastic medium vibrate parallel to thedirection of wave travel. The particles move only a little distance from theiroriginal positions. They collide with neighbouring molecules and so transferthe vibratory energy through the medium.

It’s the disturbance that constitutes the wave and it’s the disturbance thattravels and carries the energy. The individual molecules pretty much stayput, just as the individual coils on the slinky spring stay close to where theybegan in the slinky version of the longitudinal wave even though the waveflashes by.

If you yell a short blasting ‘beep’, the pressure pulse of crowded moleculescreated will push on the next layer of molecules and then the next and so on.


In that way the disturbance will move out as a wave from you, propagating onits own across the room, just as the pulse moved along the spring.

Anyone down range who happens to pick up a little of that wavefront receivesenergy that will set their ear drum vibrating in step. That is, they hearthe ‘beep’.

Longitudinal waves require a medium to travel from place to place. Forsound this is often air but sound waves can also travel through liquidsand solids.

Sound travels through liquids

A listening device on another ship or surface vessel can detect a submergedsubmarine. For this reason it is critical that submarines, as ships of war, aredesigned to run as quietly as possible.

Sound also travels through solids

Examples include:

• An approaching train may be heard more than two kilometres away byplacing one end of a metal rod on the railway line and the other end onthe ear. The sound vibrations caused by the train in the rail lines travelthrough the rod to the ear.

• People buried alive in collapsed buildings following disasters likeearthquakes are often found because they tap solid objects close to them.That sound of tapping travels through the solids to reach the surface.Tapping takes much less energy than yelling and the sound from thetapping transfers much faster through solids.

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Does sound need a medium?

Place a vibrating objet producing sound in an evacuated container.What happens?

You can see how sound depends on a medium in order to propagate if youdo the following experiment. You may do this with your teacher at yourpractical session.

Set up the equipment as shown in the diagram below.

Put a bell jar (a large bottle with no bottom in it) on a sheet of glass andseal around it with Vaseline or grease so that no air can leak through thebase of the bell jar.

Evacuate the air from the bell jar by connecting it to a vacuum pump.

An electric bell is suspended by the circuit wires. These wires passthrough a rubber stopper into the bell jar.

+–

to vacuum pump

Experimental set up to sound in an evacuated container.

At your practical session with your teacher you might see this happen.

• When the bell is switched on before the air is evacuated it can beheard ringing easily.


• As the air is gradually withdrawn from the bell jar by the vacuumpump the volume of sound from the bell decreases.

• A point is reached when the clapper on the bell is seen to bevibrating but hardly any sound is heard until air is allowed tore–enter the bell jar.

Without the presence of air sound from the bell can only reach theoutside through the wires and vibrating jar.

1 What does this say about sound’s ability to travel in a lack of a mediumsuch as air?

_____________________________________________________

2 Do you think sound could travel through the vacuum of outer space?Explain you answer.

______________________________________________________

______________________________________________________

______________________________________________________

Check your answers.

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Comparing waves

Can you relate the compressions and rarefactions of sound to the crestsand troughs of a transverse wave?

The compressions (C) of a longitudinal wave such as sound areequivalent to the crests (C) of a transverse wave. These are bothamplitude maxima.

The rarefactions (R) of a longitudinal wave are equivalent to the troughs(T) of a transverse wave. These are both amplitude minima. Thisrelationship is shown on the following figure.

R R

T T

C C

Transverse and longitudinal wave features are compared. Rarefactions (R) andtroughs (T) are equivalent. Compressions and crests (C) are also equivalent.


Compression and transverse waves

The figure on the next page shows a representation of a sound wave.

Draw a graph of the pressure versus position for this longitudinal wave inthe space beneath the wave.

The pressure is highest where the particles are closest together.

The pressure is lowest where the particles are furthest apart.

Sound wave showing compressions and rarefactions. Wavelengths (l) are

shown.

Representing compression waves

Compression waves are often represented as transverse waves indiagrams. This is true of sound in particular. The reason is probablybecause transverse waves look more like water waves that people canrelate to. The diagram below of the slinky spring shows a longitudinalwave pulse propagating.

Draw an equivalent transverse wave to represent each of the situationsdepicted in the three diagrams.

compression

compression

compression

rarefaction

rest

rarefaction


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Can you see sound waves?

The obvious answer is no, but if you use a cathode ray oscilloscope youcan see a pictorial representation of a sound wave on a screen. Whenyou go to your practical session with your teacher you may use a cathoderay oscilloscope (CRO) to ‘look’ at sound waves.

The sound wave energy is converted into an electrical signal by amicrophone in a similar manner to the way a speaker in a mobiletelephone. This signal is fed into a CRO input where it produces a curveon a screen. The microphone in this activity acts a data collector toproduce an electrical signal.

You are required to perform a first–hand investigation and gatherinformation to analyse sound wave forms from a variety of sources usingthe cathode ray oscilloscope (CRO) or a form of computer technologycalled a digital oscilloscope.

You can complete this activity by using a digital oscilloscope program thatyou can download from the Internet. Alternatively, it can be done when yougo to your practical session with your teacher. To see a site where you candown load a digital oscilloscope program see a site on the physics link pageat: http://www.lmpc.edu.au/science

If you are able to download a program from the Internet to analyse soundwaves you will need to use a microphone to input the sound signal toyour computer. If you do not have a microphone you might be able toplug the headphones from a personal stereo into the input jack of yourcomputer marked for use with a microphone and use the headphonespeaker as a microphone. Usually the sensitivity of such aspeaker/microphone is lower, but it will still work. Why this works willbe explained when you do a later module.

In the section that follows there are some computer screen captures oftraces from the screen of an oscilloscope that may be similar to tracesyou will see when you do your practical session. In these traces thehorizontal axis of the trace represents time. The vertical axis of the tracerepresents the amplitude of the sound wave producing the sound.


Sound waves and frequency

The higher the frequency of a sound the more waves that will pass apoint in a second and the higher the pitch of the sound. If you arelooking at the screen trace of sound waves of different pitch and the CROsettings are identical then the higher pitched sound will have morewavelengths on a trace.

A CRO trace of a 320 Hz tuning fork sound wave.

A tuning fork trace of a 256 Hz tuning fork sound wave.

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Note that the second trace has fewer full wavelengths showing on thescreen trace indicating that a lower frequency sound produced the trace.

Do Exercise 2.2 to 2.6 now.

Volume and amplitude

The greater the volume of a sound of a particular frequency the greater isthe sound’s amplitude.

CRO trace of a high volume 256 Hz tuning fork note.

As you can see the amplitude of the wave above is much greater than the amplitudeof the wave below. This is because the amplitude of the noise from the tuning forkabove was greater than the amplitude of the note from the same tuning fork shown inthe figure on the next page.


CRO trace of a low volume 256 Hz tuning fork note.

Do Exercises 2.7 to 2.10 now.

Now that you have learned some more about the properties of soundwaves you will learn to apply this knowledge in another part where youwill look how wave properties have been used to aid communicationusing electromagnetic waves.


Summary

• Sound waves are longitudinal waves.

• Compressions are equivalent to crests.

• Rarefactions are equivalent to troughs.

• High pitched sounds have high frequency.

• Low pitched sounds have low frequency.

• Loud sound waves have large amplitudes.

• Soft sound waves have small amplitudes.

• Sound waves can be ‘seen’ using a CRO.


Suggested answers

Here are suggested answers for many of the questions from throughoutthis part. Your answers should be similar to these answers. If youranswers are very different or if you do not understand an answer, contactyour teacher.

What are sound waves?1 Same direction.

2 Sound is therefore a longitudinal wave.

Does sound need a medium?1 Sound cannot travel in a lack of a medium.

2 Not if space is a vacuum, because vacuum implies a complete lackof a medium.


Exercises - Part 2


You have finished the learning from Part 2 of the module. You shouldnow complete the send in exercise and return it to your teacher if you area Distance Education student. By doing these exercises you should learnwhether or not you have understood the main concepts taught, andachieved the outcomes for this section of the course. Your teacher willsend comments back to you to help you achieve any outcomes you arenot currently achieving.

On the next few pages are some computer screen captures of traces fromthe screen of an oscilloscope that may be similar to those you will seewhen you do your practical session. Answer the questions that follow byreferring to these traces.

Trace1: CRO trace produced by a 256 Hz tuning fork placed about 10 cm fromthe microphone.


Exercise 2.1

Draw a pattern of compressions and rarefactions that would match thistrace (Trace 1) in the space below. Use lines close together to representcompressions and lines further apart to represent a rarefaction.

Exercise 2.2

How would you describe this wave trace (Trace 1) in terms of the size ofeach crest and trough? You can use a ruler to measure the amplitudes ofthe waves.

_________________________________________________________

_________________________________________________________

Trace 2 CRO trace produced by a 512 Hz tuning fork placed about 10 cm fromthe microphone.


Exercise 2.3

Do you think this trace (Trace 2) would represent a regular or irregularsound? Why do you think this?

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Trace 2 is the trace produced by a 512 Hz tuning fork held about 10 cmfrom the microphone. All settings on the oscilloscope are constant in theproduction of this trace (Trace 2) and the previous trace (Trace 1). Onlythe tuning fork producing the trace is different.

Exercise 2.4

What differences can you see between these two traces? Focus on theprominent features of the wave traces (wavelength, frequency, andamplitude).

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Exercise 2.5

Explain these differences in the wave traces.

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Exercise 2.6

How does the number of wavelengths on the previous two figurescompare? Is it double for the 512 Hz tuning fork trace?

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Look at the two traces from a CRO on the next page. Both Trace 3 andTrace 4 are traces of sound produced by a 512 Hz tuning fork. Thesettings on the CRO were identical and the tuning fork was held atexactly the same distance from the microphone in each case. The time


elapsed between striking each tuning fork when the CRO traces wererecorded was identical. Using this information, do Exercise 2.7 toExercise 2.10.

Trace 3 Trace from a CRO of sound produced by a 512 Hz tuning fork.

Trace 4 Trace from a CRO of sound produced by a 512 Hz tuning fork.


Exercise 2.7

How do the frequencies of these two wave traces compare? Explain youranswer.

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Exercise 2.8

Explain why the second wave trace has a smaller amplitude than the firstwave trace?

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Exercise 2.9

How do you think you could produce similar traces to these? Rememberyou cannot adjust the CRO settings and must only use one tuning fork.

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Note: For a certain type of wave such as a sound wave travelling in afixed medium, changing the amplitude of the wave does notchange the speed of the wave in that medium and changing thefrequency of the wave will not change the speed of the wave inthat medium.

For example, loud sounds travel at the same speed as soft soundseven though they have different amplitudes, and high frequencysounds travel at the same speed as low frequency sounds if thesound is travelling in a medium with constant properties.


Exercise 2.10

What implications does this information have in determining thewavelength of sound in a medium of constant properties if you changethe frequency?

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Appendix

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Part 3: Superposition


AMENDMENTS








Part 4 p 9



WARNING







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Part 3: Superposition 1

Contents

Introduction ............................................................................... 2

Adding sound waves ................................................................. 3

Superposition........................................................................................5

Complex waves......................................................................... 9

Same note? ........................................................................................10

What is an echo?..................................................................... 12

How can echoes be used? ................................................................13

Reflecting sound.................................................................................14

Superposition of echoes ....................................................................14

Summary................................................................................. 16


Exercises – Part 3 ................................................................... 19


Introduction

In the previous parts of this module you have learned about the some ofthe properties of waves. In this part you will learn about the properties ofwaves necessary to convert a wave to a signal that can carry a message.In doing this you will learn how waves can be added to produce complexwaves or annulment.


• describe the principle of superposition and compare the resultingwaves to the original waves in sound

• explain an echo as a reflection of a sound wave


• perform a first–hand investigation, gather, process and presentinformation using a CRO or computer to demonstrate the principleof superposition for two waves travelling in the same medium

• perform a first–hand investigation and gather information to analysesound wave forms from a variety of sources using the Cathode RayOscilloscope (CRO) or an alternate computer technology

• present graphical information, solve problems and analyseinformation involving superposition of waves.

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amendedOctober 2002. The original and most up–to–date version of this document canbe found on the Board’s website athttp://www.boardofstudies.nsw.edu.au/syllabus_hsc/syllabus2000_listp.html#p

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Adding sound waves

Sound waves can be used to illustrate properties of waves that are used incommunication technologies.

Can you add sound waves together? What do you think this means? Doyou think this can be done?

You are required to perform a first–hand investigation, gather, processand present information using a CRO or computer to demonstrate theprinciple of superposition for two waves travelling in the same medium.

The tuning fork notes you saw in the previous CRO traces were puretones. A pure tone is one that consists of a single frequency. Mostsounds you hear are not pure tones. They are made by combining two ormore pure tone sound waves together. The resulting sound can be verycomplicated and so is a complex wave. The following screen tracesfrom a CRO show you the sort of results you might get from adding twowaves together.

The CRO trace above was made using a 384 Hz tuning fork. This is a puretone.


The CRO trace above was made using a 512 Hz tuning fork. This is a puretone.

The CRO trace above was made from adding the sound from the 384 Hz tuningfork and the 512 Hz tuning fork. This is a complex wave.

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As you can see the addition of the two sounds made a great difference tothe shape of the CRO trace. The trace is a picture of the combinedsound. The wave form is now more complex.

Some of the features of this combined sound you can see on the CROtrace include:

• the loss of the regular sine wave shape

• the loss of a large part of the amplitude in sections of the combinedwave. In other sections the wave amplitude is higher than that ofeither of the two original waves.

Superposition

Changes in the wave trace above are due to the superposition of thedifferent waves. This means that the displacements of the differentwaves at individual points in time have been added.

If the displacements of the separate waves are opposite (for examplea crest from one wave is added to the trough of another) at the same timethen the resulting displacement at that point will be lower. If the waveshave two crests or two troughs coinciding at that point, then theamplitude of the wave will be bigger at the time when the waves areadded.

The addition of waves by superposition is shown animated at a number ofwebsites. Look at some pages that show information about superposition onthe Physics website page:


How to add waves together

The figure below shows the superposition of two waves y1 = 2sin x andy2 = 3sin x. These, when added, produce the new wave represented byy3 = 5sin x. Using graph paper makes the addition of waves simpler.

If you have a graphing calculator or have downloaded one from theInternet you should check the results in the figure below by adding thewaves together. This calculator procedure will only work when you canenter the equations representing the waveforms to be added.

On the diagrams below the horizontal axis is marked in units calledradians. There are 2p radians in one whole wavelength.


y

2p x

–1.0

–1.7

–1.7

–1.0

p

1.0

1.0

1.7

1.72.

0

p2

–2.0

3p2

0

y1 = 2 sin x

1.5

2p x

–1.5

–2.6

–2.6

–1.5p

1.5

2.6

2.63.

0

–3.0

3p2

y2 = 3 sin x

0

2.5

2p x

–2.5

–4.3

–4.3

–2.5

p

2.5

4.3

4.3

5.0

–5.0

3p2

y3 = 5 sin x

0p2

p2

Superposition of two waves to form a third different wave.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

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The effect of the addition of waves can result in lower amplitude wavesor higher amplitude waves. In the example on page 6, you saw twowaves added to produce a resultant wave with an amplitude larger thaneither of the individual waves. But if the amplitude of the crest of onewave is precisely equal to the amplitude of the trough of another wave(that is, superposition of two identical waves a half wavelength out ofphase), then annulment or complete loss of amplitude in the wave canoccur.

In the case of sound waves this means it is possible to add soundstogether to produce no sound. Alternatively if troughs coincide withtroughs and crests coincide with crests then the amplitude of the wave atthat point will be increased. The sound produced by superposition willbe louder.

