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Physics 211 – lecture 28: Sound Waves

Sound Waves - mechanical longitudinal waves

 Sound waves come from periodic pressure variations moving along in a substance.

increasing fdecreasing

infrasonic audible ultrasonic

20Hz 20kHz

Sound Spectrum – three classes of sound waves

CT

sm

airCv 2731331

Sound Speed

  Sound speed IN AIR at room temperature (20 C) is : _____________  Sound speed equation (IN AIR only):

Note – speed as density and speed as elasticity (stiffness)

property inertial

property elastic

density

modulusbulk

B

v

2

Wave Equation for Sound

Recall

For transverse, we now have longitudinal

Max longitudinal displacement

Or in terms of pressure

)sin(),( max tkxPtxP

Where maxmax svP Derivation in book

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Sound IntensityIntensity = power (or energy transfer rate) divided by area

Units: W/m2

Inverse Square Law:

2

120

0

10I where log10mI

I W

2

1

2

1

2

R

R

I

I

Decibels = measure intensity relative to the minimum intensity we can hear.The decibel is a __________ scale. Our hearing works on this scale.10 dB increase increase by factor of 10 in intensity20 dB increase increase by factor of 100 in intensity30 dB increase increase by factor of 1000 in intensityand so on…

Decibel Equation:

IsvrA

I 2max2

124

PP

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Doppler Effect Doppler Effect

The Doppler effect describes a change in frequency (pitch) of sound waves due to a moving source or moving observer. Example: train approaches with high pitched whistle, passes by, and pitch decreases.

 

Source moves: toward observer ________away from observer________

Observer moves: toward source _______away from source _________ 

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/imgsou/dopp2.gif

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Doppler Effect in Light• Red Shift - light from objects receding (moving away) from us is

shifted to the red side of the spectrum• Blue Shift - light from objects approaching (moving toward) us is

shifted to the blue side of the spectrum

ss

o fvv

vf

s

oo f

v

vvf

vo = observer velocity fo = observed frequencyvs = source velocity fs = source frequencyv = speed of sound

+ = moving away- = getting closer

+ = getting closer - = moving away

Doppler Effect Equations:Stationary observer Stationary source:  

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Example (Doppler Effect): A storm is formulating with winds of up to 150km/hr. A Doppler radar device is monitoring the storm by sending out a 35MHz signal? What frequency will bounce back to the station if the storm winds are A) approaching? B) receding ?Given                    Path                   Want           Conversions/Equations

MHzfv

xv

s

hrkm

o

sm

35150

103 8

oso ffvvshrmkm

,,

MHzfo ?

so f

v

vvf

mkmshr

1000136001

83MHz34.9999951

6MHz35.0000048

MHzx

xf

v

vvf

MHzx

xf

v

vvf

s

m

s

hr

km

m

hr

km

sm

sm

sm

so

o

sm

sm

sm

so

o

35103

66.41103 :receding

35103

66.41103 :gapproachin

66.413600

11000150

8

8

8

8

Note: Storm is like observer moving toward storm. Then, it bounces back signals with same frequency it observed.

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Example: Ch17 # 3Flowerpot 20m up falls towards 1.75m tall person. Find max time can wait before shouting from top if person below needs 0.3s to move.

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Example: Ch17 # 16Cu bar is at 99.5% of Y=13N/m^2. 500Hz sound wave is then transmitted.

a) Find displacement amplitude required to break bar

b) Find max speed of Cu atoms at breaking.c) Find sound intensity in bar.

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Example: Ch17 # 34Firework explodes 100m up. Observer directly under explosion hears average intensity of 0.07W/m^2 for 0.2s. a) Find total sound energy of explosionb) Find decibels measured by observer

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Example: Ch17 # 38Fetus ventricular wall moves in simple harmonic motion with amplitude 1.8mm at 115 beats per minute. Detector on mother procudes sound at 2x10^6Hz which travels through tissue at 1.5km/s. Finda) Max linear speed of heart wallb) Max frequency arriving at wall of heartc) Max frequency of reflected sound detected