WAVESWAVES

Vibrations (disturbances) that carry Vibrations (disturbances) that carry energy from one place to anotherenergy from one place to another

Presentation 2003 Philip M. Dauber as Modified by R. McDermott

Types of WaveTypes of Wave

Mechanical. Examples: slinky, rope, water, Mechanical. Examples: slinky, rope, water, sound, earthquakesound, earthquake

Electromagnetic. Examples: light, radar, Electromagnetic. Examples: light, radar, microwaves, radio, x-raysmicrowaves, radio, x-rays

What Does a Wave Move?What Does a Wave Move?

Energy can be transported over long Energy can be transported over long distancesdistances

The medium in which the wave exists has The medium in which the wave exists has only limited movementonly limited movement

Example: Ocean swells from distant stormsExample: Ocean swells from distant storms

Path of each bit of water is ellipse

Waves Require a MediumWaves Require a Medium

A medium is anything with massA medium is anything with mass

A medium may be solid, liquid, or gasA medium may be solid, liquid, or gas

The particles of the medium move very The particles of the medium move very small distances from their rest positionsmall distances from their rest position

The particles repeat their motion (periodic The particles repeat their motion (periodic or harmonic motion)or harmonic motion)

Periodic WavePeriodic Wave

Source is a continuous vibrationSource is a continuous vibration The vibration moves outward (but mass The vibration moves outward (but mass

does not)does not)

Wave BasicsWave Basics

Wavelength is distance from crest to crest or Wavelength is distance from crest to crest or trough to troughtrough to trough

Amplitude is maximum height of a crest or depth Amplitude is maximum height of a crest or depth of a trough relative to equilibrium levelof a trough relative to equilibrium level

Wave Basics Wave Basics (cont.)(cont.)

Wavelength is the distance between points Wavelength is the distance between points “in phase”“in phase”

A-F, B-G, C-H, D-I, and E-J are “in phase”A-F, B-G, C-H, D-I, and E-J are “in phase”

Frequency and PeriodFrequency and Period

Frequency, f, is number of crests that pass a given Frequency, f, is number of crests that pass a given point per second (measured in hertz)point per second (measured in hertz)

Period, T, is time for one full wave cycle to passPeriod, T, is time for one full wave cycle to pass T = 1/f f = 1/TT = 1/f f = 1/T

Wave VelocityWave Velocity

Wave velocity, v, is the velocity at which any part Wave velocity, v, is the velocity at which any part of the wave movesof the wave moves

If wavelength = If wavelength = v = v = ff Example: a wave has a wavelength of 10m and a Example: a wave has a wavelength of 10m and a

frequency of 3Hz (three crests pass per second.) frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of each full wave as a boxcar. What is the speed of the train?the train?

ExampleExample

A ocean wave travels from Hawaii at 10 A ocean wave travels from Hawaii at 10 meters/sec. Its frequency is 0.2 Hz. What meters/sec. Its frequency is 0.2 Hz. What is the wavelength?is the wavelength?

Longitudinal vs. Transverse Longitudinal vs. Transverse WavesWaves

Transverse: particles of the medium move Transverse: particles of the medium move perpendicular to the motion of the waveperpendicular to the motion of the wave

Longitudinal: vibrations in same direction as waveLongitudinal: vibrations in same direction as wave

Longitudinal WaveLongitudinal Wave

Can be thought of as alternating Can be thought of as alternating compressions and expansions or compressions and expansions or rarefactionsrarefactions

Longitudinal WaveLongitudinal Wave

Sound is a longitudinal wave

Sound Wave in AirSound Wave in Air

Compressions and rarefactions of air Compressions and rarefactions of air produced by a vibrating objectproduced by a vibrating object

Transverse WaveTransverse Wave

The transverse wave below is traveling toward The transverse wave below is traveling toward point Ppoint P

How will point P move?How will point P move?

Demo

Waves and EnergyWaves and Energy

Waves with large amplitude carry more Waves with large amplitude carry more energy than waves with small amplitudeenergy than waves with small amplitude

Sound amplitude is loudnessSound amplitude is loudness Light amplitude is brightnessLight amplitude is brightness

ResonanceResonance

Occurs when driving frequency is close to Occurs when driving frequency is close to natural frequency (all objects have natural natural frequency (all objects have natural frequencies at which they vibrate)frequencies at which they vibrate)

Tacoma Narrows bridge on the way to destruction– large amplitude oscillations in a windstorm

Demo

Wave ActionsWave Actions

ReflectionReflection InterferenceInterference RefractionRefraction DiffractionDiffraction Doppler EffectDoppler Effect Polarization (transverse only)Polarization (transverse only)

ReflectionReflection

Law of reflection:Law of reflection:

