AP Physics
Chapter 14
Sound
Chapter 14: Sound
14.1
14.2
14.3
14.4
14.5
14.6
Sound Waves
The Speed of Sound
Sound Intensity and Sound Intensity
Level
Sound Phenomena
The Doppler Effect
Musical Instruments and Sound
Characteristics
Homework for Chapter 14
• Read Chapter 14
• HW 14.A: pp. 478-479: 10-15,18,28,29,30.
• HW 14.B: p. 480-481: 56, 57, 70, 74-78, 84, 85.
Warmup: Cheap Seats
Physics Warmup #118
Modern baseball stadiums have a lot more to offer fans than the stadiums of
decades past. One thing they still have in common, however, are the “cheap
seats.” The back row of the upper deck will always be a long way from home plate.
Not only is it hard to see what’s going on, it is even hard to hear what’s going on.
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Suppose you are sitting in your cheap seat and you decide to listen to the
broadcast of the game on your pocket radio. When the first batter makes contact
with the ball, you hear the crack of the bat through your radio earphones before
you hear it in the ballpark! Explain why.
Answer: The radio transmission travels much farther but it travels at the speed of
light. The actual sound wave travels through the ballpark air at the speed of
sound.
14.1: Sound Waves
sound
- the sensation produced when hearing vibrations
transmitted through the air or other medium.
• Sound waves in fluids are primarily longitudinal (compressional) waves.
• Sound waves in solids can also have a transverse wave component.
• The high pressure regions of a sound wave are called condensations or
compressions.
• The low pressure regions are called rarefactions.
• All sound waves are produced by vibrating sources such as human vocal cords
or tuning forks.
A Tuning Fork as an Explanation of Sound
A tuning fork is basically a metal bar bent into a U-shape.
When struck, the prongs, or tines, vibrate with an antinode at the end of each tine.
The fork vibrates at its fundamental frequency, so a single tone is heard. A tone is
a sound with a definite frequency.
As the fork vibrates, the compression waves propagate outward.
The pressure differences in the compression waves causes the eardrum to
vibrate.
On the other side of the eardrum, tiny bones
(the hammer, anvil, and stirrup) carry the
vibrations to the inner ear.
The auditory nerve picks up the signal and
carries it to the brain.
The Sound Frequency Spectrum
The audible region of sound for humans
lies between about 20 Hz and 20 kHz.
infrasonic
– frequencies below
the range of human hearing.
• Can be generated by earthquakes,
wind, aircraft, automobiles, rapidly
moving objects.
• Elephants and cattle may give early
warnings of signs of earthquakes and
weather disturbances.
ultrasonic
- frequencies above
the range of human hearing.
• Can be generated by high-frequency
vibrations in crystals.
• Ultrasonic whistles can be used to call
dogs.
Ultrasound Applications
Ultrasound is transmitted
through tissue and is
reflected from internal
structures. The reflected
waves are detected, and the
signals are used to construct
an image, or echogram, such
as for a fetus.
Sonar is used for ranging and detecting.
Sound pulses generated by sonar apparatus
are reflected by underwater objects, and the
resulting echoes are picked up by a detector.
The time required for a sound pulse to make
one round trip, together with the speed of
sound in water, gives the distance of the
reflecting object .
14.2: The Speed of Sound
The Speed of Sound in Various Media
Medium
Speed (m/s)
Solids
• The speed of sound in a medium depends on
the elasticity or the intermolecular interactions
of the medium and the mass or density of its
particles.
Aluminum
5100
Copper
3500
Glass
5200
• Solids have more intermolecular interactions
than liquids, and liquids more than gases.
Liquids
Ethyl Alcohol
1125
• The speed of sound is generally 2 to 4 times
faster in solids than in liquids and about 10 to
15 times faster in solids than in gases such as
air.
Mercury
1400
Water
1500
Gases
Air (0°C)
331
Air (100°C)
387
Helium (0°C)
965
Hydrogen (0°C) 1284
Oxygen (0°C)
316
• The speed of sound depends on the temperature of the medium.
• The speed of sound in air increases with increasing temperature.
• For normal environmental temperatures, the speed of sound increases about 0.6
m/s for each degree Celsius above 0°C.
• A good approximation of the speed of sound in air for normal environmental
temperatures is:
v = (331 + 0.6 Tc) m/s
speed of sound in air
where Tc is the air temperature in degrees Celsius and
331 m/s is the speed of sound in air at 0°C.
• A useful general value for the speed of sound in air is 1/3 km/s or 1/5 mi/s.
Example 14.1: The speed of an ultrasonic frequency 45 kHz in air is 342 m/s.
a) What is the air temperature?
b) What is the wavelength of the sound wave?
