Chapter 14: Sound

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Chapter 14 Sound

• Producing a Sound Wave

Suggested homework problems 11,26,33,44,50

• Sound waves

• Sound waves are longitudinal waves traveling
  through a medium,
• such as air.

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Producing a Sound Wave

• Movement of air molecules in a sound wave

• When a tine swings to the right, the molecules
  in an element of air
• in front of its movement are forced closer
  together than normal
• compression

• When the tine swings to the left the molecules
  in an element of air
• to the right of the tine spread apart, and the
  density and air pressure
• in this region are then lower than normal
  rarefaction

rarefaction
compression
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Characteristics of Sound Waves

• Longitudinal wave vs. transverse wave

• The motion of the elements of the medium in a
  longitudinal sound
• wave is back and forth along the direction in
  which the wave travels.

• In a transverse wave, the vibrations of the
  elements of the medium
• are at right angle to the direction of travel
  of the waves.

• Categories of sound waves

• Audible waves Frequencies in the range of
  sensitivity of the
• human ears 20
  to 20,000 Hz

• Infrasonic waves Frequencies below the audible
  range
• Ultrasonic waves Frequencies above the audible
  range

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Characteristics of Sound Waves

• Application of ultrasound

• Ultrasonic sound waves have frequencies greater
  than 20 kHz and,
• as the speed of sound is constant for given
  temperature and medium,
• they have shorter wavelength. Shorter
  wavelengths allow them to
• image smaller objects and ultrasonic waves are,
  therefore, used as
• a diagnostic tool and in certain treatments.

• Imaging organs of a body

• Internal organs can be examined
• via the images produced by the
• reflection and absorption of
• ultrasonic waves. Use of ultrasonic
• waves is safer than x-rays but
• images show less details.
• Certain organs such as the liver
• and the spleen are invisible to
• x-rays but visible to ultrasonic waves.

• Measurement of blood flow using the Doppler
  effect

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Characteristics of Sound Waves

• Application of ultrasound (contd)

• Mechanism to produce ultrasonic waves
  (piezoelectric effect)

An alternating voltage of high frequency induces
vibration on a crystal of quartz and
strontium titanate etc. of the same
frequency. This vibration of the crystal
creates a beam of ultrasonic waves. This process
can be reversed, so the transmitter can also work
as the receiver.

• Principle of ultrasonic imaging

A sound wave is partially reflected whenever it
is incident on a boundary between two materials
having different densities. The percentage of the
incident wave intensity reflected (PR) when a
sound wave is traveling in a material of density
ri and strikes a material of density rt is given
by
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Characteristics of Sound Waves

• Application of ultrasound (contd)

• Use of ultrasound for imaging

Physicians commonly use ultrasonic waves to
observe fetuses. This technique presents far less
risk than do x-rays, which deposit more energy in
cells and can produce birth defects.

• Cavitron ultrasonic surgical aspirator (CUSA)

This device is used to surgically remove brain
tumors. The probe of the CUSA emits ultrasonic
waves (23 kHz) at its tips. When the tip touches
a tumor, the part of the tumor near the probe
is shattered and the residue can be sucked up
through the hollow probe.

• A device to break up kidney stones

• Instantaneous measurement of the distance to an
  object

Instantaneous measurement of an object to be
photographed by a camera can be done using
ultrasonic waves.
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Speed of Sound

• Speed of sound wave in a fluid

• The speed of a sound wave in a fluid depends on
  the fluids
• compressibility and inertia.

B bulk modulus of the fluid
r equilibrium density of the fluid

• Speed of sound wave in a solid rod

Y Youngs modulus of the rod
r density of the fluid

• Speed of sound wave in air

343 m/s at T20oC
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Energy and Intensity of Sound waves

• Average intensity of a wave

• The average intensity of a wave on a given
  surface is defined as
• the rate at which energy flows through the
  surface, DE/Dt, divided
• by the surface area A

SI unit watt per meter squared (W/m2)

• A rate of energy transfer is power

P the sound power passing through the surface

• Thresholds

The faintest sounds the human ear can detect at a
frequency of 1 kHz have an intensity of about
1x10-12 W/m2 Threshold of hearing
The loudest sounds the human ear can tolerate
have an intensity of about 1 W/m2 Threshold of
pain
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Energy and Intensity of Sound waves

• Intensity level in decibel

• The loudest tolerable sounds have intensities
  about 1.0x1012 times
• greater than the faintest detectable sounds.

• The sensation of loudness is approximately
  logarithmic in the human
• ear. Because of that the relative intensity of
  a sound is called the
• intensity level or decibel level, defined by

I0 1.0x10-12 W/m2 the reference intensity the
sound intensity at the threshold of hearing
Threshold of hearing
Threshold of pain
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Energy and Intensity of Sound waves

• Intensity level in decibel

• Intensity levels in decibels for different
  sources

• Example 14.2 A noisy grinding
• machine

A noisy grinding machine in a factory produces a
sound intensity of 1.00x10-5 W/m2. (a) Calculate
the intensity level of the single grinder.
(b) If a second machine is added, then
(c) Find the intensity corresponding to an
intensity level of 77.0 dB.
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Spherical and Plane Waves

• Intensity of a spherical wave

• If a small spherical object oscillates so that
  its radius changes
• periodically with time, a spherical sound wave
  is produced.

• The energy in a spherical wave pro-
• pagates equally in all directions.