Given two (or more) waves the resultant wave can be determined bygraphing. To do this you must add individual displacements at variouspoints in a systematic way.

You can see this mathematically using the example from theprevious page.

Using the principle of superposition

You are required to present graphical information, solve problems andanalyse information involving the superposition of waves.

This is most easily accomplished using a graphing calculator. You can,however, add waves together using graph paper.

On the next page is a diagram showing two waves drawn on graph paper.Add the two waves in the diagram on page 8 graphically and then draw theresultant wave.

Complete this self correcting activity on the next page before attempting thesend in exercises.


y

2p x

–0.7

5

–1.3

–1.3p

1.3

1.31.5

–1.5

0

y1 = 1.5 sin x

2.2

2p

x

2.2

1.25p

–2.2

1.25

–1.2

5

–2.5

y2 = 2.5 cos x

0–0

.75

0.75

0.75

2.5

–2.2

–1.2

5

2.5

Check your answer.


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Complex waves

As you probably know, most waves in the real world are not pure tones.They are complex waves. Complex waves can always be broken downinto a series of simple sine waves of different wavelengths andamplitudes. Of course, this is more easily said than done by us visuallybut it is possible for us to see how easily complex waves can be built upfrom the superposition of simpler ones.

wave1

wave 2

w a v e 3

wave 4 = wave 1 + wave 2 +wave 3

Superposition of waves 1, 2 and 3 producing a complex wave number 4.


The human ear passes complex sounds on to the brain. The brain canseparate out simpler waves or individual notes or sounds from complexwaves. You do this when you hear a sound and separate it out frombackground noise. The previous figure shows how a complex wave canbe built up from adding relatively simple sine waves.

Superposition of waves can cause waves to cancel out. For example, youcan get dead spots in a room when you play a single note through stereospeakers. As you move around the room where the note is being playedyou will notice that the sound has different intensities in differentlocations within the room.

Why do you think this is so?

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Check your answer.

To see how sound waves can add to produce a lower volume (called activesound absorption) you can visit some Internet websites. Look at some webpages that relate to active sound absorption at the Physics websitelinks page.


Some voice recognition techniques use the principle of superpositionextensively. In forensics it is used to identify people; by security it isused to open doors; and by banks it is used to allow a code to operateaccounts. These techniques work on the idea of waves adding to canceleach other out.

Same note?

Often the same note played by different instruments has the samefrequency but they don't sound the same. This difference in sound iscalled the timbre of the note.

The diagram opposite shows the CRO traces of the same note played bydifferent instruments: a violin, guitar, cello and flute. Each tracerepresents a record of exactly the same time interval.

You may be able to record traces similar to the ones shown at yourpractical session with your teacher. Notice the waveforms or shapes arenot the same. This explains the characteristic timbre of the instrumentmaking the sound.

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cello

flute

guitar

violin

CRO traces of the same note played by different instruments. Note thedifferences in the waveforms.

1 From looking at the features of the CRO traces how do you know thesame note is represented in each of these traces?

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2 If the trace time shown represents approximately 0.0185 s what isthe most likely frequency of the note being played to present thesetraces (256 Hz, 512 Hz, 384 Hz or 320 Hz)? Explain your answer.

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3 Why do you think the shapes of the waves in the previous diagramare not identical even though they are representing the same note?

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Check your answers.



What is an echo?

You have already learned that sound waves can be added. Now you willlearn that sound waves have other properties, one of which is reflection.

Everybody has heard an echo. It is simply sound bouncing back at you.If you yell at a brick wall or a cliff face of bare rock the sound of yourown voice comes back at you. You don’t get to hear the full sound orrange of everything you’ve said but you do get the tail of the last word.

For example if you yell a word such as ‘echo’ you will hear the ‘o’ at theend of the word. The further you are from the wall the more of the tail ofthe word you hear as an echo. If you are too close to the wall the echo islost because you drown it out with the sound of your voice.

You need to have a time lag between the bounced back signal and thesource to enable you to hear an echo. This lag time is around 0.1 s. Ifsound is travelling around 340 ms–1 this means you must be at least 17 mfrom the surface you are bouncing the sound off to hear the echo. Thisdistance enables the sound to be bounced back at you with the 0.1 s timedelay because it will take the sound wave 0.05 s to reach the wall fromyour mouth and 0.05 s to bounce back from the wall.

Sound is reflected when it hits a solid object. Notice the phase changes onreflection

Find a flat brick wall or cliff face not covered in loose material and walkdifferent distances from it yelling at the wall.

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1 At what distance from the reflective surface can you hear the first echo?

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2 What is an echo? Use examples in your answer.

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Check your answers.

How can echoes be used?

The use of echoes to determine the distance to objects has developed intopart of our everyday life. Sound waves of high pitch are emitted from asource and bounce back from objects where they are detected bypressure–sensitive detectors. These pick up the sound reflection.

The detectors are designed to time the reflection very precisely.The time it takes to receive the reflected wave or echo can be used tocalculate distance to the object. This is because assumptions are madeabout the velocity of the sound in the medium.

This method of detecting distance is used in sonic tape measures, sonicrangers, sonar, depth finders on boats, and sonic level controllers inindustry that tell you how full storage tanks are. You may use a sonicranger attached to a data logging computer later in this course when youcome to your practical session in the study of motion.


Reflecting soundYou will use two glasses or two cups to reflect sound into one ear in thisactivity.

Talk into one cup held about 10 cm from your mouth while holding theother cup about 5 cm from your ear angled towards the ear.

By adjusting the positions of the cups you can reflect the sound from the cupyou are talking into to the cup next to your ear. The sound from thecollecting cup will then reflect into your ear. This will result in you hearinga louder sound in the ear next to the cup.

1 Do you think that the angles of the cups with respect to one another areimportant for getting the loudest sound in your ear? Hint: Think aboutthe angles of the cups where you hear the sound at its loudest.

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2 Do you think there are any similarities between sound reflected offthe bottom of the cups or glasses and the reflection of light from amirror?

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Check your answer.

Superposition of echoes

Occasionally you will find a canyon or steep–sided valley where you canyell into the valley and the echo will be heard many times. This occursbecause the sound isn’t reflected straight back but rather at an angle andthen onto other surfaces, in much the same way as light coming into amirror at an angle. The multiple paths of the echo result in multiple pathlengths.

Because the speed of sound in the medium is a constant, multiple echoesmean multiple times for the reflected sound to get back to you. Thismeans you hear multiple echoes of the same original sound.

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Try this activity the next time you are in a building several stories high.Yell in a closed off stairwell of a large building. You will hear echoes as thesound bounces around in the stairwell.

Ask a friend to stand at one position in the stairwell and sing a single notewhile you walk up or down stairs. You may find dead spots where thevolume of the sound decreases.

1 What do you think causes these dead spots where the sound volumefalls?

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2 Usually in a stairwell the sound waves interfere with each other andthe echo is muffled and not as clear as if it bounced off a cliff face orbrick wall. You can’t usually clearly hear any words bounced back.

Have you noticed this? Can you explain why this might be?

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_____________________________________________________

Check your answers.

In the next part you will look at how wave properties have been used toaid communication using electromagnetic waves.

You have finished the learning from Part 3 of the module. You shouldnow return your completed send in exercises and return them to yourteacher. By doing these exercises you should learn whether or not youhave understood the main concepts taught, and achieved the outcomesfor this section of the course. This communication is essential so yourteacher can assist you to progress through the course. Remember, yourteacher is available to assist.


Summary

In this section you should prepare a summary of the information youhave learned in this part. You should make the summary using theheadings used in the unit as a guide. You should also consider how thework in this part connects to the work in the previous parts ofthe module.

• Adding sound waves

• Super position

• Complex waves

• Same note

• What is a echo

• How can echoes be used?

• Reflecting sound

• Superposition of echoes

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Suggested answers

Using the principle of superpositiony

2p x

–0.7

5

–1.3

–1.3p

1.3

1.31.5

–1.5

0

y1 = 1.5 sin x

2.2

2p

x

2.2

1.25p

–2.2

1.25

–1.2

5

–2.5

y2 = 2.5 cos x

0

2p

x

p0

–0.7

5

0.75

0.75

2.5

–2.2

–1.2

5

2.5

y3 = y1 + y2


Complex waves

This is because in some places in the room the echo from the walls andsound waves from the speakers superpose to produce annulment. Atother spots the sound waves superpose to produce sound of higheramplitude.

Same note?1 Same frequency in each case.

2 320 Hz because if 6 Hz (or full wavelengths)shown on the trace arein 0.0185 s then approximately 324 Hz in 1 s.

3 Different timbre of the notes from each instrument.

What is an echo?1 About 16.5 to 17 m.

2 A reflection of sound waves. A sonic ranger, a human voicebounced back from a wall, sonar and ultrasound imaging are allexamples of echoes.

Reflecting sound1 Yes. There is only one angle where the sound is at its loudest.

2 Yes. A similar situation happens with reflected light.

Superposition of echoes1 Superposition to produce a wave of zero amplitude at the dead spots.

2 Sound bounced back interferes with sound propagating forwardresulting in superposition of the reflected and incident waves.That produces a muffled sound.

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Exercises - Part 3


Exercise 3.1

In a region affected by two waves, one particular particle at one instantwould be displaced 0.4 m up by one wave and 0.6 m down by the otherwave if both waves were considered separately. What is the actualdisplacement of this particle?


Exercises 3.2There are three waves shown in the figure below.

two waves withzero phase diference

resultantwaves

distance

disp

lace

men

t

If the first two waves are added would they result in the third?Explain your answer.

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Exercises 3.3

On the graph paper below draw the resultant wave produced by thesuperposition of the following sine waves, A and B. Wave A hasamplitude 3 cm and wavelength 4 cm. Wave B has amplitude 1 cm andwavelength 8 cm. You will need to draw two cycles of wave A.Label waves A and B and the resultant clearly on your diagram.


Exercises 3.4

If the resultant waveform in the example below, where two waves with ahalf wavelength phase difference are superposed, was a sound wave,how loud would the sound be?

two waves with phase difference

resultantwaves

distance

disp

lace

men

t

l2


_________________________________________________________

In this Physics course you are required to perform a first–handinvestigation and gather information to analyse sound wave forms from avariety of sources using the cathode ray oscilloscope (CRO.

The trace from a CRO provides us with a snapshot of a wave. You mustremember the wave shown on the traces presented to you in this modulerepresents a grab of around 0.05 s. These small grabs can show us manyof the features of the sound. To analyse a whole sentence or even acomplete word of more than one syllable is a complex procedurealthough one that is routinely done by sound engineers in the recordingindustry. The traces shown below offer you an opportunity to analysesome relatively simple sounds.

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Exercises 3.5

A 256 Hz tuning fork trace.

How would you describe this CRO trace in terms of the regularity of thewave?

_________________________________________________________

_________________________________________________________

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Exercises 3.6

This CRO trace below is from a 384 Hz tuning fork. The settings on theCRO were identical to the trace shown above. The position of the twotuning forks from the microphone collecting the sound was identical.

A 384 Hz tuning fork trace.

What is the difference between the 256 Hz tuning fork CRO and the 384Hz CRO trace in terms of the number of wavelengths per second?

_________________________________________________________

Exercises 3.7

Compare the sound loudness level of the 256 Hz and 384 Hz tuning forksshown in the traces above. Which one would be louder? Why?

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Exercises 3.8

This CRO trace was made when the sound from the 384 Hz tuning forkand the 256 Hz tuning fork was added. This wave is now a morecomplex wave. The CRO settings used were identical to the settingsused on the previous examples.

A complex wave made from a 256 Hz and 384 Hz tuning fork wave.

a) Explain why this CRO trace is different to that of the two soundsfrom which it is made.

_____________________________________________________

_____________________________________________________

_____________________________________________________

b) Would this sound be more similar to that produced by the 256 Hztuning fork or the 384 Hz tuning fork? Explain your answer.

_____________________________________________________

_____________________________________________________


c) What features can you see in this complex wave that suggest it ismade from more than one pure waveform?

______________________________________________________

______________________________________________________

d) Can you offer an explanation for why the amplitude of thecombined waveform is lower than the original two CRO wave tracesat some points along the trace path?

______________________________________________________

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Exercises 3.9

What does the trace of a human voice look like?

The CRO trace produced by a man saying the sound of the letter A.

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The CRO trace above is that produced by a woman saying the sound of theletter A.

In looking at the two traces you may notice some similarities.

a) Would you say the sound of the human voice represents a simple ora complex waveform? Explain your answer based on the shape ofthe CRO traces shown above.

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_____________________________________________________

b) What are the similarities you can see between the two CRO traces?

_____________________________________________________

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c) What are the differences you can see between the two CRO traces?

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d) Explain the similarities or differences in terms of sound loudness andpitch.

______________________________________________________

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e) Which one of these voices do you think most closely approximates apure tone?

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f) Do you think the man or woman has the lower pitched voice?Propose a reason for your answer based on the CRO traces only.

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g) Would you say these traces are of a simple or of a complex wavemade up of many pure tones? Explain your answer.

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Part 4: Electromagnetic waves


AMENDMENTS








Part 4 p 9



WARNING







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Part 4: Electromagnetic waves 1

Contents

Introduction ............................................................................... 2

What is the electromagnetic spectrum? .................................... 3

Sources of electromagnetic radiation..................................................3

Communication devices.......................................................................8

The basic categories ..........................................................................10

Intensity of electromagnetic waves.......................................... 12

Why is attenuation important? ...........................................................12

The inverse square law......................................................................13

Modulation............................................................................... 18

Kinds of modulation............................................................................19

Microwaves are also modulated........................................................22

Appendix ................................................................................. 25


Exercises – Part 4 ................................................................... 31


Introduction

In this part you will identify the methods used to communicate withelectromagnetic waves. As well, you will learn about the role waveproperties have in enabling the encoding of the signal onto the bands of theelectromagnetic spectrum that are predominantly used incommunication systems.

In this part you will have the opportunities to learn to:

• describe electromagnetic waves in terms of their speed in space and theirlack of requirement of a medium for propagation

• identify the electromagnetic wavebands filtered out by the atmosphere,especially UV, X–rays and gamma rays

• identify methods of detection of wave bands in the electromagneticspectrum

• explain the relationship between the light intensity and the distance fromsource is an example of the inverse square law

I µ1

2d

• outline how the modulation of amplitude and frequency of visible light,microwaves and/or radio waves can be used to transmit information

• discuss the problems produced by the limited range of theelectromagnetic spectrum available for communication purposes.

In this part you will have the opportunities to:

• plan chose equipment or resources for and perform first handinvestigation and gather information to model the inverse square law forlight intensity and distance from the source

• analyse information to identify the electromagnetic spectrum rangeutilised in modern communication technologies.

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amended October2002. The original and most up–to–date version of this document can be found onthe Board’s website athttp://www.boardofstudies.nsw.edu.au/syllabus_hsc/syllabus2000_listp.html#p

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What is the electromagnetic spectrum?

In this part you will investigate how people use the electromagnetic spectrumto communicate faster and further. You have already learned some thingsabout electromagnetic waves in this module.

The electromagnetic spectrum is a continuum of electromagnetic waves.This means that electromagnetic waves of one type blend into thetype adjacent.

This spectrum is arranged according to frequency and wavelength.

Can you remember the names of the waves that make up the electromagneticspectrum? The electromagnetic spectrum includes visible light, ultravioletand infrared, microwave, radio, x–rays and gamma waves.

Can you order these wave types from the electromagnetic spectrum accordingto decreasing wavelength? Check your answer by having a look at the figureshowing the electromagnetic spectrum below.

