lec28-soundwaves.ppt 773KB Jun 23 2011 10:24:00 AM
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
B
bulk modulus
elastic property
v
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
20kHz
ultrasonic
1
Wave Equation for Sound
Recall
y ( x, t ) A sin(kx t )
For transverse, we now have longitudinal
s ( x, t ) smax sin(kx t )
Max longitudinal displacement
Or in terms of pressure
P( x, t ) Pmax sin(kx t )
Where
Pmax vsmax
Derivation in book
2
Sound Intensity
Intensity = power (or energy transfer rate) divided by area
P
P
2
1
I
2 vsmax I
2
A 4r
Units: W/m2
Inverse Square Law:
I 2 R2
I1 R1
2
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
W
m2
3
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
4
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
f o
fs
v
+ = getting closer
- = moving away
fo = observed frequency
fs = source frequency
5
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 3 x108 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
.
6
6
s
hr km 3600s
1hr 3600 s
1km 1000m
v vo
f
fs
v
approachin g :
3 x108 ms 41.6 6 ms
v vo
35MHz 35.00000486MHz
f o
f s
8 m
3 x10 s
v
receding :
3 x108 ms 41.6 6 ms
v vo
35MHz 34.999995183MHz
f o
f s
8 m
3 x10 s
v
6
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.
7
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.
8
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
9
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
10
Sound Waves - mechanical longitudinal waves
Sound waves come from periodic pressure variations moving along in a substance.
Sound Speed
B
bulk modulus
elastic property
v
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
20kHz
ultrasonic
1
Wave Equation for Sound
Recall
y ( x, t ) A sin(kx t )
For transverse, we now have longitudinal
s ( x, t ) smax sin(kx t )
Max longitudinal displacement
Or in terms of pressure
P( x, t ) Pmax sin(kx t )
Where
Pmax vsmax
Derivation in book
2
Sound Intensity
Intensity = power (or energy transfer rate) divided by area
P
P
2
1
I
2 vsmax I
2
A 4r
Units: W/m2
Inverse Square Law:
I 2 R2
I1 R1
2
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
W
m2
3
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
4
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
f o
fs
v
+ = getting closer
- = moving away
fo = observed frequency
fs = source frequency
5
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 3 x108 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
.
6
6
s
hr km 3600s
1hr 3600 s
1km 1000m
v vo
f
fs
v
approachin g :
3 x108 ms 41.6 6 ms
v vo
35MHz 35.00000486MHz
f o
f s
8 m
3 x10 s
v
receding :
3 x108 ms 41.6 6 ms
v vo
35MHz 34.999995183MHz
f o
f s
8 m
3 x10 s
v
6
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.
7
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.
8
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
9
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
10