• At a distance r the intensity of a
• spherical sound wave form the
• source is

rays
wave fronts
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Spherical and Plane Waves

• Wave fronts, rays, and plane waves

• A series of circular arcs at maximum intensity
  concentric with the
• source of spherical waves are called wave
  fronts. The distance
• between the adjacent wave fronts equals the
  wavelength l.

• The radial lines pointing outward from the
  source and perpendicular
• to the arcs are called rays.

• If the distance from the source is much greater
  than the wavelength,
• we can approximate the wave fronts with
  parallel planes called
• plane waves.

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Spherical and Plane Waves

• Example 14.3 Intensity variations of a point
  source

• A small source emits sound waves with a power
  output of 80.0 W.
• (a) Find the intensity 3.00 m from the source.

(b) At what distance would the intensity be
one-fourth as much as it is at r3.00 m?
(c) Find the distance at which the sound level is
40.0 dB?
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Doppler Effect

• Doppler effect of sound wave

• Frequency of the sound wave heard by an observer
  depends
• on the motion of the sound source and the
  observer Doppler effect.

• This phenomenon is common to all waves including
  light.

• Case 1 The observer moving to a stationary
  source

Source at rest Listener moving left
Source at rest Listener moving right
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Doppler Effect

• Case 1 The observer moving to a stationary
  source

fS frequency of the source lS wavelength of
the source v speed of sound in air fO
frequency heard by the observer
relative speed of the sound w.r.t. the observer
The observer is moving away from the source
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Doppler Effect

• Case 2 The source is moving to a stationary
  observer

When the source moves
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Doppler Effect

• Case 2 The source is moving to (away from) a
  stationary
• observer

The wavelength lO observed by the observer O is
shorter (longer) than the wavelength lS of the
source at rest.
The source moves by vsT vs/fs in one period

• for moving to
• for moving away

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Doppler Effect

• General case

When the observer moves toward the source, a
positive speed is substituted for vO. When the
observer moves away from the source, a negative
speed is substituted for vO. When the source
moves toward the observer, a positive speed
is substituted for vS. When the source moves away
from the source, a negative speed is substituted
for vS.
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Doppler Effect

• Example 14.5 The noisy siren.

An ambulance travels down a highway at a speed of
75.0 mi/h, its siren emitting sound at a
frequency of 4.00x102 Hz. What frequency is heard
by a passenger in a car traveling at 55.0 mi/h in
the opposite direction as the car and ambulance
(a) approach each other and (b) pass and move
away from each others?
First convert the speeds from mi/h to m/s.
(a)
(b)
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Interference of Sound Waves

• Two sound waves interfere each other

Imagine two sound waves from two separate sound
point sources.
destructive
constructive
d2
d1
two waves enhance each other
two waves destruct each other
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Interference of Sound Waves

• Example 14.6 Two speakers driven by the same
  source

Two speakers placed 3.00 m apart are driven by
the same oscillator. A listener is originally at
Point O, which is located 8.00 m from the center
of the line connecting the two speakers. The
listener then walks to point P, which is a
perpendicular distance 0.350 m from O,
before reaching the first minimum in sound
intensity. What is the frequency of the
oscillator? Take speed of sound in air to be 343
m/s.
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Standing Waves

• Superposition of two waves moving in the same
  direction

• Superposition of two waves moving in the
  opposite direction

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Standing Waves

• Reflection of waves at a fixed end

Reflected wave is inverted
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Standing Waves

• Standing waves on a string

Superposition of two waves moving in the
opposite direction creates a standing wave when
two waves have the same speed and wavelength.
Nnode, ANantinode
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Standing Waves

• Standing waves on a string

There are infinite numbers of modes of standing
waves
first overtone
second overtone
fundamental frequency
third overtone
L
fixed end
fixed end
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Standing Waves
Superposition of two waves moving in the
opposite direction creates a standing wave when
two waves have the same speed and wavelength.
Nnode, ANantinode
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Standing Waves

• Standing waves in air column

Sound wave in a pipe with two open ends
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Standing Waves

• Standing waves in air column

Sound wave in a pipe with two open ends
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Standing Waves

• Standing waves in air column

Normal modes in a pipe with two open ends
2nd normal mode
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Standing Waves

• Standing waves in air column

Sound wave in a pipe with one closed and one open
end (stopped pipe)
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Standing Waves

• Standing waves in air column

Normal modes in a pipe with an open and a closed
end (stopped pipe)
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• Beats

• Two interfering sound waves can make beat

Two waves with different frequency create a
beat because of interference between them. The
beat frequency is the difference of the two
frequencies.
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• Resonance

• Resonance

• When we apply a periodically varying force to a
  system that can
• oscillate, the system is forced to oscillate
  with a frequency equal
• to the frequency of the applied force (driving
  frequency) forced
• oscillation. When the applied frequency is
  close to a characteristic
• frequency of the system, a phenomenon called
  resonance occurs.

• Resonance also occurs when a
• periodically varying force is applied
• to a system with normal modes.
• When the frequency of the applied
• force is close to one of normal
• modes of the system, resonance
• occurs.

works as a stoppeded pipe
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• Resonance

• Example 14.10

The sound waves generated by the fork are
reinforced when the length of the air column
corresponds to one of the resonant frequencies of
the tube. Suppose the smallest value of L for
which a peak occurs in the sound intensity is
9.00 cm.

• Find the frequency of the
• tuning fork.

Lsmallest9.00 cm
(b) Find the wavelength and the next two water
levels giving resonance.
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• Resonance

• Resonance

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• Quality of Sound

• Timbre or tone color or tone quality

Frequency spectrum
noise
music
Harmonics
piano
piano
Harmonics