Announcements
- Homework 21: due Today
- Homework 22: due Thursday, Dec. 2
- Review session: Sunday, Dec. 5, 1-4 pm?
Chapter 17: Waves-II (Sound waves)
Reading assignment: Chapter 18.1-18.4
Homework :
(due Monday, Nov. 14, 2005):
• Sound waves are the most important example of longitudinal
waves.
• They can travel through any material, except vacuum (no one
can hear you scream in outer space).
• Speed of sound depends on material (and temperature)
Sound Waves
Sound waves are longitudinal waves.
They consist of compressed and rarified regions of gas (medium)
We can hear (audible) frequencies from about 20 Hz (low) to 15,000 Hz (high).
Infrasonic “sound” waves: below ~ 20 Hz
Ultrasonic sound waves: above ~ 15,000 Hz
Sound
- is a wave (sound wave)
- Rarefied and compressed regions
- Longitudinal wave
- air molecules move back and forth
Sound waves, hearing and the ear
http://www.innerbody.com/anim/ear.html
Notes and their
fundamental
frequency
Octaves: Frequency
doubles for each tone
Speed of Sound Waves
In gas and liquids:
v
In solids:
B
v

Y

Y… Young’s modulus (see Chapter 13.6)
B… Bulk modulus of medium (see Chapter 13.6)
…density of material
Bulk modules
determines the volume
change of an object due
to an applied pressure P.
volume stress
F/A
P
B


volume strain V / Vi V / Vi
Young’s modules
determines the length
change of an object
due to an applied force
F.
tensile stress
F/A
Y

tensile strain L / Li
Speed of Sound in air as a function of temperature
TC
Speed of sound in air : v  (331 m/s )  1 
273C
@ 20C : vS  343 m/s
TC … air temperature in degrees Celsius
Black board example 18.1
Lightning strikes 10 miles
(16090 m) away from you.
(a) How long does it take the light (c = 300,000,000 m/s) to get to you?
(b) How long does it take the sound of thunder to get to you (Temp= 20ºC = 68F ).
(c) How far does the sound travel in one second?
Periodic sound waves.
(A constant tone is a periodic sound wave)
Condensation:
Regions of compressed gas.
Rarefactions:
Regions of rarefied gas.
Distance between two compressed regions: Wavelength l
Periodic sound waves.
Displacement of small volume element:
sx, t   smax coskx  t 
Pressure variation:
Px, t   Pmax sin kx  t 
Standing waves in air colums
• Standing waves can be set up in a tube or air (pipe, flute, …)
• Distinguish between open end pipes and close end pipes
• Analogous to standing waves on a string.
• Antinode on open ends.
Both ends open:
Node on closed ends.
Standing waves in air colums
• Antinode on open ends.
• Node on closed ends.
One end closed:
In a pipe open at both ends, the natural frequencies of oscillation
form a harmonic series that includes all integral multiples of the
fundamental frequency
v
v
fn 
n
ln
2L
n  1, 2, 3, ...
In a pipe closed at one end and open at the other, the natural
frequencies of oscillation form a harmonic series that includes only
odd integer multiples of the fundamental frequency.
v
v
fn 
n
ln
4L
n  1, 3, 5, ...
Black board example 18.2
HW 18.35
A loudspeaker is adjustable in frequency from 1000
to 2000 Hz. The tube D is a piece of cylindrical
sheet-metal pipe 45. 7 cm long and open at both
ends.
(a) If the speed of sound in air is 344 m/s, what is
the lowest frequency at which resonance will
occur in the pipe when the frequency emitted by
the speaker is varied from 1000 Hz to 2000 Hz?
(b) Sketch the standing wave for each resonant
frequency.
Music instruments
Combining different
harmonics
Doppler effect
When heading into waves: Frequency becomes shorter.
When heading away from waves: Frequency becomes larger.
Doppler effect
When heading into waves: Frequency becomes shorter.
When heading away from waves: Frequency becomes larger.
Doppler effect
Moving detector
 v  vD 
f ' 
f
 v 
Moving source
 v
f '  
 v  vS

 f

+… detector moving toward source
+… source moving away from observer
- … detector moving away from source
- … source moving towards observer
If both, detector and source are moving:
 v  vD 
 f
f '  
 v  vS 
Black board example 18.3
Homework 18.47
The 16,000 Hz whine of the turbines in the jet engines of an
aircraft moving with speed 200 m/s is heard at what frequency by
the pilot of a second craft trying to overtake the first at a speed of
250 m/s?
Shock waves
When the speed of the
object, vS, exceeds the
wave speed, v.
v t
v
sin  

vs  t vs
The ratio vS/v is called the Mach number.
For sound: Mach 3 means 3x the speed of sound.