waves and sound. 1 the nature of waves 1.a wave is a traveling disturbance. 2.a wave carries energy...

Waves and Sound

1 The Nature of Waves1. A wave is a traveling disturbance.

2. A wave carries energy from place to place.

1 The Nature of Waves

Longitudinal Wave

1 The Nature of Waves

Transverse Wave

1 The Nature of Waves

Water waves are partially transverse and partially longitudinal.

2 Periodic Waves

Periodic waves consist of cycles or patterns that are produced over and over again by the source.

In the figures, every segment of the slinky vibrates in simple harmonicmotion, provided the end of the slinky is moved in simple harmonicmotion.

2 Periodic Waves

In the drawing, one cycle is shaded in color.

The amplitude A is the maximum excursion of a particle of the medium fromthe particles undisturbed position.

The wavelength is the horizontal length of one cycle of the wave.

The period is the time required for one complete cycle.

The frequency is related to the period and has units of Hz, or s-1.

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.2 Periodic Waves

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.2 Periodic Waves

Example 1 The Wavelengths of Radio Waves

AM and FM radio waves are transverse waves consisting of electric andmagnetic field disturbances traveling at a speed of 3.00x108m/s. A stationbroadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.

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16.2 Periodic Waves

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FM m 26.3Hz1091.9

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3 Wave Speed Versus Particle Speed on a String

Conceptual Example 3 Wave Speed Versus Particle Speed

Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves?

4 The Nature of Sound WavesLONGITUDINAL SOUND WAVES

4 The Nature of Sound Waves

The distance between adjacent condensations is equal to the wavelength of the sound wave.

4 The Nature of Sound Waves

Individual air molecules are not carried along with the wave.

4 The Nature of Sound Waves

THE FREQUENCY OF A SOUND WAVE

The frequency is the number of cyclesper second.

A sound with a single frequency is calleda pure tone.

The brain interprets the frequency in termsof the subjective quality called pitch.

Check your Hearing

https://www.youtube.com/watch?v=qNf9nzvnd1k https://www.youtube.com/watch?v=VxcbppCX6Rk

4 The Nature of Sound Waves

THE PRESSURE AMPLITUDE OF A SOUND WAVE

Loudness is an attribute ofa sound that depends primarily on the pressure amplitudeof the wave.

4 The Speed of Sound

Sound travels through gases, liquids, and solids at considerablydifferent speeds.

4 The Speed of Sound

Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb

There is a rule of thumb for estimating how far away a thunderstorm is.After you see a flash of lighting, count off the seconds until the thunder is heard. Divide the number of seconds by five. The result gives theapproximate distance (in miles) to the thunderstorm. Why does thisrule work?

4 The Speed of Sound

LIQUIDS SOLID BARS

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1. What is the wave speed if the period of a wave is 4 secondsand the wavelength is 1.8 m?

2 A fisherman noticed that a float makes 30 oscillations in 15seconds. The distance between to consecutive crests is 2 m.What is the wave speed?

3 What is the wavelength of a wave traveling with a speed of

6 m/s and a period of 3s?

4. What is the period of a wave traveling with a speed of 20 m/s and the wavelength is 4.0 m?

5. What is the wave speed if the period is 4.0 seconds and the wavelength is 1.8 m?

5 The Doppler Effect

The Doppler effect is the change in frequency or pitchof the sound detected byan observer because the soundsource and the observer havedifferent velocities with respectto the medium of sound propagation.

demohttp://www.animations.physics.unsw.edu.au/jw/doppler.htm#medium

visual effect:https://www.youtube.com/watch?v=h4OnBYrbCjY

Lewin demo:https://www.youtube.com/watch?v=wfcG0IRuffA

5 The Doppler Effect

A. MOVING SOURCE

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5 The Doppler Effect

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source movingaway from a stationaryobserver

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5 The Doppler Effect

Example 10 The Sound of a Passing Train

A high-speed train is traveling at a speed of 44.7 m/s when the engineersounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a personstanding at the crossing, when the train is (a) approaching and (b) leavingthe crossing?