10–11 10–9 10–7 10–5 10–2 100 103 106

0.01 nm 1 nm 0.1 mm 0.01 mm 1 cm 1 m 1 km 103 km

gammarays

x-rays ultraviolet infra-redmicrowaves

0.4–0.7mm

light TV radioradio waves electrical

power

Wavelength

Wavelength in metres

The electromagnetic spectrum is arranged in order of increasing wavelength.Adapted from OTEN, Physics for Electrical and Electronic Engineers

Source of electromagnetic radiation

The universe is made up of electromagnetic radiation sources. The Sun,Earth, and other heavenly bodies radiate electromagnetic energy of varyingwavelengths. The radiation itself is made by accelerating tiny chargedsubatomic particles such as electrons.


All electromagnetic energy passes through space at the speed of light (300million ms–1) in the form of sinusoidal (sine–shaped) or compound transversewaves. These are just complex waves made up of multiple simple wavessuperposed.

Electromagnetic radiation from space

Earth's atmosphere and ionosphere absorbs electromagnetic radiation exceptin the visible region and some high frequency radio waves in the microwaveregion. Astronomers make extensive use of radiation in these two ranges tostudy space using Earth–bound instruments. Increasingly, astronomers areusing radiation such as x–rays to study objects in space.

Satellite based devices such as the Chandra space telescope are designed tostudy x–rays produced when gas is heated to millions of degrees by violentand extreme conditions, for example, flaring stars, exploding stars, blackholes and vast clouds of hot gas in galaxy clusters.

Images from this x–ray telescope show fifty times more detail than anyprevious x–ray telescope based on the Earth’s surface, but to see these imagesthe Chandra telescope has had to be placed in an orbit a third the distance tothe moon. This is in order to escape the influence of the Earth’s magneticfield that affects the telescopes detectors and the atmosphere and changeionosphere because these both influence x–rays.

The degree to which electromagnetic waves can penetrate to the surface of theEarth varies. The diagram below shows the broad penetrating ability ofelectromagnetic waves through the atmosphere.

Wavelength

sea level

400

200

100

50

25

12

6

3

0

Alti

tude

in k

m (

not t

o sc

ale)

radiomicrowaveinfra-redUVx-rays

visi

ble

lightgamma rays

land surface

aircraft

Penetration of electromagnetic waves. If the shading changes then the penetrationlevel changes.

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1 After looking at the diagram can you see any trend in the ability ofelectromagnetic radiation to penetrate to the surface of the Earth? If so,what is that trend?

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2 What are the radiation types of the spectrum that propagate almostcompletely to the Earth’s surface?

_____________________________________________________

_____________________________________________________

3 How would you describe the ability of UV, X–rays and gamma raysin terms of their capacity to penetrate to the surface of the Earth?

_____________________________________________________

_____________________________________________________

______________________________________________________

Check your answers.

The ionosphere

The Earth is surrounded by a layer of gas called the atmosphere. Part of thatgas at high altitude is ionised (the atoms and molecules have becomecharged by losing or gaining electrons) producing a layer we refer to asthe ionosphere.

The ionosphere has been divided up into three regions (D, E, F) based on thetype of radiation absorbed in each region.

The D region is the lowest in altitude and includes the ionised zone of theatmosphere that extends to 90 km above the Earth’s surface. Hard x–rays areabsorbed in the D region. Hard x–rays have short wavelengths.

The E region peaks at around 105 km above the Earth’s surface. Soft x–rays,or longer wavelength x–rays, are absorbed in the E region.

The F region starts at around 105 km and continues to 600 km above theEarth’s surface. Extreme ultraviolet radiation with short wavelengths isabsorbed in the F region.


Ultraviolet radiation

Ozone is a critical component of Earth's atmosphere because it absorbsharmful solar ultraviolet radiation at wavelengths less than about 320nanometres (nm). Ozone is found in relatively higher concentration between10–50 km above the Earth’s surface but the ozone’s greatest concentration isbetween about 15 and 30 km above the surface of the Earth in the layer of theatmosphere called the stratosphere.

Because of the strong absorption of solar ultraviolet radiation by ozone in thestratosphere, it is virtually impossible for ultraviolet rays between 200 and300 nm to penetrate to the Earth's surface.

For example, UV with a wavelength of 290 nm is 350 million times weaker atthe Earth’s surface than at the top of the atmosphere. At 40 km above thesurface about 50% of UV with a wavelength of 290 nm has been absorbed.

UV radiation is typically divided into three parts:

• UV–a (320 to 400 nm)

• UV–b (280 to 320 nm)

• UV–c (200 to 280 nm).

1 Which of these radiations has the largest frequency? __________

2 Which has the greatest penetrating power? __________________

Check your answers.

UV–c is absorbed by small concentrations of ozone high in the atmosphere.None gets to the Earth's surface.

UV–b is mostly absorbed (about 90% or more) by the upper atmospherecalled the troposphere and about half of the UV–a is absorbed by ozone orscattered before reaching the troposphere.

Look at a detailed explanation of where different wavelengths ofelectromagnetic radiation are absorbed in the atmosphere at the Physicswebsite page.


Visible light

Evidence that visible light doesn’t penetrate through the atmosphere equallywell at all wavelengths is seen most mornings at sunrise and afternoonsat sunset.

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White sunlight is made up of all the colours of the rainbow (or visiblespectrum). It has to penetrate more of the atmosphere at sunset because it istravelling across the atmosphere not just down through it as it would atmidday. This means that those rays that don’t penetrate as well don’t reachour eyes.

Since the Sun looks red at sunset it is therefore reasonable to conclude thatred light is more penetrating than the other colours.

Red light is at the low frequency end of the visible spectrum. Violet light is atthe high frequency end of the visible spectrum. Light of low frequency istherefore more penetrating through the atmosphere than light of highfrequency. The figure below shows the wavelength of visible white light innanometres (nm).

prism

400 500 600 700

10-5 10-3 10-1 101 103 105 107 109 1011 1013 1015 1017

gammarays

x-raysrays

ultravioletrays

infraredrays radar broadcast bands AC circuits

white light

Violet light is at the 400 nm end of the visible light spectrum whereas red light is atthe 700 nm end of the visible light spectrum.

A more detailed explanation of the penetrating ability of differentfrequencies or colours of light through the atmosphere can be found at pageson the Physics website page.


Complete the chart on the next page to show the penetrating ability of allthe electromagnetic radiation wavelengths to the surface of the Earth.Use the information you have just read from the section titledElectromagnetic radiation from space.


Is there any relationship that you can see from your completed chart thatenables you to relate ability of the radiation to penetrate to the wavelength ofthe radiation?

_________________________________________________________

_________________________________________________________

_________________________________________________________

Check your answer.

transparent

10-3 10-1 100 102 103 108 109

Wavelength (nm)106

infr

ared

win

dow

s

opaque

optic

al w

indo

w

radi

o w

indo

w

Electromagnetic wave penetration through the atmosphere.


Visible light represents only a very small portion of the electromagneticspectrum.

The figure on the next page shows the electromagnetic spectrum and some ofthe devices that are used to detect some of the wave bands.

At one end the electromagnetic spectrum has radio waves with wavelengthsbillions of times longer than those of visible light and at the other end gammarays that have wavelengths millions of times smaller than visible light.

Wavelength is measured in metres or parts of a metre. Because thewavelengths of some forms of electromagnetic radiation are so small theirwavelengths are measured in nanometres. One nanometre (nm) is onebillionth of one metre or 10–9 metres.

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Produced in By Wave lengthin metres

Type Detectedby

Frequencies in cyclesper second

nuclearreactions

oscillatingnucleus g

amma

rays

x-rays

ultraviolet

visible light

infra-red

microwaves

radio

waves

x-ray tube spirallinginner

electron

spirallingouter

electron

spirallingelectron ina solar flare

sun

oscillationof charge inconductor

102010–12

10–10

10–8

10–6

10–4

10–2

100

102

104

104

106

108

1010

1012

1014

1016

1018

radiotelescope

radar

Geiger-Mullertube

The electromagnetic spectrum.

Diagram courtesy of Messel, H (1963) Science for High School Students.


After looking at the figure above list those types of electromagnetic spectrumwaves that are currently used for communication in the table below. For eachradiation type you have listed identify the radiation detector.

Electromagnetic wave type Radiation detector

Check your answer.

The basic categories

The basic categories of the electromagnetic spectrum are listed below:

Radio waves

Radio waves (AM, FM, VHF and UHF) have a range of wavelength from 10cm to 1000 m. Their uses include the transmission of radio and televisionsignals. Examples of applications include:

• television

• FM and AM radio stations

• radar whereby radio waves can create images.

• if radio waves of a few centimetre wavelengths are transmitted from asatellite or plane antenna they will bounce off the ground and see throughclouds detection of their reflections can produce a picture of what liesbelow.

Microwaves

Microwaves have wavelengths of approximately 1mm to 30cm.

Applications include the microwave oven that emits radio waves tuned to afrequency of 2450 MHz that can be absorbed by the food. The food absorbsthe energy and gets warmer.

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Microwaves emitted from the Earth, or objects such as cars, planes, and fromthe atmosphere, can be detected to give information, such as the temperatureof the object that emitted the microwaves. Microwave transmission of mobilephone calls occurs on frequencies of around 900 MHz.

Infrared waves

Infrared waves have wavelengths of around 700 nm to about one millimetre.Infrared (IR) radiation can be measured using electronic detectors or specialphotographic film.

Applications include:

• medicinal treatments for soft tissue injury

• finding heat leaks from houses

• information on the health of crops from satellite images

• ‘seeing’ forest fire hot spots even if enveloped in a curtain of smoke

• signal carriers in optical–fibres in telecommunications.

• the remote connection and operation of electronic devices such as thetelevision remote control and wireless connections to computers.

Visible light

Visible light has a wavelength of 700 to 400 nm. Applications include:remote sensing of vegetation, identification of different objects by theirvisible colours and fibre–optic telecommunications.

Ultraviolet radiation

Ultraviolet radiation has wavelengths from 400 to 10 nm. A small dose ofthis radiation is beneficial to humans, but larger doses cause skin cancer andcataracts. Applications include its use in making astronomical observationsand its use to sterilise hospital equipment.

X–rays

X–rays have wavelengths from 10 nm to 0.01 nm. Applications includemedical applications, inspecting industrial welds, and it is important to studyspace derived x–rays so we can predict space weather. They are also used inthe manufacture of electronic chips and some biomolecular materials.

Gamma rays

Gamma rays have wavelengths of less than 0.01 nm. Applications includemedical applications and their use in astronomical investigations.


Intensity of electromagnetic waves

How does distance from a source affect the intensity of an electromagneticwave? Communication using electromagnetic waves can be made overlong distances.

Make a list of all the types of communication you know that useelectromagnetic waves to carry the signal.

_________________________________________________________

_________________________________________________________

Check your answer.

Often we have to amplify signals travelling large distances. This is becausethe signals decrease in strength over distance. This decrease in strength iscalled attenuation of the signal.

Why is attenuation important?

Learning about attenuation will help you to understand why the intensity ofthe signal indicator on a mobile phone drops off away from the transmittingantenna and why the signal of your favourite radio station drops out when youare away from home.

The relationship between distance and intensity of the electromagnetic wavesignal from source should be clear to you. Increased distance results indecreased intensity of signal.

You know that the further you are from a light source, the lower the intensitythe light from the source appears to have. At 100 metres from a street lightthe illumination appears dim. It lights up the area much less brightly or withlower intensity than the area adjacent to the light. Light intensity(illuminance) is measured in units called the lux (lx). This can be done with alight meter.

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To provide some idea of what a lux is:

• sunlight on an average day ranges from 32 000 to 100 000 lx.

• rooms are lit at about 500 lx.

• moonlight lights up an area with an intensity of about 1 lx.

The inverse square law

The drop off in light intensity might follow some rules. You should performthe experiments below to determine these rules.

Aim

To model how the light intensity varies with distance from a point source oflight such as a light globe, using a balloon.

Procedure

1 Imagine the light globe is always in the centre of your balloon.The inflating balloon surface is a representation of a wavefront travellingin three dimensions from the light globe.

2 Inflate a round balloon until it has a diameter of around 10 cm.Do not tie off the balloon.

Record this as radius 1 unit in the table below.

3 Use a marker pen to draw a 1 cm by 1 cm square on the balloon wherethe balloon is thickest opposite the inflation tube where you blow up theballoon.

Record the area of the square in the table below as 1 cm2. This squarerepresents the energy of the light at that radius from the light source.

a) What will happen to the area of the square as you inflate theballoon?

__________________________________________________

__________________________________________________

b) What would be happening to the fixed quantity of energy from alight source as it is spreading out from a point source in terms of theamount of energy per unit area?

__________________________________________________

__________________________________________________


4 Inflate the balloon until it has a diameter of around 20 cm. The distanceto the centre of the balloon has now doubled.

Record this as 2 units in the table below.

5 Measure the size of the square on the balloon now.

Record the area in the table below beside 2 units.

c) Has the area of the square doubled or increased by around 4 times?

__________________________________________________

5 Inflate the balloon until it has a diameter of around 30 cm. Be careful notto explode it. The distance to the centre of the balloon has now tripled.

6 Measure the size of the square on the balloon now.

Record the area in the table below.

d) How has the area of the square increased now? Is it three timesbigger or around 9 times bigger?

__________________________________________________

Distance units from the balloon centre Area of the square

1 1 cm2

2

3

e) Describe the relationship shown by this data. That is, how does thisincrease in area relate to the distance from the source?

__________________________________________________

__________________________________________________

f) Would it be accurate to say to 'the area increase is proportional to thedistance unit squared?'

__________________________________________________

__________________________________________________

Check your answers.

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Returning to the model at the beginning of this activity where you imaginedthe balloon surface was a wavefront of light propagating in three dimensionsfrom a point source of light located in the centre of the balloon.

This model is like the situation shown in the figure on the next page.As the balloon gets bigger, the light would have propagated further fromthe source.

Light propagating in three dimensions.

You can see from your results that the area of the square drawn on the balloonincreases as a factor of the distance from the balloon centre squared.Similarly a set quantity of light energy in any wavefront would be spread overan area increasing in proportion to the distance from the source squared.

The inverse relationship of light intensity decreasing as distance, d isincreasing can be combined with this relationship to establish the relationshipbetween distance and light intensity, I as:

I µ 12

d

In practical terms this means that if you are 1 m from a light source with anintensity of 4000 lx then at 2 m the light intensity will be:

I

I

= ¥

=

400012

1000

2

The light intensity is 1000 lx.


At 3 m the light intensity will be:

I = 13

4000

I = 444

2 ¥

The light intensity is 444 lx.

1 What would be the light intensity at 4 m?

_________________________________________________

_________________________________________________

2 What would be the light intensity at 5 m?

_________________________________________________

_________________________________________________

Check your answers.

The relationship I µ 12

d is an example of the inverse square law. This law or

relationship will be encountered a number of times throughout this physicscourse.

Confirming I µ 12d

using a data logger

At your practical session with your teacher you may use a data logger to

confirm the relationship I µ 12

d. The following text describes how you

might go about this.

1 Connect the light intensity probe to your data logger.

2 Set up the data logger to collect and store data.

3 Set up the light globe in the centre of a dark room.

4 Point your light intensity probe directly at the light globe close to theglobe (around 0.01 m from it). Record the light intensity.

5 Record readings of light intensity at 1 m, 2 m, 3 m, 4 m etc .

6 Record the distance for each light intensity reading in list 2.

7. Plot your values of light intensity against the distances in list 2.This will give you a graph of light intensity versus distance from the lightglobe. Print the shape of the graph.


