Chapter 14Chapter 14

SoundSound

Using a Tuning Fork to Using a Tuning Fork to Produce a Sound WaveProduce a Sound Wave

A tuning fork will produce a pure musical A tuning fork will produce a pure musical notenote

As the tines vibrate, they disturb the air As the tines vibrate, they disturb the air near themnear them

As the tine swings to the right, it forces the As the tine swings to the right, it forces the air molecules near it closer togetherair molecules near it closer together

This produces a high density area in the airThis produces a high density area in the air This is an area of compressionThis is an area of compression

As the tine moves toward the left, the air As the tine moves toward the left, the air molecules to the right of the tine spread molecules to the right of the tine spread outout

This produces an area of low densityThis produces an area of low density This area is called a This area is called a rarefactionrarefaction

Using a Tuning Fork, finalUsing a Tuning Fork, final

As the tuning fork continues to vibrate, a succession of As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the forkcompressions and rarefactions spread out from the fork

A sinusoidal curve can be used to represent the A sinusoidal curve can be used to represent the longitudinal wavelongitudinal wave Crests correspond to compressions and troughs to rarefactionsCrests correspond to compressions and troughs to rarefactions

Speed of SoundSpeed of Sound

In a liquid, the speed depends on the In a liquid, the speed depends on the liquid’s compressibility and inertialiquid’s compressibility and inertia

B is the Bulk Modulus of the liquidB is the Bulk Modulus of the liquid ρ is the density of the liquidρ is the density of the liquid Compares with other wave speed equationsCompares with other wave speed equations

Yv

Bv

propertyinertial

propertyelasticv

T

v

Sound in Solid: Wave on string: General:

Doppler Effect, Case 1Doppler Effect, Case 1 An observer is An observer is

moving toward a moving toward a stationary sourcestationary source

Due to his Due to his movement, the movement, the observer detects observer detects an additional an additional number of wave number of wave frontsfronts

The frequency The frequency heard is increasedheard is increased

F ig 1 4 .8 , p . 4 3 5

S lid e 1 2

Doppler Effect, Case 2Doppler Effect, Case 2

An observer is An observer is moving away from moving away from a stationary sourcea stationary source

The observer The observer detects fewer detects fewer wave fronts per wave fronts per secondsecond

The frequency The frequency appears lowerappears lower

F ig 1 4 .9 , p . 4 3 6

S lid e 1 3

Doppler Effect, Source in Doppler Effect, Source in MotionMotion

As the source moves As the source moves toward the observer (A), toward the observer (A), the wavelength received the wavelength received is shorter and the is shorter and the frequency increasesfrequency increases

As the source moves As the source moves away from the observer away from the observer (B), the wavelength (B), the wavelength received is longer and received is longer and the frequency is lowerthe frequency is lower

carhorn.wavcarhorn.wav

Doppler Effect, both Doppler Effect, both movingmoving

Both the source and the observer could be Both the source and the observer could be movingmoving

Use positive values of vUse positive values of voo and v and vss if the motion is if the motion is towardtoward Frequency appears higherFrequency appears higher

Use negative values of vUse negative values of voo and v and vss if the motion is if the motion is awayaway Frequency appears lowerFrequency appears lower

Ex. 14.6 pg. 438Ex. 14.6 pg. 438

s

o

vv

vvƒƒ'

Shock WavesShock Waves

A shock wave A shock wave results when the results when the source velocity source velocity exceeds the speed exceeds the speed of the wave itselfof the wave itself

The circles The circles represent the represent the wave fronts wave fronts emitted by the emitted by the sourcesource

Shock Waves, contShock Waves, cont

Tangent lines are drawn from STangent lines are drawn from Snn to the to the wave front centered on Swave front centered on Soo

The angle between one of these tangent The angle between one of these tangent lines and the direction of travel is given lines and the direction of travel is given by sin θ = v / vby sin θ = v / vss

The ratio v/vThe ratio v/vss is called the is called the Mach NumberMach Number The conical wave front is the The conical wave front is the shock waveshock wave Shock waves carry energy concentrated Shock waves carry energy concentrated

on the surface of the cone, with on the surface of the cone, with correspondingly great pressure variationscorrespondingly great pressure variations

Interference of Sound Interference of Sound WavesWaves

Sound waves interfereSound waves interfere Constructive interference occurs Constructive interference occurs

when the path difference between when the path difference between two waves’ motion is zero or some two waves’ motion is zero or some integer multiple of wavelengthsinteger multiple of wavelengths

path difference = nλpath difference = nλ Destructive interference occurs when Destructive interference occurs when

the path difference between two the path difference between two waves’ motion is an odd half waves’ motion is an odd half wavelengthwavelength

path difference = (n + ½)λpath difference = (n + ½)λ

Fig 14.15, p. 441

Slide 17

Fig 14.15, p. 441

Slide 17

H

LHH

H

H

H

LL

L

LL

H

HH

H

L

LL

L

BeatsBeats BeatsBeats are alternations in loudness, due to are alternations in loudness, due to

interferenceinterference Waves have slightly different frequencies and Waves have slightly different frequencies and

the time between constructive and destructive the time between constructive and destructive interference alternatesinterference alternates

ffbeatbeat = |f = |f11-f-f22||

Standing WavesStanding Waves

When a traveling wave reflects When a traveling wave reflects back on itself, it creates traveling back on itself, it creates traveling waves in both directionswaves in both directions

The wave and its reflection interfere The wave and its reflection interfere according to the superposition according to the superposition principleprinciple

With exactly the right frequency, With exactly the right frequency, the wave will appear to stand stillthe wave will appear to stand still This is called a This is called a standing wavestanding wave

Standing Waves on a Standing Waves on a StringString

Nodes must occur Nodes must occur at the ends of the at the ends of the string because string because these points are these points are fixedfixed

F ig 1 4 . 1 6 , p . 4 4 2

S l i d e 1 8

Standing Waves on a Standing Waves on a String, cont.String, cont.

The lowest The lowest frequency of frequency of vibration (b) is vibration (b) is called the called the fundamental fundamental frequencyfrequency

F ig 14 .1 8 , p . 4 43

S lide 2 5

F

L2

nƒnƒ 1n

Resonance in Air Column Resonance in Air Column Open at Both EndsOpen at Both Ends

In a pipe open at both ends, the In a pipe open at both ends, the natural frequency of vibration natural frequency of vibration forms a series whose harmonics forms a series whose harmonics are equal to integral multiples of are equal to integral multiples of the fundamental frequencythe fundamental frequency

,3,2,1nL2

vnƒn

Tube Open at Both EndsTube Open at Both Ends

Standing Waves in Air Standing Waves in Air ColumnsColumns

If one end of the air column is If one end of the air column is closed, a node must exist at this closed, a node must exist at this end since the movement of the air end since the movement of the air is restrictedis restricted

If the end is open, the elements of If the end is open, the elements of the air have complete freedom of the air have complete freedom of movement and an antinode existsmovement and an antinode exists

Tube Closed at One EndTube Closed at One End

Resonance in an Air Resonance in an Air Column Closed at One EndColumn Closed at One End

The closed end must be a nodeThe closed end must be a node The open end is an antinodeThe open end is an antinode

,5,3,1nL4

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