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5 The Doppler Effect

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5 The Doppler Effect

B. MOVING OBSERVER

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Observer movingaway from stationary source

16.9 The Doppler Effect

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GENERAL CASE

Numerator: plus sign applies when observer moves towards the source

Denominator: minus sign applies when source moves towards the observer

6. Standing wave

•Wave reflection at boundaries

•Principle of superposition, interference

•Standing waves on a string

•Normal modes

Reflection of a wave pulse at a boundary

Fixed end Free end

Pulse incident from right is reflected from the boundary at left

HOW the pulse is reflected depends on the boundary conditions

For fixed end, reflected pulse is inverted

For free (in transverse direction) end, reflected pulse is same way up.

time

Frictionless sliding ring Check using phet simulation

Reflection of a wave pulse at a boundaryBehaviour at interface can be modelled as sum of two pulses moving in opposite directions at the interface:

Transverse displacement always 0 at interface

“fixed end” “free end”

Transverse force

always 0 at interface

Standing WavesA standing wave is

produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave:

• Antinodes – Areas of MAXIMUM AMPLITUDE

• Nodes – Areas of ZERO AMPLITUDE.

Comparison between standing wave and travelling wave

Travelling wave

particles undergo SHM

all particles have same amplitude

all particles have same frequency,

adjacent particles have different phase

Standing wave

particles undergo SHM

adjacent particles have different amplitude

all particles have same frequency

all particles on same side of a node have same phase. Particles on opposite sides of

node are in antiphase

Some very basic physics of stringed instruments……….

The fundamental frequency determines the pitch of the note.

the higher harmonics determine the “colour” or “timbre” of the note.

(ie why different instruments sound different)

Fundamental wavelength = 2L

From v = fλ,

f1= v/2L

So, for a string of fixed length, the pitch is determined by the wave velocity on the string…..

Example Calculation

The string length on standard violin is 325mm. What tension is required to tune a steel “A” string (diameter =0.5mm) to correct pitch (f=440Hz)?

Density of steel = 8g cm

Sound WavesThe production of sound involves setting up a wave in air. To set up

a CONTINUOUS sound you will need to set a standing wave pattern.

Three LARGE CLASSES of instruments• Stringed - standing wave is set up in a tightly stretched string• Percussion - standing wave is produced by the vibration of solid

objects• Wind - standing wave is set up in a column of air that is either

OPEN or CLOSED

Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE

Closed PipesHave an antinode at one end and a node at the other. Each sound

you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound?

You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength.

This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC.

Closed Pipes - HarmonicsHarmonics are

MULTIPLES of the fundamental frequency.

In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NOSOUND is produced

Closed Pipes - HarmonicsIn a closed pipe you have an ANTINODE at the 3rd

harmonic position, therefore SOUND is produced.

CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!

Open PipesOPEN PIPES- have an antinode on BOTH ends of the

tube. What is the SMALLEST length of pipe you can have to hear a sound?

You will get your FIRST sound when the length of the pipe equals one-half of awavelength.

Open Pipes - HarmonicsSince harmonics are MULTIPLES of the

fundamental, the second harmonic of an “open pipe” will be ONE WAVELENGTH.

The picture above is the SECOND harmonic or the FIRST OVERTONE.

Open pipes - HarmonicsAnother half of a wavelength would ALSO produce an

antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends

The picture above is the THIRD harmonic or the SECOND OVERTONE.

CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!

ExampleThe speed of sound waves in air is found to be 340

m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm.

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251.85 HZ

ExampleThe windpipe of a typical whooping crane is about

1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37°C.

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57.90 Hz

Resonance demohttps://www.youtube.com/watch?v=1K5p9DfsXGo

Destructive:https://www.youtube.com/watch?v=j-zczJXSxnw

Sound wave energy on water:“Sound,Bass,Water, Sound makes water come alive with cymatics”

Wave with Bill Nyehttps://www.youtube.com/watch?v=YsKC_EtUHcA“Bill Nye The Science Guy & Waves & Full Episode”