8. Square the values for distance you recorded. Plot the values of light

intensity against the 1

distance2 . Print the shape of the graph.

Your results might look something like this.

Light intensity (lx) List 1 Distance from light (m)List 2

Distance from lightsquared

8600 1 11

12 =

2150 2 12

142 =

950 3 13

192 =

535 4 142 = 16

344 5 152 = 1

25

If you have access to a data logger with 2 input ports and a sonic ranger aswell as a light probe use the sonic ranger and light meter to get a continuous

reading of I vs 1

d2

1 Graph the light intensity against 1d2 on the graph paper in the Appendix.

Draw a line graph and join your points with a line or curve of best fit.

2 What do you notice about the shape of your graph? Explain it.

_____________________________________________________

_____________________________________________________

_____________________________________________________

Check your answer.


Modulation

How do you add information to electromagnetic waves? When you speakhow do you add information to the signal that is your voice?You vary the amplitude and the frequency of the sound waves coming out ofyour mouth.

You have all heard a boring speaker. Sometimes what they are saying isinteresting but the tone of their voice is monotone and they simply don'tcommunicate well. It's hard to hear them clearly. Clear speakers addvariation in tone or frequency and change amplitude to make sure theirmessage gets across. They have added information to the signal of their voiceby modulating the sound wave coming from their larynx.

Electromagnetic waves can carry information. This information must beadded to the waves. The process of adding the information is calledmodulation. To modulate a radio or microwave either the amplitude or thefrequency of the wave must be changed. The other critical aspect ofinformation transfer is that the signal must be converted back into informationyou can use. That process is called demodulation.

Consider a radio wave signal being modulated. A radio wave signal occupiesa bandwidth of frequencies. This means that the electromagnetic wavetransmitted is using a number of frequencies next to each other rather than asingle frequency. In the middle of that bandwidth is the carrier wave.

What does the carrier wave do?

Nothing, it is a by-product of the radio wave transmitter. (If you can think ofyour voice as a wave being transmitted this carrier wave would be like yousaying a single note like Aa and nothing else.) The message signal is added tothat carrier wave by superposition of a signal wave.


Kinds of modulation

There are many kinds of modulation. You probably know about the two mostcommon ways: amplitude modulation (AM) and frequency modulation (FM)although you may wish to research on your own a third kind calledphase modulation.

What is amplitude modulation?

The most common place you would have heard about amplitude modulationis from AM (amplitude modulation) radio.

To add a signal to an AM radio signal the amplitude (the strength of thesignal) must be changed in a way corresponding to the information we wish tosend as a signal. The signal remains constant in frequency bandwidth butvaries in strength or amplitude of the wave. This variation in the amplitude ofthe wave is decoded by your radio to produce the signal you hear.

unmodulated carrier

modulating signal

AM modulated carrier

Amplitude modulation of a carrier wave.

You can probably recognise from the figure above that amplitude modulationis really superposition of the modulating signal carrying the messageinformation onto the carrier wave.

Look at pages that show an animated demonstration of amplitudemodulation on the Physics website page.



What is frequency modulation?

In a frequency modulated (FM) radio transmission, the frequency of the waveis varied and it is that variation that carries the information.

A limiting circuit in the radio receiver removes amplitude variations thatoccur in transmission of the radio signal. The limiting circuit keeps theamplitude of the received wave a near constant in the radio receiver and thesignal is converted back into sound by a discriminator circuit. The figurebelow shows an FM signal.

unmodulated carrier

modulating signal

FM modulated carrier

Frequency modulation of a carrier wave.

Look at some pages that give a more detailed explanation for how AM andFM works on the Physics website page.


Is frequency modulation also accomplished with superposition of a signalwave onto a carrier wave? Explain your reasoning.

_________________________________________________________

_________________________________________________________

Check your answer.


What is the advantage of FM over AM?

Most natural and artificial sources of radio noise (the signal you don’t wanton your radio and that is called static) is AM in nature. This means that noisecombines with the AM signal by superposition of waves to produce a morecomplex and different wave form than the one transmitted. As a result theinformation from the AM radio station is easily altered.

equals modified AM signal – this isthe static

plus noise signal

amplitude modified signal

Figure: AM signal plus noise.

The effects of noise are much reduced in FM radio signals by the limitingcircuit therefore, you don’t need to worry about the strength of the signalreceived but rather rely on the frequency changes to provide the radio signal.It is much harder to change the frequency by interference hence the musicreceived is closer to that broadcast.


Does AM have any advantages over FM?

FM radio channels require a large bandwidth of the electromagnetic spectrum.The range of frequencies required to transmit the signal is large. Since theelectromagnetic spectrum is limited in the range of frequencies available thatmeans that the number of FM channels transmitted is limited.

AM radio requires a much smaller bandwidth of frequencies for transmissionso the number of potential AM channels transmitted is much larger.

Microwaves are also modulated

There is no difference between frequency modulation of microwaves that areused to send signals from mobile phones and radio waves.

The reasons microwaves are used in mobile telephone systems arelisted below.

• microwaves constitute a different bandwidth of frequencies of theelectromagnetic spectrum to radio waves. Crowding of the bandwidths isa problem.

• microwaves do not spread out very much so most of the energy makes itto the next receiver dish from the transmitter. This results in signal witha potential range of up to 100 km. Such a system is important to sendinformation over long distances on mobile phone networks.

• it is possible to send a large number of signals at once using the samebeam, up to 20 000 telephone calls at once, because the range offrequencies in the microwave transmission range is large.

The disadvantages of using microwaves

The main disadvantage of microwaves as a signal carrier is that they require aline of sight connection from one antenna to the next. If you live in the cityyou may have noticed many of these antennae.

Are any of these antennae located around your local area? Is it obvious thatthese antennae have a line of sight connection? Because microwavetransmitters need a line of sight connection to get good area coverage, anetwork needs a huge number of antennae.

All of the major communication networks have maps showing mobile phonenetwork coverage.


Look at the NSW coverage maps for OPTUS Mobile. This can be found atthe Physics website page.


There is another disadvantage of microwaves being used as a signal carrier.You know that microwaves heat food by water molecules absorbing themwhich increases the energy of the water molecules. Hence in microwavebandwidth frequencies, transmission range is affected by atmosphericconditions like the moisture content or rain. Also oxygen absorption of themicrowave energy is a problem and can affect microwave transmission.

Modulation of microwaves and light

Some examples of modulation of light signals are listed below.

• The earliest modulation of light signal by amplitude modulation wasprobably the helioscope, where a signal on or off was flashed tocommunicate over a distance.

• The lighthouse provides a good example of amplitude modulation of alight signal to warn ships of danger. A common frequency modulationdevice in use in many towns and cities today is the traffic light. Thefrequency of the light is varied or modulated to tell you whether to stop,go, or prepare to stop.

• Light is just another part of the electromagnetic spectrum. It thereforebehaves in a similar way to other electromagnetic waves and will allowtransmission of AM signals from a light laser to a receiver. The signal isamplitude modulated because the frequency of light from a particularlaser is fixed.

• The signal strength of the laser light can be varied as a response to soundat a microphone producing small differences in the size of an electriccurrent. This signal is added onto the light from the laser.

Look at some pages that relate to infrared laser communication of data.These can be found at the Physics website page.


At your practical session your teacher may show you a device such as theLaserDot® transmitter and receiver that will send and receive sound wavestransmitted across an open space by an amplitude modulated laser beam.

This open-to-air laser device will transfer a sound signal around 200 mwithout the use of fibre-optic cable with high reliability.


When using the LaserDot®‚ device that sends the signal by amplitudemodulation would you expect the intensity of the light from the laser to beconstant or would you expect it to vary? Explain your answer.

_________________________________________________________

_________________________________________________________

Check your answer.

An object in the path of the laser beam can disrupt a laser signal beamedacross an open space.

If you can think of a way to avoid this problem, write it down in the spacebelow.

_________________________________________________________

_________________________________________________________

_________________________________________________________

If the laser signal is fed into a fibre-optic cable, the distance of transmissioncan be greatly increased because the beam is protected from interruption.New high purity fibre-optic cable systems can transfer light of frequencies inthe infrared range around 100 km without the need to boost the signal.

Before you will understand how these cables work it will be necessary for youto learn about reflection and refraction. You will do this in the next part ofthis module.

Do return exercise 4.7 now.


Appendix


Suggested answers

Electromagnetic radiation from space1 Longer wavelength electromagnetic waves are more penetrating than

short wavelength electromagnetic waves in general.

2 Radio waves, most microwaves and visible light.

3 UV, X-rays and gamma rays are almost completely filtered out by theatmosphere.

Ultraviolet radiation1 UV-c

2 UV-a

Visible light

Longer wavelengths are more penetrating.


Electromagnetic wave type Radiation detector

Radio waves Radio/ transistor radio/ television

Microwaves Mobile phones

Infrared waves Receiver

Visible light Laser receiver/the eye


Intensity of electromagnetic wavesTelevision, radio, telephone, the Internet, mobile phone calls.

The inverse square lawa) It increases.

b) Decreases with increasing distance.

c) 4 times.

d) 9 times.

Distance units from the balloon centre Area of the square

1 1 cm2

2 4 cm2

3 9 cm2

e) Area increases by a factor equal to the square of the increase in distance.

f) Yes.

1 250 lx

2 160 lx

Confirming I µ 12d

using a data logger

1

Light intensity (lx)

0

5

1

1

2

2

3

0 200 400 600 800 1000


2 Undergoes exponential decay. Intensity exponentially decreases withincreasing distance but in theory never reaches zero intensity.

What is frequency modulation?Yes. The carrier wave has been modified by superposing the signal.

Modulation of microwaves and lightVariable intensity because the light is amplitude modulated.


Exercises - Part 4


Exercise 4.1

The use of the electromagnetic spectrum for wireless communication islimited to using bands from radio waves up to light. Why would it bedifficult to use higher frequency bands of the electromagnetic spectrum tocommunicate by wireless?

_________________________________________________________

_________________________________________________________

_________________________________________________________

Exercise 4.2

Over a week you are probably using a large number of communicationdevices. Some devices you may have used are listed in the table below. Listany other devices you use for communication. Identify the part of theelectromagnetic spectrum each device is using

Communication device Type of electromagnetic wave used

telephone

television

radio


Exercise 4.3

The intensity of light received from a light source is proportional to thereciprocal of the distance squared. The table that follows shows the averagedistance of the inner planets of our solar system from the Sun. Complete thetable of light intensities from the Sun at each of the named planets aftercalculating the intensity values relative to the light intensity received onEarth.

Planet Mean distance fromthe Sun (km)

Light intensity (lx)

Mercury 57.7 ¥ 106

Venus 107 ¥ 106

Earth 149 ¥ 106 32 000

Mars 226 ¥ 106

Exercise 4.4

Australian colour TV channel broadcast standards (2000) are described ashaving the following characteristics:

Channel width 7 MHz sideband transmission

Vision carrier 1.25 MHz above lower edge ofchannel

Vision modulation negative amplitude modulation

Lines per picture 625 lines interlaced 2:1

Line frequency 15625 Hz

Primary sound carrier 5.5 MHz above vision carrier

Secondary sound carrier 242.1875 kHz above primary soundcarrier

Sound modulation FM


This tells us that the picture on your TV is the result of 625 amplitudemodulated signals each producing a line of signal. The sound on your TV isan FM signal. Explain why you often lose the picture in poor reception areasbut are still able to receive sound.

_________________________________________________________

_________________________________________________________

_________________________________________________________

Exercise 4.5

Locate an AM/FM radio that shows the stations on the tuner dial. Read offthe following information from the radio.

a) What is the range of frequencies for radio stations in the FM band inAustralia?

_____________________________________________________

_____________________________________________________

_____________________________________________________

b) Typical FM radio stations have carrier frequencies separated by0.2 MHz. How many FM radio stations could fit into the range offrequencies used in Australia for FM radio?

_____________________________________________________

_____________________________________________________

_____________________________________________________

c) Read off the range of frequencies available to AM radio stations from aradio.

_____________________________________________________

_____________________________________________________

_____________________________________________________

d) Each AM station takes up a 9 kHz band width. How many stations couldbroadcast in this band?

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________


Exercise 4.6

Explain why fibre-optic cables in commercial use transfer radiation offrequencies in the infrared range over long distances rather than usingradiation in the ultraviolet range? Explain your answer by referring to thepenetrating ability of visible light.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

Exercise 4.7

Discuss problems produced by the limited range of the electromagneticspectrum available for communication purposes. You should consider thisquestion as having two aspects. They are the actual distance over which thecommunications can occur and the limited number of frequencies available inthe communications bands of the electromagnetic spectrum. Limit youranswer to 200 words.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

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Part 5: Reflection and refraction


AMENDMENTS








Part 4 p 9



WARNING







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Part 5: Reflection and refraction 1

Contents

Introduction ............................................................................... 3

What is reflection?..................................................................... 5

Rules of reflection.................................................................................6

Reflection and communication ................................................ 12

Types of radio waves .........................................................................12

Curved mirrors ........................................................................ 14

Mirror terminology ..............................................................................15

What happens when rays strike? ......................................................15

Uses of reflecting surfaces ...................................................... 18

Position and nature of an image........................................................18

Using a spoon as a curved mirror .....................................................22

Other applications of curved surfaces ..................................... 26

The astronomical telescope...............................................................26

Torches...............................................................................................27

The satellite dish ................................................................................27

Refraction of waves................................................................. 29

Refraction can be seen in water ........................................................29

What causes the bending? ................................................................31

Snell’s law...........................................................................................34


What is total internal reflection?............................................... 42

What is an optical–fibre? ......................................................... 45

How does an optical–fibre work? ......................................................45

Lenses .................................................................................... 47

Convex and concave lenses .............................................................48

Summary ................................................................................. 50

Appendix.................................................................................. 51

Suggested answers ................................................................. 53

Exercises – Part 5.................................................................... 57

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Introduction

This part should enable you to understand how reflection and refractionare used in communication.


• describe and apply the law of reflection and explain the effect ofreflection from a plane surface on waves

• describe ways in which applications of reflection light, radio wavesand microwaves have assisted in information transfer

• describe one application of reflection for each of the following

– plane surfaces

– concave surfaces

– convex surfaces

– radio waves being reflected by the ionosphere

• explain that refraction is related to the velocities of a wave indifferent media and outline how this may result in the bending of awavefront

• define refractive index in terms of the changes in the velocity of awave in passing from one medium to another

• define Snell’s Law: 1

2

vv

ir

=sinsin

• identify the conditions necessary for total internal refraction withreference to the critical angle.

• outline how refraction and/or total internal reflection is used inoptical fibres


• perform first–hand investigations and gather information to observethe path of light rays and construct diagrams indicating both thedirection of travel of the light rays and a wave front


• present information using ray diagrams to show the path of wavesreflected from:

– plane surfaces

– concave surfaces

– convex surface

– the ionosphere

• perform an investigation and gather information to graph the angleof incidence and refraction for light encountering a medium changeshowing the relationship between these angles

• perform a first–hand investigation and gather information tocalculate the refractive index of glass or perspex

• solve problems and analyse information using Snell’s Law

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amendedOctober 2002. The original and most up–to–date version of this document canbe found on the Board’s website athttp://www.boardofstudies.nsw.edu.au/syllabus_hsc/syllabus2000_listp.html#p.

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What is reflection?

Communication technologies use reflection and refraction ofelectromagnetic waves.

You know what a reflection is. You look at reflections of yourself everyday in a mirror or glass. The reflection is the wave energy that cannotpenetrate a surface bounced back from that surface.

