Waves and SoundWaves and Sound

AP IAP I

Definition of a waveDefinition of a wave

A disturbance that propagates A disturbance that propagates from 1 place to another. from 1 place to another.

Characterized by a large transfer Characterized by a large transfer of energy without a large transfer of energy without a large transfer of medium of medium

Types of wavesTypes of waves

Mechanical waves:Mechanical waves: require a require a medium (air, water, ropes) to medium (air, water, ropes) to traveltravel

Electromagnetic waves:Electromagnetic waves: do not do not require a medium to travel (light, require a medium to travel (light, radio) radio)

Mechanical WavesMechanical Waves

Transverse:Transverse: the displacement of the the displacement of the individual particles is perpendicular to individual particles is perpendicular to the direction of propagation.the direction of propagation.

Mechanical WavesMechanical Waves

Longitudinal:Longitudinal: The displacement of The displacement of the individual particles is parallel to the individual particles is parallel to the direction of propagation.the direction of propagation.

Mechanical WavesMechanical WavesSurface waves:Surface waves: the displacement the displacement

of individual particles is circular of individual particles is circular (result of both transverse and (result of both transverse and longitudinal motion)longitudinal motion)

Waves in motionWaves in motion

Longitudinal and Transverse Wave Motion

Properties of wavesProperties of waves1.1. AmplitudeAmplitude (A): the maximum displacement (A): the maximum displacement

from equilibrium position, measured in meters.from equilibrium position, measured in meters.2.2. WavelengthWavelength ( λ): the distance between 2 ( λ): the distance between 2

particles that are in phase with each other, particles that are in phase with each other, measured in meters. measured in meters.

Wave diagram Wave diagram (link)

Properties of wavesProperties of waves

3.3. FrequencyFrequency (f): number of (f): number of complete waves that pass a complete waves that pass a point in one second, measured point in one second, measured in 1/seconds or Hertz (Hz) in 1/seconds or Hertz (Hz)

4.4. PeriodPeriod (T): the time it takes for (T): the time it takes for one complete wave to pass a one complete wave to pass a given point, measured in given point, measured in seconds. seconds.

Properties of wavesProperties of waves

Velocity of propagationVelocity of propagation (v): (v): horizontal speed of a point on horizontal speed of a point on a wave as it propagates, a wave as it propagates, measured in m/s.measured in m/s.

Relationships/equationsRelationships/equations

T =1/ fT =1/ f

or f = 1/Tor f = 1/Tv = f × λv = f × λ

PhasePhase

In-phase: when waves In-phase: when waves are synchronized (crest are synchronized (crest meets crest)meets crest)

Out-of-phase: waves are Out-of-phase: waves are not synchronized not synchronized Opposite phase (180Opposite phase (180º º

out-of-phase): crest out-of-phase): crest meets troughmeets trough

ReflectionsReflections Fixed End: Fixed End:

Explanation Animation

Open End:Open End: Explanation Animation

Between different mediums scroll down scroll down

(What do you notice about the (What do you notice about the phases? Transmitted? Reflected?)phases? Transmitted? Reflected?)

Principle of SuperpositionPrinciple of SuperpositionOccurs when two waves travel Occurs when two waves travel

through the same medium at the through the same medium at the same time.same time.

Each wave affects the medium Each wave affects the medium independently.independently.

The displacement of the medium is The displacement of the medium is the algebraic sum of the the algebraic sum of the displacements.displacements.

Animation

InterferenceInterference

Constructive:Constructive: occurs when wave occurs when wave displacements are in the same displacements are in the same direction (in-phase)direction (in-phase)

Destructive:Destructive: occurs when wave occurs when wave displacement are in different displacement are in different directions (out-of-phase)directions (out-of-phase)

Animation(try at home)(try at home)

What is Sound?What is Sound? Longitudinal Longitudinal Mechanical Mechanical (link) Rarefaction: low Rarefaction: low

air pressureair pressure Compression: Compression:

high air pressurehigh air pressuremodule (sources of sound)(sources of sound)

Speed of soundSpeed of sound

Depends on…Depends on… TemperatureTemperature

• V air = 331m/s +(0.6 m/s/V air = 331m/s +(0.6 m/s/ºC)*T ºC)*T Density/kind of mediumDensity/kind of medium

