16.6 The Speed of Sound
• Sound travels through gases, liquids, and
solids at different speeds.
• Room temperature: speed of sound in air
is 343 m/s (767 mi/h) and greater in liquids
and solids.
• Sound travels more than four times faster
in water and more than seventeen times
faster in steel than it does in air.
• Sound travels slowest in gases, faster in
liquids, and fastest in solids.
• Issac Newton was the first to measure
sound.
• http://www.youtube.com/watch?v=PzUU4
G4uW18&feature=related
Sound in a gas
• Only when molecules collide that the
condensations and rarefactions of a sound
wave can move from place to place.
• Speed of sound in a gas to have the same
order of magnitude as the average
molecular speed between collisions.
Speed in Ideal Gas
• Translational rms (root mean square) speed given
in the following equation
14.6
T = Kelvin
M = mass
k = Boltzmann’s constant (relation between absolute
temp. and the KE contained in each molecule of
an ideal gas)
Overestimates the speed of sound. It gives the
correct dependence on Kelvin temperature and
particle mass.
Speed of sound in an ideal gas
(16.5)
y = cp/cv ratio of specific heat capacity at
constant pressure cp to the specific heat
capacity at constant volume cv. (adiabatic)
Ideal monatomic gas: y = 5/3 (atoms are not
bonded together)
Y = 7/5 for ideal diatomic gases (composed of 2
atoms)
Y is here because the condensations and
rarefactions of a sound wave are formed by
adiabatic compressions (impassable) and
expansions of the gas.
Example 4: An Ultrasonic Ruler
Practice Problem 44
Homework
• Pg. 506
• Ques. 29, 30, 31
Sonar
• Sound navigation ranging
• Used to determine water depth and locating
underwater objects, such as reefs, submarines,
and schools of fish.
• Ultrasonic transmitter and receiver mounted on
the bottom of a ship.
• Transmitter emits a short pulse of ultrasonic
sound, later the reflected pulse returns and is
detected by the receiver.
• Depth determined the time it took for the sound
to return.
http://www.youtube.com/watch?v=Xc2EZjG0b8U
&feature=related
Liquids
• In a liquid, the speed of sound depends on
the density p and the adiabatic bulk
modulus Bad of the liquid:
(16.6)
Liquids
• Adiabatic bulk modulus Bad (substance's
resistance to uniform compression) is
used when calculating the speed of sound
in liquids.
• In seawater sound is 1522m/s (4x greater
than in air).
In Medicine
• Ultrasonic probe called an A-scan is used
to measure the length of the eyeball in
front of the lens, thickness of the lens, and
the length of the eyeball between the lens
and the retina.
• Needed information is the speed
of sound in the material in front
of and behind the lens of the
eye is 1532m/s and that within
the lens is 1641m/s.
Solid Bars
• When sound travels through a long
slender solid bar, the speed of the sound
depends on the properties of the medium
according to
16.7 Sound Intensity
• Sound waves carry energy that can be
used to do work.
• Sonic boom: can carry enough energy to
cause damage to windows and buildings.
• The amount of energy transported per
second by a sound wave is called the
power of the wave and is measure in SI
units of joules per second (J/s) or watts
(W).
• http://www.youtube.com/watch?v=QX04yS
m4TTk&feature=related
• http://www.youtube.com/watch?v=kUm5EiaAxo&feature=related
• http://www.youtube.com/watch?v=PMg_nd
-O688
Sound Intensity I
• Power spreads out as it leaves the source.
• It spreads out but has the same power
even when spread out over a greater area.
• Sound Intensity I: sound power P that
passes perpendicularly through a surface
divided by the area A of that surface:
Example 6: Sound Intensities
• The sound intensity is less at the more
distant surface, where the same power
passes through a threefold greater area.
The ear of a listener, with its fixed area,
intercepts less power where the intensity,
or power per unit area, is smaller. Thus
listener 2 intercepts less of the sound
power than listener 1. With less power
striking the ear, the sound is quieter.
Threshold of Hearing
• For a 1000Hz tone, the smallest sound
intensity that the human ear can detect is
about 1x10^-12W/m2. (threshold of
hearing)
• Intensities greater than 1 W/m2 can be
painful and result in permanent hearing
damage if continuously exposed to them.