The behaviour of the wave energy at the surface follows strict rules.You may already know some of these rules from your earlier work onreflecting sound and echoes.

To assist in understanding how reflection works with light you can use anartificial construction line called a ray. A ray, as shown in the figurebelow, is a line drawn at 90∞ to a wavefront.

rays andwavefronts

wavefront

ray

Rays at 90∞ to wavefronts show the direction of energy flow.


Rays are simply lines of construction that indicate the direction in whichthe wave energy is travelling.


Rays, being straight lines, are easier to use than wavefronts in diagramsto illustrate the behaviour of waves. They make it simpler to analysewave behaviour on paper. By following the path of the ray you can seewhat the wave is doing.

Rules of reflection

What are the rules that determine what happens to reflected waves?

The easiest way to determine what happens to reflected waves is toconsider light waves as an example. When light waves (or rays) hit asmooth surface such as a mirror, they are reflected. The light ray thatstrikes the surface is called the incident ray. The light ray that isreflected back is called the reflected ray.

The incident ray, the reflected ray and the normal at the point ofincidence all lie in one plane. That means they can all be drawn asthough they lie on one flat sheet of paper.

The angle of incidence, i, equals the angle of reflection, r, when bothangles are measured to the normal. That means with respect to a linedrawn at 90∞ to the surface where the ray strikes. The figure below

shows the features of reflection.

i r

normal angle of reflection

reflected ray

incident ray

angle of incidence

mirror surface

Reflection of light from a plane mirror.Adapted from OTEN, Physics for Electrical and Electronic Engineer.

The second statement is known as the Law of reflection and isrepresented mathematically by the expression:

the angle of incidence = the angle of reflection.

–i∞ = –r∞

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The reflection of light from a flat mirror, also called a plane mirror, canproduce a blinding glare. This occurs when a number of parallel rays areincident on a mirror, the reflected rays will also be parallel (see the figureopposite).

reflected raysincidentrays

normals

reflecting surface

Reflection of multiple rays from a plane mirror. Note that for each separateincident ray the law of reflection applies.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Observing reflection

You have probably looked at reflection many times already. The activitybelow requires you to observe the law of reflection more formally.

Do the following:

• Shine a torch beam on a mirror in a darkened room.

• Look at the angle of incidence.

Does it appear that the angle of incidence is approximately equal to theangle of reflection? You should notice that the angle of incidence isequal to the angle of reflection.

When the light is incident upon an irregular surface, the laws ofreflection still hold for each particular ray of light, but the normal rays tothe surface are not parallel, so the light is reflected in many differentdirections. This produces diffuse reflection and is illustrated in thefollowing figure.


normal rays are notparallel

incidentrays

Diffuse reflection where each individual ray obeys the law of reflection butcollectively the reflection is diffuse.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Light reflecting off the water in a pond can produce a mirror–likereflection or a diffuse reflection.

What do you think the condition of the pond or swimming pool surfacewould be like to produce

a) a mirror–like reflection?

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b) a diffuse reflection?

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Check your answer.

How do images form from reflected light?

1 Find a large mirror located in a room.

2 Stand directly in front of the mirror as in the figure below.Walk forward until your face almost touches the mirror.

When you stand in front of a plane (flat) mirror, every point on yourbody reflects light. Your body is serving as a source of light waves.Some of these waves will strike the mirror, reflecting in just the rightdirection to enter your eye, where the light is focused to form an image.

The image is seen as though it is an object behind the mirror. Everypoint on your hand, for example, will have its corresponding image pointbehind the mirror, recreating the appearance of that hand.

Someone else looking into the mirror, as in the figure below, may seerays that reflect off the mirror that don't enter your eye.

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object mirror image

Reflection of your image in a plane mirror.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Describe your image in the mirror in terms of its way up, its left and right,its size and its distance back from the mirror compared to your distance backfrom the mirror.

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You should have described an image in the plane mirror that isundistorted, right–side up (upright), the same size (life–size) andstanding just as far behind the reflecting surface as you are in front of it.

The image is also laterally inverted that means that left becomes rightand right becomes left, for example, the image of your left hand appearsto be the right hand of the image.

Locating an image from a plane mirror

Suppose that a point, P, is a source of light rays from a pin for example.You can find the position of its image in a plane mirror represented bythe symbol P’ by drawing the construction rays shown in thefigure below.


yy'

xx'

source P P' image

ray A

ray B

O

mirror

Image formation in a plane mirror.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

A geometric construction can be used to locate an image from a planemirror. The procedure for the construction is as follows.

1 Draw two rays, A and B, from P to the mirror using a pencil. Then lookat mirror and draw in the path of the reflected rays. These are easilyseen as the reflected pencil line leading to the reflected image of the pin.

2 Because these rays are reflected:

– i = – r

3 This is shown by y and y' and x and x' on the figure. Note, thereflected rays (A and B) are diverging or moving apart. The normalrepresented by the dotted line hits the mirror surface at 90∞ and is

reflected straight back.

4 To find an image point we extend the construction lines of thereflections, including the normal behind the mirror, to where theyintersect at point P'. This is the image position. If you have done thereconstruction properly you will find that P' is as far behind themirror as P is in front. That is, the object distance from the mirror isequal to image distance behind the mirror.

The image in the mirror is not a real image. This means P' is called avirtual image and the rays of light do not actually pass through or comefrom P', they only appear as if they do.

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A test of whether an image is 'real' or not is whether the image can beprojected on a screen such as a white sheet of paper. This image cannotso therefore it is not a real image.

Do Exercises 5.1 and 5.2 now.


Reflection and communication

You may have seen old movies where a mirror used reflected sunlight toflash messages. This system used a code based on the length of flashessimilar to Morse code. This device was called a heliograph. Heliographswere used as communication devices in the late 19th and early 20th

century.

Types of radio waves

Today many of the radio waves we use to communicate are reflectedfrom the ionosphere. These radio waves are known as sky waves.Radio waves are divided up into three groups outlined below:

Surface waves

Surface waves follow the Earth’s surface and have maximum rangearound 1000 km for low frequency waves.

Sky waves

Sky waves have high frequencies and are bounced off the ionosphere.They can also bounce off the Earth back toward the ionosphere. Becausethe curve in the ionosphere is so great the radio waves are effectivelyreflected by a plane surface. An interesting point is that the height atwhich the ionosphere begins varies throughout the day so the effectivecommunication range of sky wave transmissions also varies with the timeof day. If you are a short wave radio enthusiast you would know that thesignal you receive on your radio from long distance transmissions isclearer during the night. This is because the ionosphere rises to a greateraltitude above the surface of the Earth at night.

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To go to a good links page that gives you some of the history and a host ofinteresting links about the ionosphere and radio go to a link on the physicslinks page at:http://www.lmpc.edu.au/science

Space waves

Space waves have frequencies above 30 MHz. The ionosphere doesn'treflect space waves. These waves are directed at satellites and are onlyuseful for line of sight type communications.

The following figure shows these three types of radio waves and thepassage of travel they follow.

transmitter

Earth

ionosphere

satellite

space waves

surface waves

skywaves

How the different radio waves carry communications. Note that the sky wavesliterally bounce off the ionosphere. The higher the ionosphere, the longer therange of the reflected sky radio wave.

1 Why do you think the low frequency surface radio waves are the mostpenetrating?

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2 How do you think sky wave radio signals could carry messages allaround the world from a single transmitter?

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Check your answers.


Curved mirrors

Plane mirrors are the most common mirrors that we use, but curvedmirrors are widely used in many applications.

Can you think of any places where curved mirrors might be used?

List the places you have seen curved mirrors used.

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There are many types of curved mirrors. Restrict your attention to onlyone type of curved mirror, the spherical mirrors.

The reason spherical mirrors are used a lot is they are easy to make.Spheres of glass are easily blown by glass blowers. All you have to do issilver one side of the glass to make a spherical mirror.

Because the spherical mirror is made from a sphere the terminology usedin describing these mirrors is taken from a sphere and used to describefeatures of a mirror.

a large hollow three-dimensional sphere

C

P

principal axis

A spherical mirror forms part of a sphere The distance PC is said to be theradius of curvature of the mirror because it is the radius of the sphere fromwhich the mirror was made. P is the pole–the central point of the mirror, lyingon an axis that is an extension of the diameter of the mirror that we call theprincipal axis of the mirror.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

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C

concave mirror

reflectingsurface

C

reflectingsurface

convex mirror

Concave and convex mirrors showing the reflecting surfaces.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Look at the figures then cross out the incorrect word in each statement aboutcurved mirrors.

a) A convex mirror has the reflecting surface on the (outside/inside) of thecurve.

b) A concave mirror has the reflecting surface on the (outside/inside) ofthe curve.

Mirror terminology

To accurately describe how rays are reflected and curved mirrors formimages you have to use certain terms. Those terms include:

• The sphere centre given the symbol C.

• P the pole of the mirror as shown in the figures below of concaveand convex mirrors.

• The principal axis is a line extended along the diameter of the spherefrom which the mirror could have been made. That diameter passesthrough C and P.

What happens when rays strike?

When light rays strike a concave spherical mirror surface parallel withthe principal axis they are reflected and converge to a single point.This point is called the principal focus or focal point of the mirror.The principal focus is labelled F in the figure below. It is the point where

all the reflected rays meet. This point is 1

2 the centre of curvature radius.

This 1

2 the radius of the sphere from which the mirror could be made.


concave mirror

f

principal axis FC

A concave mirror. This type of mirror is also called a converging mirror becausethe reflected rays converge at a point on the same side of the mirror as thesource of the light.

With a convex mirror, incident rays hitting the mirror parallel to theprincipal axis are reflected and diverge. If you project these reflectedrays backwards, behind the mirror you find a point on the principal axisfrom which these rays appear to come. This is similar to finding theimage produced by a plane mirror. This point is the principal focus, orfocal point of the mirror.

C

convex mirror

focal length, f

Pprincipal axis F

A convex mirror. This type of mirror is also called a diverging mirror becausethe reflected rays appear to diverge from a single point behind the mirror. Thepoint from which the reflected rays appear to diverge is called the focal point ofthe mirror.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

The principal focus is labelled F in the figure and is the point where allthe backward projections of the reflected rays meet. These are shown as

dotted lines. The principle focus is equal in length to 1

2 the centre of

curvature radius of the sphere from which the mirror could be made.Note that the focus is, in fact, behind the mirror. The focal length is fromthe mirror to the principal focus. Because this is the case the convexmirror can never produce a real image that can be projected onto a screen(although it can be seen by an observer).

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For both the concave and convex spherical mirrors, the focal point, F, ishalfway between P and C, that is:

F = PC

2

Where F is focal length or the distance from the pole of the mirror to thefocus and PC is radius of curvature for the mirror.

Reversing incident rays

The paths followed by light rays are reversible. This is known as theprinciple of reversibility of rays.

C principal axisF

incident ray

incident ray

A convex mirror with the incident rays directed towards the principal focusshowing the rays are reflected back from the mirror parallel to the principal axisof the mirror. A ray projected through the centre of curvature of the mirror isreflected back on itself. This is shown as the dashed line.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

principal axis FC

A concave mirror with the incident rays directed through the principal focusshowing the rays are reflected back from the mirror parallel to the principal axisof the mirror. A ray projected through the centre of curvature of the mirror isreflected back on itself.Adapted from OTEN, Physics for Electrical and Electronic Engineers.


Uses of reflecting surfaces

When mirrors are used so that the reflected rays are all parallel, they areknown as collimators, and the reflected beam is described as acollimated beam. Collimators are used in torches, searchlights, radarand microwave transmitters, and in spotlights and driving lights.

Position and nature of an image

You can use ray tracing to determine the position and nature of an imageformed by a curved mirror.

Start with the concave mirror, but you will see that the principles are thesame for the convex mirror.

The image and its nature are determined by constructing any two of thefollowing three rays.

1 The first ray is drawn from the top of the object (as this will fix thetop of the image) through the centre of curvature, to the mirror, andreflects back upon itself (being incident normally on the mirror).

2 The second ray is again drawn from the top of the object. This rayenters the mirror parallel to the principal axis, and, upon reflection,passes through the principal focus; or appears to come from the focalpoint of a convex mirror.

3 This ray is drawn from the top of the object, through the principalfocus, or proceeding towards it and, upon reflection, leaves themirror parallel to the principal axis.

The intersection of any two of these three rays defines the position, andalso the nature, of the image formed by the mirror.

The location of images from concave and convex mirrors is shown stepby step in the figures on the next page.

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O

F

f P

1

C

1

axis

o

O

F

f P

2

1

i

I

C

1 3

axis

o

O

F

f P

2

1

i

I

C

1

axis

o

Ray 1 is drawn from the top of the object through the centre of the mirror.

Ray 2 is drawn from the top of the object parallel to the top of the objectand reflects back through the focus. The intersection of ray 1 and ray 2locate the image

Ray 3 is drawn from the top of the object through the principal focusand is reflected parallel to the principal axis. It confirms the image locationat the intersection of all three rays.



For the concave mirror

The first ray is drawn from the top of the object, through C to the mirrorsurface, reflects back upon itself.

The second ray is drawn parallel to the principal axis, reflecting backthrough F.

A third ray drawn through the focus from the top of the object is reflectedback parallel to the principal axis.

Where these rays intersect is where the image, I, is formed. The natureof this image is:

• real — a screen placed at the image position would have an image ofthe object projected on it. The rays actually pass through the imageposition.

• inverted — the image is upside down relative to the object;

• diminished (magnification < 1). This means the image is smallerthan the object. This can be seen by taking a look.

The diagrams opposite show the procedure of drawing in the three raysnecessary to locate an image using a concave mirror.

For the convex mirror

The first ray is drawn from the top of the object, and projected behind themirror through C, reflects back upon itself.

The second ray is drawn parallel to the principal axis then through F.

A third ray drawn through the focus from the top of the object is reflectedback parallel to the principal axis.

The projected rays are broken lines to indicate that the light doesn’tactually travel from these points behind the mirror. The image is formedat this point of intersection, and its nature is:

• virtual – the rays don’t actually pass through the image, the lightonly appearing to come from this point which is behind the mirror

• upright – the image is the same way up as the object

• diminished. You can see this by looking at the image. It is smaller.

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FI

Paxis

3

12

O

C

o i

f

FI

Paxis

1

O

C

o

f

FI

Paxis

12

O

C

o

f

Ray 1 drawn from the top of the mirror and projected back through C.

Ray 2 drawn parallel to the principal axis and after reflection from the mirror appears to have come from F.

Ray 2 drawn as though it is to pass through F but is reflected parallel to theprincipal axis.

i



Using a spoon as a curved mirror

To get a good understanding of how convex and concave mirrors workyou can use a stainless steel or silver plated round soup–spoon as both aconcave mirror and a convex mirror.

Using a soup–spoon as a concave mirror

Get yourself a soup–spoon. Use the bowl shape of the spoon facing you dothe following activities.

25 cm

you

soup spoon

Describe what you see happening to an image of the letter ‘R’ drawnabout 1 cm high on a sheet of paper. This ‘R’ drawn on paper will beyour object.

Hold the spoon at about 25 cm from the ‘R’ and look at the image of the‘R’ in the spoon as shown in the figure below.

focus

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1 Draw what you see in the spoon drawn previously.

2 Describe the image as diminished/magnified and upright/inverted.

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_____________________________________________________

3 Slowly move the spoon towards the ‘R’ on the paper. Describe whathappens to the image.

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Bring the spoon closer to the ‘R’ slowly. The image shoulddisappear completely at one point. At this point, the ‘R’ on paper isat the focal length of the spoon. The image produced by the concavemirror of the spoon would be focussed at an infinite distance fromthe concave surface.