Check for Understanding
1. A sound wave with a frequency of 15 Hz is in what region of the sound
spectrum?
a) audible
b) infrasonic
c) ultrasonic
d) supersonic
Answer: b
Check for Understanding
2. A sound wave in air
a) is longitudinal
b) is transverse
c) has longitudinal and transverse components
d) travels faster than a sound wave through a liquid
Answer: a
Check for Understanding
3. The speed of sound is generally greatest in
a) solids
b) liquids
c) gases
d) a vacuum
Answer: a
Check for Understanding
4. Explain why sound travels faster in warmer air than in colder air.
Answer: Sound is a traveling disturbance like any other wave. The speed
of the air molecules is greater in warmer air so the air molecules can pass
the disturbance along faster.
Check for Understanding
5. The speed of sound in air
a) is about 1/3 km/s
b) is about 1/5 mi/s
c) depends on temperature
d) all of these
Answer: d
Check for Understanding
6.
Check for Understanding
6.
Warmup: Can You Hear Me Now?
Physics Warmup #121
The loudness of sound can be measured in units called decibels (dB). The sound
level of a person talking in a normal conversation is typically in the 60-dB range.
Continued exposure to sound levels over 85 dB can cause permanent ear
damage. People who work in loud environments, such as factories with large
machines, are required to wear ear plugs.
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Modern technology has made it possible to play music in car stereos that far
exceed 85 dB. Many teenagers spend significant amounts of money to raise the
decibel level of their car stereos to 120 dB and beyond. As a result, some
communities have passed laws limiting the sound level at which music can be
played. Express your view on the need for such laws.
14.3: Sound Intensity and Sound
Intensity Level
• intensity (I) is the rate at which power is transferred, per unit area.
I = energy/time = power
area
area
• The SI unit of intensity is W/m2.
• It is used most frequently with sound or light waves.
• The intensity is inversely proportional to the square of the distance from the point
source.
• Therefore, intensity follows the inverse square law.
Question: What other physical phenomena follow the inverse square law? You may
use your Gold Sheet to answer.
Answer: gravitational force, electric force
• The energy emitted from a point source spreads out equally in all directions.
• Since intensity is power/area I = P = P__
surface.
A 4 R2
where the area is that of a spherical
• The intensity then decreases with the distance from the source as 1
R2.
• Two intensities at different distances from a source of constant power can be
compared as a ratio:
I2 = P/4 R22 = R12
I1 = P/4 R12 = R22
or
I2 =
I1
R1
R2
2
• Doubling the distance decreases the intensity to a quarter of its original value.
• Sound intensity is perceived by the ear as loudness.
• On the average, the human ear can detect sound waves (at 1 kHz) with an
intensity as low as Io = 10-12 W/m2. This is called the threshold of hearing.
• At an intensity of Ip = 1.0 W/m2 sound is uncomfortably loud and may be painful to
the ear. This is called the threshold of pain.
• The ratio between the two intensities Ip = 1.0 W/m2 = 1012.
Io = 10-12 W/m2
• For a sound to be audible, it must have a frequency between 20 Hz and 20 kHz,
and have an intensity greater than Io.
Sound Intensity Level – The Decibel
(threshold of hearing)
• Perceived sound is loudness is not directly proportional to intensity.
• Doubling the perceived loudness corresponds to an approximate increase in
intensity by a factor of 10.
example: A sound with an intensity of 10-5 W/m2 would be perceived to be
twice as loud as one with an intensity of 10-6 W/m2.
• At the threshold of hearing, I = Io, so,  = 10 log Io = 10 log 1 = 0 dB
Io
• At the threshold of pain,  = 10 log 1.0 W/m2 = 10 log 1012 = 10 (12) = 120 dB
Io
• The 12 orders of magnitude of sound intensity is only a difference of
120 dB – 0 dB = 120 dB, on the decibel scale.
Sound
Intensity
Levels
and the
Decibel
Scale
Sound intensity and sound intensity level are two very different things.
• Intensity is a direct way to measure energy and is additive.
example: The sum of a 1.0 W/m2 sound and a 2.0 W/m2 sound will result
in a sound of intensity 1.0 W/m2 + 2.0 W/m2 = 3.0 W/m2.
• Intensity level is based on a logarithmic scale and therefore is not additive.
example: The sum of a 10 dB sound and a 20 db sound will NOT make a
sound of 10 dB + 20 dB  30 dB.
Example 14.3: Mrs. Pizarchik’s lecturing voice has a power of about 0.50 mW. If this
power is assumed to be uniformly distributed in all directions,
a) What is the sound intensity at a distance of 5.00 m from her?
b) If you double the distance between you and the instructor, what is the new sound
intensity?
c) What is the new sound intensity if you are 5.00 m apart and she raised her voice
to double her power output?