Angle of incidence equals angle of Angle of incidence equals angle of reflectionreflection

i r

Hard Reflection of a PulseHard Reflection of a Pulse

Fixed endpointFixed endpoint

Reflected pulse is invertedReflected pulse is inverted

Soft Reflection of a PulseSoft Reflection of a Pulse

Free endpointFree endpoint

Reflected pulse not invertedReflected pulse not invertedDemo

InterferenceInterference

Amplitudes of two (or more) waves in the Amplitudes of two (or more) waves in the same place at the same time add same place at the same time add algebraically (principle of superposition)algebraically (principle of superposition)

Constructive interference:Constructive interference:

Destructive InterferenceDestructive Interference

Equal amplitudes:Equal amplitudes:

Unequal Amplitudes:Unequal Amplitudes:

Demo

Standing WavesStanding Waves

Result from interference and reflection for Result from interference and reflection for the “right” frequencythe “right” frequency

Points of zero displacement - “nodes” (B)Points of zero displacement - “nodes” (B) Maximum displacement – antinodes (A)Maximum displacement – antinodes (A)

Formation of Standing WavesFormation of Standing Waves

Two waves moving in opposite directionsTwo waves moving in opposite directions

Examples of Standing WavesExamples of Standing Waves

Transverse waves on a slinkyTransverse waves on a slinky Strings of musical instrumentStrings of musical instrument Organ pipes and wind instrumentsOrgan pipes and wind instruments Water waves due to tidal actionWater waves due to tidal action

Demo

Standing Wave Patterns on a Standing Wave Patterns on a StringString

““Fundamental” = Fundamental” =

22ndnd Harmonic = Harmonic =

33rdrd Harmonic = Harmonic =

First Harmonic or FundamentalFirst Harmonic or Fundamental

Second HarmonicSecond Harmonic

Third HarmonicThird Harmonic

Wavelength vs. StringWavelength vs. Stringlengthlength

String length = How many String length = How many waves?waves?

L =

String length = How many String length = How many waves?waves?

L = 3/2

Wavelength vs. String LengthWavelength vs. String Length

Wavelengths of first 4 harmonicsWavelengths of first 4 harmonics

Frequencies are related by whole Frequencies are related by whole numbersnumbers

ExampleExample ff1 1 = 100 Hz fundamental= 100 Hz fundamental ff2 2 = 200 Hz 2= 200 Hz 2ndnd harmonic harmonic ff3 3 = 300 Hz 3= 300 Hz 3rdrd harmonic harmonic ff4 4 = 400 Hz 4= 400 Hz 4thth harmonic harmonic etcetc Other frequencies exist but their amplitudes Other frequencies exist but their amplitudes

diminish quickly by destructive interferencediminish quickly by destructive interference

Wave velocity on a stringWave velocity on a string

Related only to properties of mediumRelated only to properties of medium Does not depend on frequency of waveDoes not depend on frequency of wave vv2 2 = T/m/l Tension divided by mass per = T/m/l Tension divided by mass per

unit length of stringunit length of string

First Three Harmonics in Open First Three Harmonics in Open TubeTube

Amplitudes are largest at the open ends

Amplitudes zero at the nodes

Tube Closed at One EndTube Closed at One End

L/4

L = /4

L = /4

No even harmonics present f = vair/

Pressure in Closed TubesPressure in Closed Tubes

BeatsBeats

Two waves of similar frequency interfereTwo waves of similar frequency interfere

Beat frequency equals the difference of the two interfering frequencies

RefractionRefraction

Wave moves from one medium into anotherWave moves from one medium into another The speed of the wave changesThe speed of the wave changes The wavelength of the wave changesThe wavelength of the wave changes The frequency of the wave stays the sameThe frequency of the wave stays the same The wave changes directionThe wave changes direction

RefractionRefraction

Angle of incidence Angle of incidence angle of refraction (generally) angle of refraction (generally)

Reflection/Refraction in RopeReflection/Refraction in Rope Notice what happens to amplitude, phase, and wavelength:Notice what happens to amplitude, phase, and wavelength:

DiffractionDiffraction

Part of wave hits a barrier and is cut offPart of wave hits a barrier and is cut off The rest of the wave continuesThe rest of the wave continues Continuing wave expands behind barrierContinuing wave expands behind barrier

Demo

Doppler EffectDoppler Effect Observer or source movingObserver or source moving Observed frequency changesObserved frequency changes

– If observer and source are closing, frequency is higher If observer and source are closing, frequency is higher than normalthan normal

– If observer and source are separating, frequency is If observer and source are separating, frequency is lower than normallower than normal

Frequency change for sound is pitchFrequency change for sound is pitch Frequency change for light is colorFrequency change for light is color

Demo

PolarizationPolarization

Only for transverse wavesOnly for transverse waves Allows only vibrations in one plane to passAllows only vibrations in one plane to pass All other planes of vibration are absorbed All other planes of vibration are absorbed Polaroid lensesPolaroid lenses 3D glasses3D glasses

Demo

AcknowledgementsAcknowledgements

Some diagrams and animations courtesy of Some diagrams and animations courtesy of Tom Henderson, Glenbrook South High Tom Henderson, Glenbrook South High School, IllinoisSchool, Illinois