Record that distance in centimetres as the focal length of your spoon.

Bring the mirror closer to the ‘R’ than the focal length as shown inthe diagram below.

focus

4 Draw what you see on the bigger, blank spoon shape. The reflectedimage of ‘R’ should now change. How does it change?

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_____________________________________________________


5 Does bringing the mirror even closer to ‘R’ make the image moremagnified/diminished?

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6 The image of the ‘R’ inside the focal length of the spoon mirror issaid to not be a real image. Does this mean it cannot/can beprojected onto a screen?

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Check your answers.

Using a soup–spoon as a convex mirror

Get yourself a soup–spoon and with the bowl shape of the spoon facingaway from you, do the following activities. Describe what you seehappening to an image of an ‘R’ drawn on paper.

Slowly bring the mirror towards your ‘R’ as shown in the figure below.

1 Describe what happens to the image.

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_____________________________________________________

2 How would you describe the change in the size of the image as thedistance between the spoon and your ‘R’ gets larger?

______________________________________________________

______________________________________________________

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3 Is this a real image or not? Explain your answer. Remembering thenature of an unreal image from the results of the concave mirroractivity above will help you here.

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Many cars have add on convex mirrors in rear vision mirrors. Theycome with a warning that objects viewed in these mirrors may becloser than they appear.

4 Explain why. Base your answer on observations with the spoonconvex mirror.

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5 What do you think is the advantage of using convex mirrors fordriving rear view mirrors and also for security mirrors in shoppingareas?

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Check your answers.


Other applications of curved surfaces

The astronomical telescope

The telescope of the type shown in the picture below was invented byIsaac Newton in the late 17

th

century. It is called the Newtonianreflecting telescope.

eyepiece lens

parallel light rays from a star

plane mirror

main curved mirror

A Newtonian reflecting telescope. The main light collecting mirror is a concavespherical mirror or a parabolic mirror. The parabolic mirror has an advantagethat it tends to focus the light collected by the mirror to a point more accurately.The secondary mirror is a plane mirror.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Most large astronomical telescopes are like this one or are a variationof it.

The main mirror in astronomical telescopes is coated with aluminium andis a front silvered mirror. The largest optical telescopes of this kind arethe Gemini telescopes. They have an 8 m diameter main mirror made insegments. They are located in Mauna Kea in Hawaii and the Atacamdesert in Chile at altitudes of around 4000 m. The Anglo AustralianTelescope at Siding Springs, near Coonabarabran, New South Wales hasa 3.9 m diameter single segment main mirror.

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The larger the main mirror in the telescope the greater the light collectingability of the telescope. The more light that is collected the brighter theimage that will be formed of the astronomical object.

Can you suggest a reason why telescopes are often located at high altitudes?Hint: Think about the penetrating ability of electromagnetic radiationfrom space to the Earth’s surface.

_________________________________________________________

_________________________________________________________

_________________________________________________________

Check your answer.

Torches

Torches often use a concave spherical mirror. Some torches make a spotbeam where others make a flood beam. Whether the light spreads out ornot depends on the placement of the filament of the light globe in front ofthe mirror.

Use the rules for reflection of light from a concave spherical mirror to workout why a torch produces a flood or a spot beam? Write your explanationbelow.

_________________________________________________________

_________________________________________________________

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Check your answer.

The satellite dish

Satellite dishes receive weak signals from satellites in space. Thesesignals are received by the dish as parallel rays hitting the dish surface.A large dish collects the weak intensity signal and focuses the signal byreflection to a receiver aerial at the focus of the satellite dish. Thisincreases the strength of the signal received.

The figure on the next page shows a satellite dish and its receiver aeriallocated at the focus.


A satellite receiving dish showing the focussing of the incoming rays to theaerial.

The radio waves hit the satellite dish parallel and are reflected andfocussed by the satellite dish at a point to provide a stronger signal.

Some torches like the Mag Light‚ brand have a beam that can be adjusted

to produce a flood or spot beam. How do you think these torches that have ascrew up/screw down reflector can be made to produce both a flood and aspot beam?

_________________________________________________________

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Check your answer.

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Refraction of waves

Refraction is the phenomenon where waves appear to bend as the wavepasses from one medium to another. You have seen the bending effectwhen you put a straight stick into clear water such as a fish tank. Thisapparent bending effect is shown below. In this case, you are the seeingthe refraction of light rays.

observer

water

surface

apparent bend

apparent positionof stick

Apparent bending of a stick in water due to refraction of light at the interfacebetween water and air.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

Refraction can be seen in water

Refraction can be seen with water waves where the water changes depth.

At your practical session with your teacher you may perform an experimentsimilar to this one to study refraction of water waves. You could use theripple tank or a shallow baking dish.

1 Place a glass slab around 5 mm thick in the tray with water in it to adepth of around 6 mm.


2 Set up a source of plane water waves such as those produced by aruler vibrating back and forwards with regular frequency.

3 Set up the depth of the water over one end of the slab to about onemillimetre, and at the other end about five millimetres. The plane(straight) waves travelling from the deeper water (6 mm deep) to theshallow water (1 mm over the slab) slow down and bunch up.

The wavelength of those waves decreases as shown in the figure below.

source of plane waves

depth ª 5 mm

slab

depth ª 1 mm where

waves slow

down

Plane water waves in a ripple tank showing the bunching up of the waves overthe slab in the shallower water. Note that the frequency or number of wavesdoesn’t change when the waves bunch up. Only the wavelength and speed ofthe waves moving forward have changed.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

If you arrange the position of the glass slab in the water so that theincident water waves strike the shallow water over the slab at an angle.The same slowing effect on the waves occurs, but now it creates theappearance that the waves have bent. The waves in the shallow waterhave a shorter wavelength. This is shown in the following figure.

source of plane waves

depth ª 1 mmdepth ª 5 mm

Plane waves travelling from deep to shallow water in a ripple tank. As eachwavefront encounters the shallow water that portion of the wave slows down.This creates a bend in the wave. This bending is called refraction.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

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The refraction of water waves in the tray is characteristic of all waves.The different water depths is the same as a change in the medium.

Each type of wave has a fixed velocity in any given medium. In the caseabove each different water depth is a different medium. Wave velocitychanges when a wave goes from one medium into another. However, thefrequency, does not change. Therefore in the wave equation below, thewavelength, l, must change.

fv=l

What causes the bending?

You already know it is the change in velocity as the wave goes from onemedium to another.

1 Look back at the diagram of the apparent bending of the stick at theinterface between air and water. In which medium do you think lightwaves are travelling slower? Explain your answer by referring to thewater waves being refracted.

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_____________________________________________________

2 If the water waves hit the change in medium (change in depth) at 90∞(a normal) then bending won’t occur but the change in the velocityand wavelength of the wave will occur.

How do you think you could see evidence of a change in velocity ifthere is no bending?

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_____________________________________________________

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Check your answers.

Consider a situation, where plane waves are moving from a mediumwhere they travel at high velocity into a medium where they travel atlower velocity if the waves strike the interface at 90∞. This is shown in

the figure on the next page.


medium 1v1

medium 2v2

surface wheremedium 1 andmedium 2 meet

1

2

Wavefronts hitting a change in medium at 90∞.

l1 > l2

Notice how the wavelength decreases in medium 2. That is:

l1 > l2

when

v1 > v2

If wavefronts strike a boundary between two mediums at an angle otherthan 90∞, a change in wave direction results, along with a decrease in

speed and wavelength. This is shown in the following figure.

medium 1v1

medium 2v2

surface wheremedium 1 andmedium 2 meet

1

2

In this figure the velocity in medium 2 is less than the velocity inmedium 1 and the wavelength in medium 2 is therefore less than the


wavelength in medium 1.Diagrams using wavefronts are difficult toanalyse so rays are used instead. Remember when you used rays whenyou learned about reflection. This makes the diagram from above looklike the diagram shown in the figure below.

normal

incident ray

i

r

medium 1v1 1

medium 2v2 2

refracted ray

v1 > v2 1 > 2

r > i

Refraction of a ray drawn to represent a wavefront. Using rays you can easilymeasure an angle of incidence and an angle of refraction. As the beam raypasses from medium 1 where the wave is travelling faster to medium 2 wherethe ray is travelling slower the ray is bent toward a normal ray.

Recall that the rays are drawn perpendicular to wavefronts and that theangle of incidence and the angle of refraction are both measured from thenormal at the point of incidence at the medium interface.

Does this sound familiar? Think about reflection!

Notice carefully, that:

i ≠ r

This is because this is not reflection, it is refraction!

Write, in your own words, a definition for refraction.

_________________________________________________________

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Write, in your own words, a definition for reflection.

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3 What happens when a wave goes from one medium to another where itsspeed is lower? Answer in terms of the ray bending towards or awayfrom the normal.

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4 When a wave goes from one medium into another where its speed ishigher, the ray bends away from the normal.

How does the angle of incidence compare in size to the angle ofrefraction in this situation?

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Check your answers.

Snell’s law

This law can be expressed in terms of the situation shown below.

i

r

refracted ray

medium 1V1

l1

normal

incident ray

medium 2V2

l2

Refraction of waves away form the normal. This occurs when the speed of thewave is slower in medium 1 than medium 2. That is v1 < v2 , l1 < l 2 and r > i.


The relationship between speeds, wavelengths and angles of incidenceand refraction was determined experimentally in 1621 by WillebrordSnell, and today it is known as Snell’s law.


Snell’s law can be expressed mathematically, as follows.

sin isin r

vv

nnn

constant1

21 2

2

1

= = = = =Æll

1

2

The constant is called the refractive index n1 2Æ . The subscript numbers

following the n tell us it is the refractive index for waves going frommedium 1 into medium 2. That is, the refractive index of medium 2relative to medium 1.

Snell’s law applies equally to waves slowing down or speeding up asthey go from one medium to another.

n1 and n2 are absolute refractive indices. (Refractive indices means morethan one refractive index.)

This means that the refractive index has been measured with respect to avacuum that by definition, has an absolute refractive index of exactly1.0000 (for light).

The situation for defining refractive index relative to a vacuum is shownbelow.

i

rrefracted ray

medium 1

vacuumnv = 1.0000v = c (for electromagnetic radiation)

normal

incident ray

Absolute refractive index is compared to a vacuum as in space.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

The table on the next page lists the absolute refractive indexes for somecommon materials.


Substance Density (kg m3) Velocity of light inthe medium (ms–1)

Absolute refractiveindex

vacuum 0 3 ¥ 108 1.000 000

air 1.29 2.999 ¥ 108 1.0003

water 1 ¥ 103 2.26 ¥ 108 1.33

dense crown glass 3.6 ¥ 103 1.92 ¥ 108 1.56

flint glass 3.0 ¥ 103 1.86 ¥ 108 1.61

denser flint glass 4.7 ¥ 103 1.72 ¥ 108 1.74

perspex 1.19 ¥ 103 1.5 ¥ 108 2.00

diamond 3.5 ¥ 103 1.24 ¥ 108 2.42

Notice that the absolute refractive index for air is 1.0003. Unless we areusing five significant figure accuracy, we can use the approximation that:

The refractive index of air is 1.0 or, nair = 1

Using Snell's law

r

normalincident light

40˚

air

water

Ray diagram showing refraction of light as it passes from air into water.Adapted from OTEN, Physics for Electrical and Electronic Engineers.


Look at the example of a problem using Snell’s law below.

Light enters water, from air, at an angle of 40∞ (shown in the figure

opposite). Using the information shown in the diagram and from thetable above, the angle of refraction and the speed of light in the water canbe determined.

Since, by Snell’s law:

sin isin r

vv

nnn

constant1

21 2

2

1

= = = = =Æll

1

2

and since the light here is going from air to water, then air is medium 1and water is medium 2, so:

sin isin r

vv

nnn

constant1

21 2

2

1

= = = = =Æll

1

2

So sin isin r

nn

sin rn sin i

n

r sin

w

a

a

w

=

=

= ¥ ∞

=

== ∞

1 00 40

0 483

0 483

29

1

. sin

.

.–

1.33

Also vv

nn

vn vn

m s

a

w

w

a

wa a

w

–1

=

=

= ¥ ¥

= ¥

1 00 3 0 10

2 26 10

8

8

. .

.

1.33

Determining the angle of refraction

Now look at the example of a problem using Snell’s law to determine theangle of refraction.

Consider a ray of light passing from water into air, so that the angle ofincidence is 29∞. This is shown in the figure following.


r

normal

29˚

air

water

Light rays passing from water to air. The light passing into a lower refractiveindex material is bent away from the normal.Adapted from OTEN, Physics for Electrical and Electronic Engineers.

This time water is medium 1 and air is medium 2 since the light is goingfrom water into air. So Snell’s law becomes:

sin isin r

vv

nnn

sin isin r

nn

sin rn sin i

n

r sin 0.645

w

aw a

a

w

a

w

w

a

–1

= = = =

=

=

= ¥ ∞

=

=

Æll

w

a

1 33 29

0 645

. sin

.1.00

\ = 40∞

If you compare both figures above you can see the principle ofreversibility in action. That is, if the ray direction is reversed, it traces itsformer path, regardless of any reflection or refraction it may haveexperienced.

You have two devices that are able to refract waves very well–your eyes.They refract incoming light and this light forms an image at the back ofthe eye, on the retina.


Determining refractive indexes

You will need to determine the refractive index of either glass or perspex.One way to do this is to use a rectangular glass or perspex slab and measurethe refractive index of light passing through the slab. The procedure to dothis is simple. Note that the figures and angle changes shown on thediagrams below are exaggerated and will not give the true refractive indexvalue for glass or perspex.

1 Place a rectangular slab of glass or perspex on a page from anexercise book that is in turn on a newspaper and trace around it.

pins

2 Leave the slab in place and on one side of it push two pins throughthe page and into the newspaper, as shown in the diagram above sothat they stand upright.

3 Now look through the slab from the opposite side of the slab to thepins and adjust your line of vision until the two pins appear to lineup directly behind one another.

4 When the two pins appear to be lined up, insert another two pins intothe paper so that all four pins appear to line up when viewed fromthe side of the slab.

pins

pins

All four pins appearto be directlybehind one anotherwhen observedfrom the side

5 Remove the slab.


6 Remove the pins and carefully mark their positions as indicated bythe pin holes with an x.

7 Draw a line through the two x marks on each side of the slab with aruler. Extend each line until it meets the outline of the slab asshown.

8 Now draw another line that connects these two lines as shownbelow. You should see the lines on each side of the slab are parallelbut they do not connect.

9 Draw in the normals at the point where the incident ray of light fromthe two pins meets the slab as shown on the figure below.


normal

i

r

10 Measure the angles i and r. Use Snell's law to calculate therefractive index of the slab material. Remember that the refractiveindex of the air is 1 for this calculation.

11 Repeat this experiment using five different angles of incidence.

12 Calculate the average value for the refractive index of the perspex orslab of glass.

Plot the sine of the angle of incidence versus sine of the angle ofrefraction as a line graph on the graph paper in the appendix. Use a lineof best fit. Determine the slope of the line using rise/run method. This isthe refractive index.

How does the value of the refractive index determined from the slope ofthe line compare to the average value of refractive index you calculatedabove?

_________________________________________________________

_________________________________________________________

It should be the same or very close to the average calculated value of therefractive index. Making multiple measurements increases the reliabilityof your data.



What is total internal reflection?

You learned in the previous section that the change in direction of a wavepassing from one medium to another can be calculated if you know therefractive indexes of the two materials.

