Chapter 14Chapter 14

Sound

Sound WavesSound Waves

Sound is longitudinal pressure (compression) waves

Range of hearing: 20 Hz to 20,000 Hz

PAIN DEMO

Speed of Speed of SoundSound

B

v

KT

sm

vair 273)331(

Liquids and Gases: B is bulkmodulus, is mass/volume

Y

v Solids: Y is Young’s modulus

331 m/s is v at 0° C;T is the absolute temperature.

Example 14.1Example 14.1

John Brown hits a steel railroad rail with a hammer.Betsy Brown, standing one mile down the track, hearsthe bang through the cool 32 F air while her twin sister Boopsie is lying next to her and hears the bang through the steel by placing her ear on the track.DATA: Ysteel=2.0x1011 Pa, steel=7850 kg/m3

What is the time difference between the moments when Betsy and Boopsie hear the bang?

4.54 s

Intensity of Sound Intensity of Sound WavesWaves

AP

tAE

I

SI units are W/m2

Power

Area

Intensity is proportional to squareof amplitude (pressure modulation)

Intensity Range for Human HearingIntensity Range for Human Hearing

Threshold of Hearing• 10-12 W/m2

• P ~ 10-10 atm !

Threshold of Pain• 1.0 W/m2

Decibel ScaleDecibel Scale

10/0

10

10

log10

II

II

o

Sensation is logarithmic

• I0 is threshold of hearing (0 dB)• Threshold of Pain is therefore 120 dB

Intensity vs. Intensity LevelIntensity vs. Intensity Level

• INTENSITY is P/A, W/m2 • INTENSITY LEVEL is in decibels (dimensionless)

Threshold of Pain DemoThreshold of Pain Demo

Example 14.2Example 14.2A noisy machine in a factory produces a sound with a level of 80 dB. How many identical machines could you add to the factory without exceeding the 90-dB limit?

9 more machines

Spherical Spherical WavesWaves

Energy propagates equally in all directions

24 r

PI

21

22

2

1

r

r

I

I

Example 14.3Example 14.3

A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 50 dB by an observer 10 km away. Treating the horn as a point source and neglect any absorption of sound by the air or ground,

a) What is the average power generated by the horn?

b) What intensity level of the horn’s sound is observed by someone waiting at an intersection 50 m from the train?

a) 126 W

b) 96 dB

Example Example 14.414.4

Bozo Bob buys a 20-W train whistle and figures out that he won’t have any trouble standing 2 meters from the whistle since his stereo speakers are rated at 100 W and he has little trouble with the speakers turned all the way up. What is the intensity level of the whistle?

116 dB

Doppler Doppler EffectEffect

A change in the frequency experienced by an observer due to motion of either the observer or the source.

DOPPLER DEMO

Doppler Effect, Moving ObserverDoppler Effect, Moving Observer

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

S lid e 1 2

vvv oƒƒ'

When not moving,

vf When moving,

)(' obsvvf

If observer moves away:If observer moves away:

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

S lid e 1 3

vvv oƒƒ'

Example 14.5Example 14.5

Mary is riding a roller coaster. Her mother who is standing on the ground behinder her yells out to her at a frequency of 1000 Hz, but it sounds like 920 Hz.(vs=343 m/s)

a) What is Mary’s speed?

b) What frequency would Mary hear if she were approaching her mother?

a) 27.4 m/s

b) 1088 Hz

Doppler EffectDoppler EffectSource in MotionSource in Motion

'

''

1

'

vf

vvv

v

Tv

s

s

s

svvv

ff

'

Doppler Effect, Source in MotionDoppler Effect, Source in Motion

svvv

ff

'

Approaching source:

Source leaving:

svvv

ff

'

Example 14.6Example 14.6

An train has a brass band playing a song on a flatcar. As the train approaches the station at 21.4 m/s, a person on the platform hears a trumpet play a note at 3520 Hz.DATA: vsound = 343 m/s

a) What is the true frequency of the trumpet?

b) What is the wavelength of the sound?

c) If the trumpet plays the same note after passing the platform, what frequency would the person on the platform hear?

a) 3300 Hz

b) 9.74 cm

c) 3106 Hz

Fig 14.11, p. 439

Slide 15

Shock Waves (Sonic Booms)Shock Waves (Sonic Booms)

When the source velocity approaches the speed of sound,

Application: speed radarApplication: speed radar

Application: weather radar Application: weather radar

Both humidity (reflected intensity) and speed of clouds(doppler effect) are measured.

Doppler Effect: Doppler Effect: Both Observer and Source MovingBoth Observer and Source Moving

s

o

vvvv

ƒƒ'

Switch appropriate signs if observer or source moves away

Example 14.7Example 14.7

At rest, a car’s horn sounds the note A (440 Hz). The horn is sounded while the car moves down the street. A bicyclist moving in the same direction at 20 mph hears a frequency of 415 Hz. DATA: vsound = 343 m/s.

a) What is the speed of the car if the cyclist is behind the car?

b) What is the speed of the car if the bicyclist is ahead of the car?

a) 30.1 m/s = 67.4 mph

b) -11.2 m/s = -25.0 mph (no solution with car moving in same direction)

BeatsBeats

Interference from two waves with slightly differentfrequency

Beat Frequency DerivationBeat Frequency Derivation

After time Tbeat, two sounds will differ by one complete cycle.

beatbeat

beat

beatbeat

Tf

ffT

TfTf

nn

1

1

1

1

21

21

21

21 fffbeat

Beats DemoBeats Demo

Standing Waves in Air Standing Waves in Air ColumnsColumns

Tube Closed at One Tube Closed at One EndEnd

4)12( nn

Tube Open at Both Tube Open at Both EndsEnds

2 nn

Same expression for closed at both ends

Example 14.8Example 14.8

An organ pipe (open at one end and closed at the other) is designed to have a fundamental frequency of 440 Hz.Assuming the speed of sound is 343 m/s,

a) What is the length of the pipe?

b) What is the frequency of the next harmonic?

a) 19.5 cm

b) 1320 Hz

Interference of Sound WavesInterference of Sound Waves

Assume sources “a” and “b” are “coherent”. If observer is located ra and rb from the two sources,

minimumfor)21(

maximumfor

nrr

nrr

ba

ba

Example 14.9Example 14.9A pair of speakers separated by 1.75 m are driven by the same oscillator at a frequency of 686 Hz. An observer starts at one of the speakers and walks on a path that is perpendicular to the separation of the two speakers. (Assume vsound = 343 m/s)

a) What is the position of the last intensity maximum?

b) What is the position of the last intensity minimum?

c) What is the position of the first intensity maximum?

a) 2.81 m

b) 6.00 m

c) 27 cm