Check for Understanding
1. If the air temperature increases, would the sound intensity from a constant
output point source
a) increase
b) decrease
c) remain unchanged
Answer: c
2. The decibel scale is referenced to a standard intensity of
a) 1.0 W/m2
b) 10-12 W/m2
c) normal conversation
d) the threshold of pain
Answer: b
Check for Understanding
3. When sound passes from air into water
a) its wavelength does not change
b) its frequency does not change
c) its velocity does not change
d) all of the above are true
Answer: b
4. As the temperature of the air increases, what happens to the velocity of
sound? (Assume that all other factors remain constant.)
a) It increases.
b) It decreases.
c) It does not change.
Answer: a
Homework for Chapter 14.1-3
• HW 14.A: pp. 478-479: 10-15,18,28,29,30.
Warmup:
Run the sound simulation.
http://phet.colorado.edu/en/simulation/sound
14.4: Sound Phenomena
• Since sound is a wave, it has wave characteristics. It can be:
reflected – waves bounce off objects or surfaces
refracted – waves change direction due to a medium or density change.
•Temperature causes differences in air density.
diffracted – waves bend around corners, spread out beyond openings, or around
objects.
•The object needs to be small compared to the wavelength.
• Large wavelength, low frequency sounds diffract the most.
• Sound waves interfere when they meet.
constructive interference – two crests or two troughs coincide; in phase
destructive interference – a crest and a trough coincide; out of phase
Reflection of Sound
• The reflection of sound follows the law
"angle of incidence equals angle of
reflection", sometimes called the law of
reflection. The same behavior is observed
with light and other waves, and by the
bounce of a billiard ball off the bank of a
table.
• The reflected waves can interfere with
incident waves, producing patterns of
constructive and destructive interference.
This can lead to resonances called
standing waves in rooms. It also means
that the sound intensity near a hard
surface is enhanced because the
reflected wave adds to the incident wave,
giving a pressure amplitude that is twice
as great in a thin "pressure zone" near
the surface.
Refraction of Sound
•Sound propagates in all
directions from a point
source. Normally, only
that which is initially
directed toward the
listener can be heard,
but refraction can bend
sound downward.
• Normally, only the
direct sound is received.
But refraction can add
some additional sound,
effectively amplifying the
sound.
• Natural amplifiers can
occur over cool lakes.
Diffraction of Sound
Diffraction of Sound
The long wavelength sounds of the bass drum will diffract around the corner
more efficiently than the more directional, short wavelength sounds of the
higher pitched piccolo.
Interference
• Sound waves from two point
sources spread out and interfere.
• At points where they arrive in
phase (zero phase difference),
constructive interference occurs.
• At points where the waves arrive
completely out of phase (phase
difference of 180°), destructive
interference occurs.
• The phase difference at a
particular point depends on the
path lengths the waves travel to
reach that point.
Interference Simulation
http://www.falstad.com/interference/
Check for Understanding
1.
Check for Understanding
2.
Check for Understanding:
3. As a person walks between a pair of loudspeakers that produce tones
of the same amplitude and frequency, he hears a varying sound
intensity. Explain.
Answer: The varying sound intensity is caused by the interference effect.
At certain locations there is constructive interference and at other
locations, there are destructive interference.
Warmup: Did You Hear What I Saw?
Physics Warmup #119
Lightning and thunder are created at the same time by the same event. The speed
of light is 186,000 miles per second, while the speed of sound in air is typically
around 700 miles per hour. As a result, you see the lightning before you hear the
thunder.
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You might have heard the old rule of thumb that every five seconds that elapse
between seeing the lightning and hearing the thunder represents one mile of
distance between you and the lightning. Use the speeds of light and sound to
check the accuracy of that statement.
Answer: Yes!
time for light to travel 1 mile:
t = d = 1 mile
v 186,000 mi/s
time for sound to travel 1 mile:
700 mi/hr = 0.194 mi/s
t=d=
1 mi
v
0.194 mi/s
= 5.4 x 10-6 s (instantaneous)
= 5.1 seconds
14.5: The Doppler Effect
The Doppler Effect
• If there is relative motion between a sound source and an observer, the observer
will detect a frequency which is different from the frequency of the source.
• This phenomena is called the Doppler effect. It is named after the Austrian
physicist, Christian Doppler (1803-1853) who first described the effect.
• Generally, if the source and the observer are moving toward each other, the
observed frequency is higher than the source frequency.
• If the source and the observer are moving away from each other, the observed
frequency is lower than the source frequency.
View Applet: http://www.loncapa.org/~mmp/applist/doppler/d.htm
The Doppler Effect
Sound waves bunch up in front of a moving source – the whistle- giving a higher
frequency there. They trail out behind the source, give a lower frequency there.
The pitch is the perceived frequency.
