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Sound
Chapter 15
Producing a Sound Wave
• All sound waves begin in a vibrating object.
• Source vibrates at an audible frequency.
• Sound waves are longitudinal waves traveling through a
medium.
• Elements of a medium are displaced in a direction parallel to
the direction of wave motion.
• A tuning fork can be used as an example of an object
producing a sound wave.
Using a Tuning Fork to Produce a Sound Wave
• A tuning fork will produce a pure
musical note.
• As the tines vibrate, they disturb the air
near them.
• As the tine swings to the right, it forces
the air molecules near it closer
together.
• This produces a high density area in
the air.
• This is an area of compression.
Using a Tuning Fork
• As the tine moves toward the
left, the air molecules to the
right of the tine spread out.
• This produces an area of low
density.
• This area is called a
rarefaction.
Using a Tuning Fork
compression
rarefactions
• As the tuning fork continues to vibrate, a succession of
compressions and rarefactions spread out from the fork.
• A sinusoidal curve can be used to represent the longitudinal
wave.
• Crests correspond to compressions and troughs to rarefactions.
Categories of Sound Waves
• Audible waves
• Lay within the normal range of hearing of the human ear.
• Normally between 20 Hz to 20,000 Hz.
• Infrasonic waves
• Frequencies are below the audible range.
• Earthquakes are an example.
• Ultrasonic waves
• Frequencies are above the audible range.
• Dog whistles are an example.
• These sound waves are generated using the piezoelectric
effect.
Generating Ultrasonic Waves
• Demonstrates the piezoelectric effect.
• Electricity provides the mechanical energy to vibrate the
crystal at certain frequency.
Speed of Sound in Air
• In air, the speed of sound depends on the wavelength, the
frequency, and the temperature:
v = ƒλ
• Remember this equation from chapter 14.
• The speed of sound increases by about 0.6 m/s for each 1oC
increase in the temperature of the air.
Speed of Sound in Air
• The speed of sound in a medium also depends upon
the temperature.
• For sound in air:
m
T

v   331 
s  273 K

• 331 m/s is the speed of sound at 0° C (273 K).
• T is the absolute temperature.
Sample Problem
Find the wavelength in air at 20o C of an 18 Hz sound
wave, which is one of the lowest frequency that is
detectable by the human ear.
Speed of Sound in a Fluid
• In a liquid, the speed depends on the fluid’s compressibility
and inertia:
v 
B

• B is the Bulk Modulus of the fluid.
• ρ is the density of the fluid.
• Compares with the equation for a transverse wave on a string:
Speed of Sound in a Solid
• The speed depends on the rod’s compressibility and inertial
properties:
v
Y

• Y is the Young’s Modulus of the material.
• ρ is the density of the material.
• Speed of sound in solids greater than speed of sound in fluids.
Typical Values for Elastic Moduli
Comparison of Speed of
Sound in Various Mediums
• Speed of sound in gases and
liquids are more temperature
dependent than the speed of
sound in solids.
• Thus there is a dependence upon
the temperature of the medium.
Intensity of Sound Waves
• The average intensity (I ) of a wave on a given surface is defined as
the rate at which the energy flows through the surface divided by the
surface area, A:
1 E 
I 

A t
A
• The direction of energy flow is perpendicular to the surface at every
point.
• The area is perpendicular to the direction of energy flow.
• The rate of energy transfer is the power.
• Units are W/m2.
The Ear
• The ear serves as an “area”
that “concentrates” the sound
and increases the intensity of
sound.
• Threshold of hearing:
• Faintest sound most humans
can hear
• About 1 x 10-12 W/m2
• Threshold of pain:
• Loudest sound most humans
can tolerate
• About 1 W/m2
• The ear is a very sensitive
detector of sound waves.
• It can detect pressure
fluctuations as small as about 3
parts in 1010.
Intensity Level of Sound Waves
• The human ear’s sensation of loudness is not a direct linear
relationship to the intensity of the sound.
• The sensation of loudness is logarithmic in the human hear.
• β is the intensity level or the decibel level of the sound.
• This is the relative loudness of the sound.
• Can be calculated using:
 I 
  10 log  
 Io 
• Io is the threshold of hearing ( = 10-12 W/m2)
Various Intensity Levels
• Threshold of hearing is 0 dB.
• Threshold of pain is 120 dB.
• Jet airplanes are about 150
dB.
• Table 14.2 lists intensity
levels of various sounds.
• Multiplying a given intensity
by 10 adds 10 dB to the
intensity level.
Frequency Response Curves
• Bottom curve is the
threshold of hearing.
• Threshold of hearing
is strongly dependent
on frequency.
• Easiest frequency to
hear is about 3300
Hz.
• When the sound is
loud (top curve,
threshold of pain) all
frequencies can be
heard equally well.
Doppler Effect
• A Doppler effect is experienced whenever there is relative
motion between a source of waves and an observer.
• When the source and the observer are moving toward each other,
the observer hears a higher frequency.
• When the source and the observer are moving away from each
other, the observer hears a lower frequency.
• Although the Doppler Effect is commonly experienced with
sound waves, it is a phenomena common to all waves.
• We will examine three cases:
• Case 1: A stationary source & moving observer
• Case 2: A moving source & stationary observer
• Case 3: Moving source & moving observer
Frequency of Sound: Two Stationary Objects
• Wave fronts have a certain wavelength
and thus will have a certain frequency
as well.
• A stationary observer to the right of the
wave front will experience the same
frequency as emitted by the source,
with no change to the observed
frequency.
• fsource = fobserved
• When either the object or source
moves the observed frequency
changes.
• This produces the Doppler effect.
Doppler Effect Case 1:
(A stationary source & moving observer)
• An observer is moving
toward a stationary
source.
• Due to his movement,
the observer detects an
additional number of
wave fronts.
• Thus the velocity of the
observer will factor into
the frequency
observed.
• The frequency heard is
increased.
Doppler Effect Case 1: Equation
• When moving toward the
stationary source, the
observed frequency is:
 v  vo 
ƒo  ƒ s 