Imagine a ray of light entering a low refractive index medium from ahigh refractive index medium. What happens? The light ray bends awayfrom the normal. The farther the incident ray is from the normal, thefarther the refracted ray will be from it as well. This situation is similarto the situation shown in the figure below.

i

rnormal

A ray moving from a more dense to a less dense medium.

A small change in the angle of incidence causes a bigger change in angleof refraction (due to the refractive indexes of the two materials). It istherefore possible to have an angle of incidence where the ray can’t exitthe optically denser material. This is because it is refracted to such anextent that it is bent to 90° from the normal. This situation is shown inthe figure below.

normal

criticalangle

A ray incident at a change in refractive index that cannot escape the highrefractive index material such as this one is at the critical angle.


The angle of incidence in this special case is called the critical angle.

When the critical angle of incidence of a ray for the two substances isexceeded, total internal reflection occurs. This means that instead of aray being refracted and exiting the optically denser material the incidentray is reflected inside the material. From that point the ray will obey thelaws of reflection off the surface between the two materials and isessentially trapped internally as shown in the figure below.

i r

normal

i = r

A ray undergoing total internal reflection.

You can find the critical angle of refraction at a boundary between twomediums where the refracted ray cannot leave the first medium to enterthe second of lower density using Snell’s Law:

sin isin r

vv

nnn

1

21 2

2

1

= = = =Æll

1

2

where 1 and 2 subscripts represent values for the first and secondmaterials the light enters, and i corresponds to the angle of incidence, andr the angle of refraction.

In the case of the critical angle, you know that the angle of refraction, is90°. The sin 90∞ is equal to 1 so this simplifies the equation to:

sin i1

vv

nnn

1

21 2

2

1

= = = =Æll

1

2

The figure below shows the conditions necessary for the critical angle.Note that the ray hits the interface between the two media and thentravels along parallel to the medium interface. The ray will still exit thedenser medium at the end of the shaded rectangle, in this figure.

normal

criticalangle

A ray undergoing refraction that is trapped in the denser medium.


Calculating the critical angle

Using Snell’s law

n1 sin ic = n2 sin 90∞.

Because the angle of refraction is 90∞.

When ic = critical angle.

Therefore

sin i = nnc

2

1

(note that n1 > n2) for light to bend away from the normal.

This simple calculation will give the critical angle.

What would the formula be for light going from a more dense medium intoair?

_________________________________________________________

Check your answer.

The critical angle, ic, occurs only at the interface where a higherrefractive index material meets with one that is of lower refractive index,and not vice versa.

You may have seen total internal reflection in fish tanks or if you goswimming and are under water looking up at an angle. The surface ofthe water will look silver in that case because of total internal reflection.

At your practical session with your teacher you may shine a light raythrough the narrow end of a rectangular glass slab gradually increasing theangle of incidence until the beam emerges parallel to the opposite face.Any small increase in the angle of incidence beyond the critical angle willresult in the beam being internally reflected.


What is an optical-fibre?

Total internal reflection has many practical uses, one of which is inoptical–fibres.

The optical–fibre is one application of refraction that is now an almostessential link in the telecommunications area. Optical–fibres are thincylinders of ultrahigh purity glass that have a central region called a coreand an outer region called the cladding.

The structure of an optical fibre is shown in the figure below.

i rlower refractive index

high refractive index

lower refractive index

normal

A light ray passing along an optical–fibre. The light is internally reflected at theinterface between the higher refractive index core and the lower refractive indexcladding but it still then obeys the law of reflection with the angle of incidence =the angle of reflection.

How does an optical–fibre work?

Light entering the optical–fibre is guided along the core because of adifference in the optical density between the higher refractive index coreand the lower refractive index cladding. To assist this process thediameter of the core of most modern optical–fibres is made so small,around 10 mm, that only those rays parallel to the axis of the fibre can be

guided along the fibre.

The light waves transmitted by an optical–fibre are reflected off theboundary between the high and low refractive index material, as shownin the diagram of a cross–section of a fibre above. The smaller therefractive index of the cladding compared to the refractive index of the


core, the smaller the critical angle is, allowing total internal reflection tooccur more easily.

Optical–fibres are used in a number of ways including:

• communication for carrying signals precisely, and at the speed oflight. This is faster than energy transmission by electrons in electricsignals.

• medicine. Optical–fibres are used by operating doctors to viewpreviously inaccessible places, such as the inside of a lung.

Optical–fibres are helpful in that:

• they allow the transmission of light to or from places not usuallypossible.

• they can be bent, allowing light to be refracted easily and preciselyaround many corners without the use of mirrors or reflective prisms(as are used in binoculars).


Lenses

One of the main uses for refraction is the lens. Lenses can be used toform images, not by reflecting light, but by bending it.

The diagram below shows wavefronts being refracted by a lens.

object – sourceof light energy

O

real image – point towhich light waveenergy is concentrated

focusF

region in which lightwaves are made totravel more slowly

Wavefronts being refracted by a lens.

Because it is easier to use rays to explain refraction in lenses therefraction of light by lenses is typically shown using rays. This bendingof light occurs in lenses of optical instruments such as microscopes,binoculars, spectacles, telescopes, cameras and slide projectors.


Convex and concave lenses

Lenses like mirrors are of two basic types. Converging also known asconvex lenses and diverging known as concave lenses.

Converging lenses focus parallel light rays to a point called the focus.The diagram below shows a converging lens refracting light to a focus.

principal axis

F F'O

A converging lens (convex lens) focuses rays to a point.Adapted from OTEN, Physics for Electrical and Electronic Engineers

Diverging lenses spread parallel light rays out. They appear to haveoriginated from a point where they originate from. The diagram belowshows a diverging lens.

F O F'

A diverging lens (concave lens).Adapted from OTEN, Physics for Electrical and Electronic Engineers

You may have a converging lens at home. The magnifying glass is aconverging lens. Have you ever tried to concentrate the Sun’s rays at apoint to start a fire? If you have, you have seen the focussing of light at apoint by a converging or convex lens.


Uses of lenses

Lenses are used by people to:

• correct visual defects,

• see things that are too far away to be seen without help,

• see things that are very small.

To do these tasks we use converging or diverging lenses.



Summary

In this part you have learned about reflection and refraction ofelectromagnetic waves. These important properties of electromagneticradiation are used widely in applications involving communication andoptics. There is another property of electromagnetic radiation calledpolarisation that enables us to use electromagnetic radiation effectively.You will learn about this in the next part of this module.

Reminder: In part 6 return exercises you will need to identify datasources and collect information about the Internet and the way that it usesthe digital process to send information from one computer to another.You should continue to collect this information in preparation forthis exercise.

Complete a summary of the information you have learned about in thispart in the space below. Use the headings from each section as a guide.In your summary consider how this part has related to the previous partsof this module.


Appendix


Suggested answers

Observing reflectiona) Mirror–like you would need a smooth surface.

b) Diffuse you would need a rough or disturbed surface.

Types of radio waves1 They have the longest wavelengths. Longer wavelength

electromagnetic waves tend to be more penetrating.

2 The signal bounces from the ionosphere and the surface of the Earthuntil it reaches the other side of the Earth.

Curved mirrorsa) A convex mirror has the reflecting surface on the inside of the curve.

b) A concave mirror has the reflecting surface on the outside of thecurve.

Using a soup–spoon as a concave mirror

1 soup-spoon

upside downlaterallyinverted(slightlymagnifiedcompared tooriginal object)


2 Diminished and inverted.

3 Gets bigger stays inverted then at the focal length disappears thencloser to the focal length it is upright and magnified.

4greatlymagnifiedrightway upbut back tofront

The image is now magnified and upright.

5 More magnified.

6 Cannot be projected onto a screen.

Using a soup–spoon as a convex mirror1 Gets bigger, stays upright.

2 Image gets more diminished.

3 No it cannot be projected onto a screen.

4 You can see more of the road behind you but the image is alwaysdiminished so the objects are always closer than they appear.

5 Greater angle of vision that you could see with a plane mirror.

The astronomical telescope

Less of the atmosphere for the electromagnetic waves to penetrate athigher altitude.

Torches1 If the filament is at the focus then the torch will make a spot beam.

If the filament is above or below the focus then the torch willproduce a flood beam.


2 If you screw the reflector to a position where it has the focus of thereflector at the filament position you will get a spot beam. If thereflector is screwed so the filament is above or below the reflectorfocus the torch will produce a flood beam.

What causes the bending of waves?1 Light waves travel slower in the water. The stick appears to bend

away from the normal.

2 The waves bunch up so they have a smaller wavelength.

3 When a wave goes from one medium into another where its speed ishigher, the ray bends away from the normal.

4 The angle of incidence is less than the angle of refraction.

Calculating the critical angle

Sin ic = 1/n since the refractive index of air is essentially 1.


Exercises - Part 5


Exercise 5.1

An object is placed two metres in front of a plane mirror.

Complete the diagram to show the image formed from reflected lightfrom the plane mirror.

object mirror

Object in front of a plane mirrorAdapted from OTEN, Physics for Electrical and Electronic Engineers

Describe the image.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________


If the object is moved to half a metre from the mirror what will be thedistance between the image and the object?

_________________________________________________________

_________________________________________________________

Exercise 5.2

Two similar plane mirrors are placed together at 90∞ to each other as

shown in the figure below. Show that any ray incident on either mirrorwill be reflected back along a parallel path because of the law ofreflection.

M1

M2

Two plane mirrors at 90∞ to one another.


Exercise 5.3(a) Using the figure below determine the refractive index of the material

through which a light ray would pass to produce this figure. Assumethe ray is passing from air into the material. Use Snell’s law. Youwill need to use a protractor to measure the angles r and i. Note thisis not glass nor is it a Perspex slab.


normal

i

r

(b) Explain using Snell’s law why the angle of emergence of thelight ray from the slab above is the same as the original angle ofincidence.

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

Exercise 5.4

Calculate the critical angle between the core and cladding in anoptical–fibre with the core having a refractive index of 1.46 and thecladding a refractive index of 1.35.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________


Exercise 5.5

Light of wavelength 600 nm and frequency 5 1014¥ Hz (in air isrefracted into glass having a measured refractive index of 1.5. Calculatethe values of:

(a) the velocity

(b) the wavelength

(c) the frequency of the light in the glass.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

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_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

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_________________________________________________________

_________________________________________________________

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Part 6: Applications


AMENDMENTS








Part 4 p 9



WARNING







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Part 6: Applications 1

Contents

Introduction ............................................................................... 2

Polarisation ............................................................................... 3

Polarisation in telecommunications .....................................................5

Global positioning system ......................................................... 6

Digitising information ................................................................. 9

How do digital signals work? ...............................................................9

Digitising a signal ...............................................................................11

Summary................................................................................. 20

Appendix ................................................................................. 21


Exercises – Part 6 ................................................................... 25

Bibliography ............................................................................ 33

Student evaluation of module


Introduction

This part relates to the module by establishing a connection betweenadvances in technology and their relationship to physical principles.through a contextual link. The send in exercises at the end of thismodule refer back to learning you have done throughout the entiremodule.


• identify types of communication data that are stored or transmitted indigital form

• discuss the developments in technology that allowed the productionof communication technologies, such as CD technology and GlobalPositioning Systems (GPS)

In this part you will be given the opportunities to:

• identify data sources, gather, process and present information fromsecondary sources to identify areas of current research and use theavailable evidence to discuss some of the underlying physicalprinciples used in one application of physics related to waves, suchas:

– global positioning system

– CD technology

– the Internet (digital process)

– DVD technology.

Extract from Physics Stage 6 Syllabus © Board of Studies NSW, amended Occtober2002. The original and most up–to–date version of this document can be found on theBoard’s website at:http://www.boardofstudies.nsw.edu.au/syllabus_hsc/syllabus2000_listp.html#p

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Polarisation

Polarisation

The polarisation of light by refraction was first discovered in 1669 byErasmus Bartholin by looking at objects drawn on paper through acrystal of the transparent mineral, Iceland spar. Iceland spar makes allobjects seen through it appear double. These double images are linearlypolarised in different directions.

The reason for this is that the light passes through the crystals alongdifferent paths called optical axes. These have different refractiveindices. This means the light travels with different velocities in differentplanes of the minerals.

Light can be polarised because it is a transverse wave. Longitudinalwaves cannot be polarised.

Normal unpolarised light vibrates in all planes as shown in the figure onthe left below. Essentially the vibrations are in a 360∞ plane. Linear

polarisation as shown in the figure on the right restricts the vibration ofthe transverse wave to one plane ( in this case the Z–X plane).

x

y

z

x

y

z

Nonpolarised and linearly polarised light.


Polarisation can also be achieved by passing a nonpolarised wavethrough a polarising material. This material is called a polariser.

A Polaroid® sheet can be used to polarise light. It acts as a polariser.The Polaroid® sheet is plastic made up of long molecules that allowelectromagnetic waves to pass in one plane only.

After light has passed through the polariser (Polaroid®) it is changed tovibrate only in the one plane as shown in the figure below. This is calledplane polarised light.

Polarised light can pass through a second sheet of Polaroid® if itspolarising orientation is in the same direction as direction of polarisationof the light.

If a second sheet of Polaroid® is placed in the path of the polarised lightthat has its polarising orientation at 90∞ to the first sheet of Polaroid®

then the light will be completely blocked. This second sheet ofPolaroid® is called an analyser.

incident lightlightblocked

long molecules at right anglesto those in polariser

Unpolarised light passes through the polariser to become plane polarised. It isthen cut out completely by the analyser.

If the second Polaroid® sheet (analyser) is oriented in the same directionas the first Polaroid®‚ then there will be no change in the level ofpolarisation of the light.

incident lightlightpasses

polariser allows to pass onlythose waves which vibrate in theplane of the long molecules

Two sheets of polarising material. The second sheet has no effect on the lightpassing through the first.

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All electromagnetic waves can be polarized. That is because allelectromagnetic waves are transverse waves.

Polarisation in telecommunications

Yes, polarisation is used in telecommunications. Look at all externalaerials for television receivers. How are the aerials oriented? They areall horizontal.

The antennas are all horizontal because the signal from the televisiontransmission tower is sent as a wave polarised in the horizontal direction.This makes it easier for the television signal to get around barriers inits path.

Another example of polarisation in telecommunications is the mobilephone signal.

1 How are the aerials oriented at least those visible on phones with anexternal aerial?

_____________________________________________________

2 What does this tell you about the polarisation direction of the signalsent by mobile phone transmission antennas?

_____________________________________________________

Check your answers.

A practical application of mobile phone microwave transmissions beingpolarised vertically is if your mobile phone signal is weak it may beimproved by holding the phone vertically!


Global positioning systems

The global positioning system (GPS) comprises a set of 24 satellitesorbiting the Earth in precise locations around 17600 km above thesurface of the Earth and a series of ground stations. More satellites arebeing launched regularly. These will further improve the system.The ground stations are in constant communication with the satellites byradio communication. That communication accurately tells the satellitesexactly where they are with respect to the surface of the Earth atany time.

Each satellite has an on–board atomic clock that gives it a precise timebase. Each signal that is sent by a satellite contains information about thetime that the signal was sent and from which satellite the signal was sent.To ensure accuracy you must correct for any delays the signalexperiences as it travels through the atmosphere. Remember therefractive index of the atmosphere changes as the composition anddensity of the atmosphere changes vertically.

Why might correction for any delay the signal experiences as it travelsthrough the atmosphere be essential to determining position?(Hint: Think about echo location and the wave equation).

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

Check your answer.

The need for a travel time correction means that the more satellites yourGPS receiver can see (a direct line of sight connection between thesatellite and GPS is required) the more accurately it can determine yourposition.