Applications of the Doppler Shift
radar (radio detecting and ranging)
Radio waves are emitted, reflected, and
recaptured by the gun. If your car is moving
towards the patrol car, the reflected waves
have a higher frequency. The Doppler shift
depends on the speed. A computer calculates
the speed and displays it for the police officer.
Doppler radar
Doppler radar can measure the Doppler
frequency shift in addition to the
magnitude of the echo signal reflected
from precipitation. The Doppler shift is
related to the velocity of the
precipitation blown by wind either
toward or away from the radar
installation.
The Doppler Effect for Light Waves
When a distant light source moves away
from us, the frequency of the light we receive
from it is lowered. Light is shifted toward the
red (long-wavelength) end of the spectrum,
known as the Doppler red shift.
Similarly, the frequency of light from an object approaching us is increased, and
light is shifted toward the blue (short wavelength) end of the spectrum. This
produces Doppler blue shift.
The amount of frequency shift depends on the
speed of the source.
The Doppler shift of light from astronomical
objects is very useful to astronomers. For
example, in this picture the velocity of the
Sun’s corona is mapped as plasma moves
toward (blue shifted) or away from (red
shifted) the satellite which is capturing data.
Check for Understanding:
1. Is there a Doppler effect if a sound source and an observer are moving with
the same velocity?
Answer: No. There is no relative velocity between the observer and the
source.
2. What would be the effect if a moving source accelerated toward a stationary
observer?
Answer: An increasing sound frequency is observed since the source is
moving toward the observer and its speed increases.
Check for Understanding:
3. Astronomers have observed that all distant galaxies appear red-shifted. Is
this evidence for an expanding, contracting, or stationary universe?
Answer: Expanding, because red shift indicates they are moving away from
each other.
Check for Understanding:
4. Traffic radar is based on
a) beats
b) the Doppler effect
c) interference
d) refraction
Answer: b
Davy Jones Plays His Pipe Organ
http://www.youtube.com/watch?v=L0JbaZtoKAs
14.6: Musical Instruments and
Sound Characteristics
• Musical instruments provide good examples of standing waves and boundary
conditions.
• Example: a guitar. For a stretched string, fixed at each end, the natural
frequencies are
fn = n(v/2L) = nf1 (for n = 1,2,3…)
where v is the velocity of the wave
L is the length of the string
• The velocity of the wave on the string depends on the tension and
inertia of the string.
• The effective length of the string is varied by finger location and
pressure.
• The natural frequencies for pipes (where v is the speed of sound in air) are
fn = v/n = n(v/2L) = nf1 (for n = 1,2,3…) pipe open on both ends
fm = v/m = m(v/4L) = mf1 (for m = 1,3,5…) pipe closed on one end
Open organ pipe
Closed organ pipe
Organ Pipes
• Standing waves can also be set up in wind instruments, such as the organ pipe.
• Pipe organs have fixed length pipes which may be opened or closed.
• Longitudinal standing waves are formed in vibrating air columns in pipes.
• An open pipe has antinodes at both ends.
• A closed pipe has a closed (node) end and
an open (antinode) end.
• To solve problems with pipes, always begin with
the length of the pipe. If it is open at both ends,
the biggest wave that can fit the pipe has a
wavelength twice the pipe’s length. If it is closed at
one end, the biggest wave is four times longer than
the pipe.
Example 14.9: A 3.00 m long pipe is in a room where the temperature is 20°C.
a) What is the fundamental frequency if the pipe is open?
b) What is the frequency of the second harmonic if the pipe is open?
c) What is the fundamental frequency if the pipe is closed?
d) What is the frequency of the second harmonic of the pipe is closed?
beats
- rhythmic interference that occurs when two notes of unequal but
close frequencies are played.
Two traveling waves of equal amplitude and slightly different frequencies interfere
and give rise to pulsating tones called beats. The listener will hear these beats at a
beat frequency:
fb =  f1 - f2 
https://www.youtube.com/watch?v=eVIKrAdpuqU
Example 14.6: A music tuner uses a 256 Hz tuning fork to tune the frequency of
sound from a musical instrument. It the tuner hears a beat frequency of 2.0 Hz,
what is the frequency of the sound produced by the instrument?
Check for Understanding:
1. When you blow across the top of a bottle with water in it, why does the
frequency of the sound increase with increasing levels of water?
Answer: As the level of water increases in the bottle, the length of the air
column above the water decreases. This decrease in length of the air column
decreases the wavelength and increases the frequency.
Check for Understanding:
2. Beats are a direct result of
a) interference
b) refraction
c) diffraction
d) the Doppler effect
Answer: a
Check for Understanding:
3. Traffic radar is based on
a) beats
b) the Doppler effect
c) interference
d) refraction
Answer: b
Check for Understanding:
4.
Homework for Chapter 14.4-6
• HW 14.B: p. 480-481: 56, 57, 70, 74-78, 84, 85.