 v 
• When moving away from
the stationary source,
substitute –vo for vo in
the above equation.
+Vo
-Vo
Doppler Effect Case 2:
(A moving source & stationary observer)
• The observed frequency will
depend on the velocity of
the source and the position
of the observer
• As the source moves
toward the observer (A), the
wavelength appears shorter
and the frequency
increases.
• As the source moves away
from the observer (B), the
wavelength appears longer
and the frequency appears
to be lower.
Doppler Effect Case 2: Equation
 v 
ƒo  ƒ s 

 v  vs 
• Use the –vs when the source
is moving toward the
observer and +vs when the
source is moving away from
the observer.
Doppler Effect Case 3
(Moving source & moving observer)
• Both the source and the observer could be moving:
• Use positive values of vo and vs if the motion is toward.
• Frequency appears higher.
• Use negative values of vo and vs if the motion is away.
• Frequency appears lower.
Sample Problem
A trumpet player sounds C above middle C (524 Hz)
while traveling in a convertible at 24.6 m/s. If the car is
coming toward you, what frequency would you hear?
Assume the temperature is 20o C.
Standing Waves
• When a traveling wave
reflects back on itself, it
creates traveling waves in
both directions.
• The wave and its reflection
interfere according to the
superposition principle.
• With exactly the right
frequency, the wave will
appear to stand still.
• This is called a standing
wave.
Characteristics of Standing Waves
• Different frequencies will
yield different standing
waves.
• The more loops the higher
the frequency.
• The wavelength and
frequency for each type of
standing wave can be
calculated.
• The frequency used to
generate the wave with
only one antinode is as
the fundamental
frequency.
Standing Waves on a String
• Standing waves can very easily be generated on a string or
rope.
• A simple change in the frequency of vibration will alter the type of
standing wave we get.
• Nodes must occur at the ends of the string because these
points are fixed.
Allowed and Forbidden Frequencies
• The allowed
standing waves
correspond to
whole number
integers of the
fundamental
frequency.
• We can
calculate for the
frequency of the
nth harmonic
using:
n
ƒ n  n ƒ1 
2L
F

Standing Waves in Air Columns
• When we blow across a pipe we create standing longitudinal
waves, similar to the standing transverse waves generated
in the string.
• Characteristics of these standing waves are similar to the
standing transverse waves.
Tube Open at Both Ends
• If the end is open, the elements of the air have complete
freedom of movement and an antinode exists.
Frequencies in Air Column Open at Both Ends
• In a pipe open at both ends, the natural frequency of
vibration forms a series whose harmonics are equal to
integral multiples of the fundamental frequency:
v
ƒn  n
 n ƒ1
2L
n  1, 2, 3,
• This is almost exactly the same as the standing transverse
wave.
• The velocity is the velocity of sound in air.
• All harmonics are present.
Tube Closed at One End
• If one end of the air column is closed, a node must exist at this
end since the movement of the air is restricted.
Frequencies in an Air Column Closed at One
End
• The closed end must be a node.
• The open end is an antinode.
• There are no even multiples of the fundamental harmonic:
v
fn  n
 n ƒ1
4L
n  1, 3, 5,
• Thus not all harmonics are present.
Sample Problem
When a tuning fork with a frequency of 392 Hz is used
with a closed-pipe resonator, the loudest sound is
heard when the column is 21.0 cm and 65.3 cm long.
What is the speed of sound in this case?
Sound
Chapter 15
THE END