Because of the satellite’s high altitude and the curvature of the Earth itmay be possible to see up to nine satellites at any time. Because the

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speed of transmission of the radio signal from the GPS is known, thedistance of each satellite from the GPS receiver on an imaginary spheredrawn on the surface of the Earth is able to be very accurately calculated.

Since the precise position of all GPS satellites is known because ofinformation sent from stationary ground stations, the multiple possibleposition readings on a semicircle on the Earth’s surface from a number ofsatellites (at least 3) gives the position of the GPS receiver.

That position can be calculated as at the intersection of a number ofspheres of possible position. Only one solution for the GPS receiverlocation is possible as there is only one intersection of the three (or more)semicircular arcs. This means the position of your GPS receiver isaccurate to high precision.

The GPS satellites allow anyone owning a global positioning systemreceiver to locate the position of their GPS receiver very precisely on thesurface of the earth. If a GPS receives the signal from three satellites itcan be located by a process called triangulation in terms of longitude andlatitude. If the GPS can detect the signal from a fourth satellite it canalso provide details about your GPS receiver’s altitude.

Modern GPS receivers can record multiple readings of position over timeat time intervals able to be set by the user. This means that it is thereforeeasy to determine where the GPS receiver has been in the recent past.These modern GPS receivers are data loggers.

satellite 1

satellite 2satellite 3

satellite 4

Satellites send information about their position andtime of sending to the receiver in the GPS unit .

Ground stations track satellitesand send information about theposition of satellites to the satellites.

Receiver calculates the one point where the possiblepositions according to all satellites intersect.

A carequippedwith a GPS.

According to the signalfrom satellite 3 thereceiver may beanywhere along this arc.

The satellites constantly broadast tothe GPS receivers on the ground.

Satellite 1indicates the receiveris along this arc

Satellite 2indicates the receiveris along this arc

How the global positioning system works.


For some more information on how a GPS works see links on the Physicswebsite page on the LMPC science web page at:


Use the data in the text above to make a list of the technologicaldevelopments that were required before the GPS system could be putin place.

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

Check your answers.

Many modern mobile telephones have a built in GPS capability. In thefuture you will always be able to tell exactly where you are with yourown personal communication device – the mobile phone.

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Digitising information

Often data is sent along fibre–optic cables as a digitised signal.Mobile phones now use a digital signal for data transmission, televisionis broadcast as a digital signal in many parts of the world, the Internetworks because of digital transmission, and we all use digital storagedevices to reproduce the highest possible quality sound reproductionfrom compact discs and DVDs.

How do digital signals work?

All digital signals work in basically the same way. A digital signal ismade from an initial frequency modulated (FM) or amplitude modulated(AM) signal.

The best way to think of the digitising process applied on the signal(called quantisation) is to remember when you were younger and playedjoin the dots. The actual wave shape is not sent by the signal but rather aseries of signal (= 1) or no signal (= 0) messages separated by aprecise time.

In 8–bit processing the signal is represented as a series of numbers from0 to 7 that are all possible to represent as binary digits using somecombination of three 0’s or 1’s.

These numbers representing the binary code are shown in the table in theactivity that follows. The value from 0 to 7 can then be used by decodingdevice to reconstruct the wave.

The quantisation process is shown in the figure on the following page.

To increase the accuracy of the wave reconstruction we can do two things.What are they?

_________________________________________________________

_________________________________________________________

Check your answer.


the original waveformlooks like this

time

time0

1

2

3

4

5

6

7

8

9

10

7 8 9 8 5 4 3 2 5 6

To digitise the waveformwe take regular snapshotswith each snapshotseparated precisely by thesame time period.

original waveform

reassembled waveform

To increase the accuracyof the waveform receivedcompared to that sent weincrease the frequency ofsamples and the numberof possible values of thewave height.

time0

5

10

15

20

25

30

35

The greater the number of samples per unit time and the smaller the divisions representingthe wave height the more accurate the wave reconstruction that is possible and themore like the original waveform the reconstruction is.

time0

1

2

3

4

5

6

7

8

9

10

7 8 9 8 5 4 3 2 5 6

These numbers receivedare reassembled into awave.

Note the reassembledwave isn’t a good matchto the original.

The digitising process of a signal.

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Digitising a signal

You should now try to digitise the signal shown below and reconstructthe signal. Follow the procedure described below.

You can practice the digitising process by completing this activity.You will need the wave pattern and the binary code in the Appendix.

1 Cut along the dotted lines of the wave pattern.

2 Cut two slits in the paper encoding device.

3 Pull your wave through stopping every 5 seconds on the horizontalscale to determine the quantisation value according to the slit scale.

4 Use the binary table to convert these values to a binary code.

5 Record the values on the signal in the slit scale number section in thetable below.

You will have to make decisions as to the slit scale value if the waveis between values as you can’t have a half value. As a rule takevalues up on the slit scale if half or more than halfway to the nextvalue and down to the next value on the slit scale if less than halfwayto the next value.

6 Reconstruct a wave based on these binary values alone. Do this byplotting your binary values on the graph and by joining the dots onyour wave with a ruler.

1 How does this reconstructed wave compare in shape to the original?

_____________________________________________________

2 If you were to sample every 1 s instead of every 5 s how would therepresentation of the wave reconstructed based on quantised data bedifferent?

_____________________________________________________

Check your answers.

The wave signal conversion process to a digitised signal occurs bysampling the electrical wave for the purpose of generating the numbersthat form part of the on (1) or off (0) data stream representing the wave.Each sample, or digit, in the stream of numbers is called a ‘bit’.

Satisfactory reproduction of the sound of a human voice can occur usingdigital phones, for example, if a sound wave in the range of 400 to 3400Hz is sampled at a rate that generates 64 000 bits or samples each second.

Any transmission medium which has the capacity to carry 64 000 bits persecond (equivalent to 64 000 electrical pulses or light pulses second) will


therefore be able to carry the digital transmission representing sound inthe frequency range 400 to 3400 Hz.

Digital signals in telecommunications

Digital signals have great advantages over analogue signals because thenoise factor is irrelevant as long as the signal is registerable as an on =1or off = 0. If this distinction can be made the signal can be reassembledby the decoding device.

repeater(digital)

repeater(analogue)

bumps are noise

bumps are noise

A digital and analogue signal plus noise before and after clean up by a repeaterstation.

The noise added to analogue signals can result in loss of signal quality.Also if it is necessary to amplify the signal because of attenuation, thenoise is also amplified. This makes the analogue signal even noisier.

The on–off signal of the digital signal is clearer after amplificationbecause it is easy to tell whether it is a 1 or a 0 and it can be then cleanedup. This is shown in the figure above.

The figure opposite shows a digital signal affected by noise. Note theprimary signal is still clear despite the noise.

The first telecommunications equipment to use digitising was Morsecode. Each letter of a message was made to represent a series of dots (onsignal with current flowing along the wire conductor for a short duration)and dashes (off signal with current flowing along the wire conductor fora longer duration).


plus noise

digitised signal

equals modified digital signal – but itis still clear whether the value is a oneor a zero

0

1

A digital signal is affected by noise. The nature of the signal is, however, stillclear.

A compact disc (CD) player is a digital device that interprets bumps on aspiralling track on the mirrored surface of a CD as bits. The tracks on theCD are narrow and the space between them is uniform as shown in thefigure below. These bits, represented by these pits are assembled intobytes that are then played back through a digital-to-analogue converter toproduce sound or picture signals in a computer or stereo.

The CD itself is a three-layered plastic disc as shown in the figure on thenext page. The disc has the pits impressed into it during manufacture.These pits are read by the CD player focussed laser as the CD spins.

The spin rate of the CD is adjusted to ensure the laser covers a constantlength of track per unit time. This ensures a regular data stream to adigital-to-analogue converter. The bits are read by a laser beamreflecting off the pits to an optical electrical sensor. The pits reflectdifferently than the rest of the CD. The signal is read as a 0 (no pit) or 1(pit) in digital form and is passed to a computer chip that can reassemblethe bits into bytes. This enables sound or picture signals to bereconstructed.A CD can store around 600 megabytes of information.


spin in the direction of the CD

Compact disc tracks spiral out from the centre. The laser passesalong a track at constant speed because as the laser path movesout from the centre the spin rate of the CD slows.

laser path

1 600 nm

500 nm

Laser light hits a bump that equals 1 or a no bump which equals 0.The 1s and 0s are reassembled into numbers and used to reconstructthe original sound (or picture) signal.

another track

one track

125 nm

polycarbonate plastic

labelacrylic

aluminium

pits that make bumpson the other side

pits are pressed intothe polycarbonate discin circular tracks,representing a digital signal

laser lightdirectedthis way

1.2 mm

(1.25 x 10–7 m)

How the CD works and is constructed.

The more recent means of storing digital information on a disk is theDVD.A DVD works similarly to a CD but has increased storage capacitybecause the pits are smaller (less than half that of the CD), and the tracksare closer together (less than half the separation distance). This meansmore bytes per disk. DVD used in conjunction with readers can alsotransfer data faster than from CD’s because the density of theinformation is about four times greater on a DVD than on a CD. Thathas significant implications for data throughput rates. DVD technologyis obviously capable of faster data throughput.


A DVD may also have dual layer format. This means that the surface ofthe DVD has 2 layers of reflective materials stacked on top of each other.The layers have differences in their ability to reflect so it is possible forthe focus of the laser to be adjusted to reflect off one of the layers only.As a result the dual layer format DVD can hold almost twice the amountof information as a single layer DVD. This means a DVD can hold up to8 hours of video. That represents around 18 Gbytes of information. Toenable the finer focusing of the laser required to read the data containedin the smaller and closer pits on the DVD as compared to the CD asmaller wavelength radiation laser is used in DVD readers.

More information about how a DVD and CD works can be found on theInternet. Look at some pages that relate to CD and DVD technology on thePhysics website page.

http://www.lmpc.edu.au./science


Summary

As a summary for the unit draw a concept map that links as many aspossible of the ideas and main concepts developed in this module.


Appendix

cut off here

0

7

6

5

4

3

2

1

cut slit in paper along this dotted line

Feed wave pattern strip into heremoving the strip along one timedivision each go. Record under eachtime division the number from the slitscale. Convert each time divisionnumber to a binary number.

bina

ry c

ode

000

111

110

101

100

011

010

001

slit

scal

e

10 20 30 40 500 time

slit

scal

enu

mbe

rbi

nary

cod

enu

mbe

r

cut out wave pattern along the dotted lines

cut out wave pattern along the dotted lines


Suggested answers

Here are suggested answers for many of the questions from throughoutthis part. Your answers should be similar to these answers. If youranswers are very different or if you do not understand an answer, contactyour teacher.

Polarisation in telecommunication1 They are all oriented vertically.

2 They are polarised vertically.

What is the global positioning system?

The minor change in velocity could result in the distance beingmiscalculated from the equation: distance = velocity ¥ time. If the

velocity is wrong the distance is wrong, hence the arc of possibleposition determined by the satellite will be wrong.

Radio waves, rocketry, atomic clocks, computers, satellites,geostationary orbits, ground based satellite trackers, the GPS unit itself.

How do digital signals work?

Take more samples at closer time intervals and increase the number ofdivisions of the vertical scale.

Digitising a signal1 A bad copy that doesn’t truly represent the original.

2 A more accurate representation of the wave.


Exercises - Part 6


Exercise 6.1

Identify each of these waves as travelling in one two or three dimensions.

Sound from a thunderclap ________________________________

Radio waves from a star _________________________________

A compression pulse in a slinky spring _____________________

A water wave from a point source _________________________

Radio waves broadcast from a tall aerial ____________________

Sound from a submarine underwater _______________________

Exercise 6.2

In many science fiction movies the exploding space ship makes a largebang that is heard by others in a distant space ship observing. Explainwhich part of this scenario is true and which is not. Base your answer onyour knowledge of the properties of light and sound waves.

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Exercise 6.3

Describe the relationship between the particle motion and the direction ofenergy transfer for the following waves.

Sound from a thunderclap ________________________________

Radio waves from a star __________________________________

A compression pulse in a slinky spring ______________________

A water wave from a point source __________________________

Radio waves broadcast from a tall aerial _____________________

Sound from a submarine underwater ________________________

Exercise 6.4

Sketch a regular sine wave and on that wave label the following features:

• crest

• trough

• wavelength

• amplitude.

Exercise 6.5

An electromagnetic wave has a frequency of 7 ¥ 1014 Hz and a

wavelength of 5 nm. What is the wave velocity?

_________________________________________________________

Exercise 6.6

Is the wave from the question above travelling in a vacuum or anothermedium? Explain your answer.

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Exercise 6.7

The following CRO traces were made using identical oscilloscopesettings by sound waves from sources identical distances from themicrophone. Identify which of the traces represents a sound with thehigher frequency. Explain your answer.

a

b

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Exercise 6.8

Which of the two preceding CRO traces would represent the loudestsound? Explain your answer.

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Exercise 6.9

If the first trace a) from above represents a sound wave of 320 Hz whatwould be the approximate frequency of the second sound wave thatproduced trace b)? Describe or show the method you used to calculatethis. You may like to draw on the diagrams and refer to them if it willhelp your explanation.

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Exercise 6.10

Discuss why it would not be possible to have an unlimited number of FMradio stations broadcasting in the one city.

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Exercise 6.11

Australian colour TV channel broadcast standards (2000) are describedas having the following characteristics:

Channel width 7 MHz sideband transmission

Vision carrier 1.25 MHz above lower edge ofchannel

Vision modulation negative amplitude modulation

Lines per picture 625 lines interlaced 2:1

Line frequency 15625 Hz

Primary sound carrier 5.5 MHz above vision carrier

Secondary sound carrier 242.1875 kHz above primary soundcarrier

Sound modulation FM

(a) Explain why there is a need for two sound carrier frequencies.

_____________________________________________________

_____________________________________________________

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(b) Explain why you still get good sound quality reception during athunderstorm but picture quality declines.

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Exercise 6.12

To reduce the thickness of spectacles the optometrist suggested to herpatient that she might switch to perspex lenses rather than glass.Knowing what you do about lenses and refractive indices of glass andperspex explain why the optometrist would have suggested this change.

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Exercise 6.13

Identify data sources and collect information about the Internet and theway that it uses the digital process to send information from onecomputer to another. You might use newspaper computer lift-outs,computer magazines, television, books, or the Internet itself to do this.You should submit diagrams where appropriate and use no more than200 words. Include a list of references you referred to in preparing youranswer.

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Bibliography

Board of Studies. 2002, Physics Stage 6 Syllabus.

Messel, H. 1963, Science for High School Students. The NuclearFoundation, University of Sydney.

OTEN. 1993, Physics for Electrical and Electronic Engineers, Sydney.

PHY.Pre 43200 The world communicates

Student evaluation of the module

Name: _______________________ Location: ______________________

We need your input! Can you please complete this short evaluation toprovide us with information about this module? This information willhelp us to improve the design of these materials for future publications.

1 Did you find the information in the module clear and easy tounderstand?

_____________________________________________________

2 What did you most like learning about? Why?

_____________________________________________________

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3 Which sort of learning activity did you enjoy the most? Why?

_____________________________________________________

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4 Did you complete the module within 30 hours? (Please indicate theapproximate length of time spent on the module.)

_____________________________________________________

_____________________________________________________

5 Do you have access to the appropriate resources? eg. a computer,the internet, scientific equipment, chemicals, people that can provideinformation and help with understanding science

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_____________________________________________________

Please return this information to your teacher, who will pass it along tothe materials developers at OTEN – DE.

Learning Materials ProductionOpen Training and Education Network – Distance Education

NSW Department of Education and Training

8.2 world_communicates

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