Sound
Sound travels as a longitudinal wave
(like a slinky).
 A sound wave needs a medium in
which to travel (like air or water).
 The speed of sound in air depends
on the temperature of the air.
 Vsound = (331 m/s)  [1 + (T/273)]
 T = temperature of air in º C.
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Speed of sound - example
What is the speed of a sound wave
in air at 22.0º C (room
temperature)?
 Vsound = (331 m/s)  [1 + (T/273)]
 Vsound = (331 m/s)  [1 + (22/273)]
 Vsound = 344 m/s
 Use this value for the speed of
sound if a temperature isn’t given.
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Sound and music
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Musically, each note has a characteristic
frequency.
For example, a low C has a frequency of
261.6 Hz, a D has a frequency of 293.7
Hz, an E has a frequency of 329.6 Hz
Note that this does NOT correspond to a
directly linear relationship between note
and frequency.
Standing waves
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A standing wave is the result of
identical waves traveling in opposite
directions.
It has nodes (a stationary amplitude
of zero) and anti-nodes (a maximum
amplitude that is stationary).
Nodes and anti-nodes on a
standing wave
Strings and music
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Plucking, striking, or bowing a string sets
up a standing wave.
Nodes (stationary zero amplitude) must
exist at the ends of the string (cuz the
ends are attached and can’t move)
Antinodes (stationary maximum
amplitude) exist at regularly spaced
intervals throughout the string.
Air columns and music
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An instrument often consists of a column
of air that resonates at frequencies.
The length of the column of air
determines the frequency at which it
resonates (and so the note that is heard).
The length can be changed by opening
and closing keys (like on a trumpet or
flute) or by extending the slide of a
trombone.
We study 2 types of air columns:
Closed-end air columns:
A closed-end air column is closed at
one end.
 A node must be at the closed end.
An anti-node must be at the open
end.
 A wave (with wavelength λ) will
resonate in a closed end air column
of length L if: λ = 4L.
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Open-end air columns:
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An open-end air column is open at both
ends.
Anti-nodes must be at each open end.
A wave (with wavelength λ) will resonate
in an open end air column of length L if: λ
= 2L.
Both open and closed end air columns will
resonate at more than 1 frequency (called
harmonics).
Open & Closed End Air Columns
Sound demo and activity
Demo of sound in a vacuum.
 Speed of sound of music lab.
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Beats
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When 2 notes of different frequencies
sound at the same time, a phenomenon
called “beats” occurs in which the
loudness varies at a regular intervals.
The frequency of the beats = |f2–f1|
If 450 Hz and 457 Hz are sounded at the
same time, an observer will hear 7 beats
per second.
Beats picture
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If we added the amplitude of waves a +
b, we would get wave c.
If t2 = 1 sec, then wave a has 2.5
waves/second = 2.5 Hz. Wave b = 3 Hz.
fbeats = .5 Hz (once every 2 seconds it has
complete destructive interference - a
node)
Octaves
A note an octave above is twice the
frequency.
 So if a note had a frequency of 250
Hz, what would be the frequency of
the note an octave above?
 2(250 Hz) = 500 Hz
 What would be the frequency of the
note an octave above that?
 2(500 Hz) = 1000Hz
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Echoes
An echo travels there and back
again.
 It travels twice the distance in twice
the time.
 If it takes t seconds for the echo to
return from a surface, then it took
½t to get to the surface.
 If a surface is d meters away, then
the echo will travel 2d meters.
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Echoes - example
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If a physics student screams towards the
whiteboard, and hears the echo of her
scream 0.26 seconds later, how far away
is the whiteboard? Assume room
temperature.
The time it took the scream to reach the
whiteboard is ½ (.26 s) = 0.13 s.
v = d/t
344 m/s = d/.13 s
d = 45 m (big classroom!)
Doppler Effect
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Doppler effect – a change in the
observed frequency of waves (light or
sound) stemming from motion of the
source and/or observer relative to each
other.
Lucky you, you live in the MidWest and
hear the Doppler effect regularly.
Hint: it is a train whistle
Doppler is due to relative motion
between source and observer
In figure a, the source is stationary and λ (the distance btwn the
waves) is constant. In figure b, the source is moving towards
observer A, and λ decreases for observer A. At the same time, λ
increases for observer C (because the source is moving away).
Doppler simulation
This simulation shows waves being
generated by a moving source.
 The wavelength is shorter in front of
the moving source, and longer in
back of the moving source.
 Click here for the simulation.
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Doppler Equations
For observer and source
approaching each other:
 fo = f (v + vo) / (v – vs)
 Where fo = observed frequency (Hz)
 f = frequency of sound or light (Hz)
 v = velocity of sound or light (m/s)
 vo = velocity of observer (m/s)
 vs = velocity of source (m/s)
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Doppler Equations
For observer and source moving
away from each other:
 fo = f (v - vo) / (v + vs)
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Doppler Example
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What is the observed frequency of a 225
Hz train whistle as heard by a passenger
in a car moving at 10 m/s towards a train
that is oncoming at 25 m/s? Assume
room temperature.
f = 225 Hz
v = 344 m/s
vo = 10 m/s
vs = 25 m/s
Doppler Example
 fo = f (v + vo) / (v - vs)
 fo = 225 Hz (344 m/s + 10 m/s) / (344 m/s – 25
m/s)
 fo
= 250 Hz
Doppler Explanation
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Note that the frequency is higher when
the observer and source are approaching
each other. This corresponds to a higher
pitch.
Similarly, the frequency (and pitch) is
lower when the observer and source are
moving away from each other.
In part, this lower pitch is why a receding
train whistle is called a “melancholy” or
“plaintive” sound.
See? Physics really is everywhere.
Remember waves that are closer together
are higher in frequency and pitch, farther
apart are lower in frequency and pitch
Doppler effect influences sound,
light, and any type of wave
References
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http://www.revisionworld.com/files/wave.jpg
http://www.physics.uc.edu/~sitko/CollegePhysicsIII/14Sound/Sound_files/image035.jpg
http://electron9.phys.utk.edu/phys135d/modules/m10/im
ages/stand.gif
http://www.pas.rochester.edu/~afrank/A105/LectureVI/FG
03_005_PCT.gif
http://www.ifa.hawaii.edu/~stockton/a110/imag
es/Doppler_effect.jpg
http://www.phschool.com/atschool/science_activity_librar
y/images/properties_sound_doppler.jpg
http://www.ifa.hawaii.edu/~barnes/ast110_06/tsaas/Dop
pler_effect.jpg