Transcript Sound Waves Sound Waves

Physics 211 – lecture 28: Sound Waves
Sound Waves - mechanical longitudinal waves
 Sound waves come from periodic pressure variations moving along in a substance.
Sound Speed
v
B
bulk modulus
elastic property



density
inertial property
 Sound speed IN AIR at room temperature (20 C) is : _____________
 Sound speed equation (IN AIR only):
vair  331
Note – speed  as density 
m
s
1
and
TC
273C
speed  as elasticity (stiffness) 
Sound Spectrum – three classes of sound waves
infrasonic
audible
increasing f
decreasing 
20Hz
ultrasonic
1
20kHz
Wave Equation for Sound
Recall
For transverse, we now have longitudinal
Max longitudinal displacement
Or in terms of pressure
P( x, t )  Pmax sin( kx  t )
Where
Pmax  vsmax
Derivation in book
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Sound Intensity
Intensity = power (or energy transfer rate) divided by area
P
P
2
1


I 


v

s
I
max
2
2
A 4r
Units: W/m2
Inverse Square Law:
I 2  R2 
  
I1  R1 
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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 intensity
20 dB increase  increase by factor of 100 in intensity
30 dB increase  increase by factor of 1000 in intensity
and so on…
Decibel Equation:
I 
  10 log  
 I0 
where I 0  1012 mW2
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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
Doppler Effect Equations:
Stationary observer
 v 
 f s
f o  
 v  vs 
+ = moving away
- = getting closer
vo = observer velocity
vs = source velocity
v = speed of sound
Stationary source:
 v  vo 
fo  
 fs
 v 
+ = getting closer
- = moving away
fo = observed frequency
fs = source frequency
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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
Note: Storm is like observer moving toward storm. Then, it bounces back signals with same frequency it observed.
v  3x108 ms
vo  150 km
hr
f s  35MHz
150
km  m
f o  ? MHz
hr  s
v, vo , f s  f o
km  1000m  1hr 
m

41
.
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6



 s 
hr  km  3600 s 
1hr  3600s
1km  1000m
 v  vo 
f 
 fs
 v 
approachin g :
 3x108 ms  41.6 6 ms 
 v  vo 
35MHz  35.00000486MHz
fo  
 f s  
8 m

3
x
10
 v 
s


receding :
 3x108 ms  41.6 6 ms 
 v  vo 
35MHz  34.999995183MHz
fo  
 f s  
8 m

3x10 s
 v 


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Example: Ch17 # 3
Flowerpot 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 # 16
Cu 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 # 34
Firework explodes 100m up. Observer directly
under explosion hears average intensity of
0.07W/m^2 for 0.2s.
a) Find total sound energy of explosion
b) Find decibels measured by observer
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Example: Ch17 # 38
Fetus 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. Find
a) Max linear speed of heart wall
b) Max frequency arriving at wall of heart
c) Max frequency of reflected sound detected
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