• Gases <liquids<solidsGases <liquids<solids

• Chart of speeds

Speed of soundSpeed of sound

PitchPitchHow we perceive variations in frequencyHow we perceive variations in frequencyAudible range 20-20,000 Hz Audible range 20-20,000 Hz ((listen))

• Infrasonic vs. ultrasonicInfrasonic vs. ultrasonic

Most sensitive to 1,000 to 5,000HzMost sensitive to 1,000 to 5,000HzLoudness can distort our perception of Loudness can distort our perception of

pitch pitch (listen tape)(listen tape)

Module (pitch) (pitch)

Doppler EffectDoppler EffectVariation in the frequency of Variation in the frequency of

sound due to the relative sound due to the relative motion of the sound source or motion of the sound source or the listener.the listener.

Animation1Picture of a sonic boomVideo of sonic boommythbuster

Doppler Effect ResultsDoppler Effect Results

As an moving sound source approaches As an moving sound source approaches a listener the frequency (pitch) increase.a listener the frequency (pitch) increase.

As a moving sound source passes by a As a moving sound source passes by a listener the frequency (pitch) decreases.listener the frequency (pitch) decreases. *Same effect if sound source is stationary *Same effect if sound source is stationary

and listener is moving.and listener is moving.

Calculating Frequency changeCalculating Frequency change

f’ = f (v ± vf’ = f (v ± vRR / v± v / v± vss))f’ = new frequencyf’ = new frequency

• f = original frequency of f = original frequency of source soundsource sound

•v: velocity of soundv: velocity of sound

•vvRR: velocity of receiver: velocity of receiver

•vvss: velocity of source: velocity of source

ResonanceResonanceCausing the vibration of an object by the Causing the vibration of an object by the

influence of another vibrating body.influence of another vibrating body. Must match the natural frequency of Must match the natural frequency of

vibration of the object vibration of the object Whole-number multiple of the natural Whole-number multiple of the natural

frequency work too.frequency work too. Breaking a glass with resonance Boy breaks glass with voiceBoy breaks glass with voice

Standing wavesStanding wavesCaused by the interference of Caused by the interference of

reflected waves with incident waves reflected waves with incident waves from the source.from the source.

Nodes:Nodes: pts of no displacement pts of no displacementAntinodesAntinodes: pts of maximum : pts of maximum

displacementdisplacementApplet Applet (try at home)(try at home)

Wine glass harpWine glass harp

Vibrating Columns of AirVibrating Columns of AirColumn will emit a sound when the air Column will emit a sound when the air

inside achieves resonance.inside achieves resonance. DEMO DEMO (cardboard moose call)(cardboard moose call)

Frequency of vibration depend onFrequency of vibration depend onLength of columnLength of columnType of columnType of column

• Open endOpen end• Closed endClosed end

Calculations for closed pipeCalculations for closed pipeFundamental frequency Fundamental frequency

ff11= v /4L (L=length of air column)= v /4L (L=length of air column)

HarmonicsHarmonics ffnn = nf = nf11 (n=1,3,5,…) (n=1,3,5,…) λλ =4L/n =4L/n

Note: only ODD harmonics are producedNote: only ODD harmonics are producedAnimation Animation

Fundamentals and HarmonicsFundamentals and Harmonics

Fundamental Frequency:Fundamental Frequency: lowest lowest frequency of vibrationfrequency of vibration

Harmonics:Harmonics: whole number whole number multiples of the fundamentalmultiples of the fundamental Note: the fundamental frequency is Note: the fundamental frequency is

the 1the 1stst harmonic. harmonic.Animation Animation

Closed (at one end) pipeClosed (at one end) pipe

The standing wave created hasThe standing wave created hasNode at closed-endNode at closed-endAntinode at open-endAntinode at open-end

NN AA

Open pipeOpen pipe

The standing wave created hasThe standing wave created has Antinode at both endsAntinode at both ends

• PVC pipe musicPVC pipe music

AAAA

Calculations for open pipeCalculations for open pipeFundamental frequency Fundamental frequency

ff11= v /2L (L=length of air column)= v /2L (L=length of air column)

HarmonicsHarmonics ffnn = nf = nf11 (n=1,2,3,…) (n=1,2,3,…)λλ =2L/n =2L/n

Note: ALL harmonics are producedNote: ALL harmonics are producedanimationanimation