• A source emits sound uniformly in all
directions, the intensity depends on
distance.
• If the source is at the center of an
imaginary sphere. The radius of the
sphere is r. Since all the radiated sound
power P passes through the spherical
surface of A =
, the intensity at a
distance r is.
Example 7: Fireworks
16.8 Decibels
• Measurement unit used when comparing
two sound intensities.
• Io is the intensity of the reference level to
which I is being compared and is often the
threshold of hearing.
• Threshold of hearing:
Io = 1.00x10^-12W/m^2
Smallest sound a human ear can detect.
• I is 9dB greater than Io.
• B is called the intensity level, it is not an
intensity and does not have intensity units
of W/m^2.
• Decibel is dimensionless.
• What if I = Io?
• 0dB
• Doesn’t mean sound intensity is zero.
• The sound is interpreted by the brain as
loud or soft, depending on the intensity of
the wave.
• Greater intensities --- louder the sound.
• Though doubling the intensity does not
double the loudness.
• 1dB change in intensity level creates a
small change in loudness to an average
listener.
Example 9: Comparing Sound
Intensities
• To double the loudness of a sound the
intensity must be increased by more than
a factor of two.
• Intensity level increases by 10dB, the new
sound seems approximately twice as loud
as the original sound.
• 70dB seems twice as loud as 60dB
• http://www.youtube.com/watch?v=NcAeK0
yz_Fk
Practice Problem 59.
An amplified guitar has a sound intensity
level that is 14 dB greater than the same
unamplified sound. What is the ratio of the
amplified intensity to the unamplified
intensity?
16.9 The Doppler Effect
• When the source approaches the pitch is
high, as the sources passes the pitch
suddenly drops.
• Austrian physicist Christian Doppler
Doppler effect
• Change in frequency or pitch of the sound
detected by an observer because the
sound source and the observer have
different velocities with respect to the
medium of sound propagation.
Moving Source
• As the source is approaching the
condensations of sound are now closer
together, resulting in a decrease in the
wavelength of the sound.
• “bunching up” occurs because the moving truck
“gains ground” on a previously emitted
condensation before emitting the next one.
• Condensations are closer together, the
observer standing in front of the truck senses
more of them arriving per second (greater
frequency)
• Behind the moving source the
condensations are farther apart than they
are when the truck is stationary.
• Increase in wavelength; lowers frequency;
lower pitch.
• Vs = velocity of the source of sound
• VsT = the distance the source moves
closer or away to the observer.
• The distance between successive
condensations is no longer the wavelength
but is the wavelength that is shortened or
lengthened by the amount VsT.
• Frequency perceived by the stationary
observer as Fo, where the subscript “o”
stands for “observer”
• Fo is equal to the speed of sound V
divided by the shortened wavelength.
• Expression for Fo can be arranged to give
the following result:
Fo – Fs = Doppler Shift
Magnitude depends on the ratio of the
speed of the source Vs to the speed of the
sound V.
When the siren moves away from, rather
than toward, the observer, the wavelength
becomes greater than the original
wavelength.
Source moving away from stationary
observer.
• http://www.fearofphysics.com/Sound/dopw
hy1.html
Example 10: The Sound of a
Passing Train
A high-speed train is traveling at a speed of
44.7 m/s when the engineer sounds the
415Hz warning horn. The speed of sound
is 343m/s. What are the frequency and
wavelength of the sound, as perceived by
a person standing at a crossing, when the
train is (a) approaching and (b) leaving the
crossing?
Moving Observer
• Sound source is stationary
• Observer moves
• Vot = distance covered by observer
• Observer encounters mover
condensations. Distance /distance of
wavelength
Observer moving toward stationary source.
• Observer moving away from stationary
source
General Case
• Both the sound source and the observer
are moving with respect to the medium of
sound propagation.
• Medium is stationary
Eq. 16.11-16.14 are combined
Source and
Observer both
moving
In Numerator:
• Plus sign when the observer moves
toward the source.
• Minus sign when the observer moves
away the source.
In Denominator:
• Minus sign when the source moves toward
the observer.
• Plus sign when the source moves away
from the observer.
In class partner open book quiz.