PHYSICS 231 Lecture 35: Sound

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PHYSICS 231Lecture 35 Sound
Hello Darkness, my old friend Ive have come to
talk to you again, Because a vision softly
creeping, Left its seed while I was sleeping, And
the vision that was planted in my brain Still
remains, Within the sound of silence. Paul
Simon-1964

• Remco Zegers
• Question hours Thursday 1200-1300
  1715-1815
• Helproom

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Sound longitudinal waves
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The speed of sound
Depends on the how easy the material is
compressed (elastic property) and how much the
material resists acceleration (inertial
property) v?(elastic property/inertial
property) v?(B/?) B bulk modulus ?
density The velocity also depends
on temperature. In air v331?(T/273 K) so
v343 m/s at room temperature
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Quick quiz

• The speed of sound in air is affected in changes
  in
• (more than one possible)
• wavelength
• frequency
• temperature
• amplitude
• none of the above

answer c)
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Intensity
Intensity rate of energy flow through an area
Power (P) J/s
A (m2)
IP/A (J/m2sW/m2)
example If you buy a speaker, it gives power
output in Watts. However, even if you put a
powerful speaker in a large room, the
intensity of the sound can be small.
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Intensity
Faintest sound we can hear I1x10-12 W/m2 (1000
Hz) Loudest sound we can stand I1 W/m2 (1000
Hz)
Factor of 1012? Loudness works logarithmic
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decibel level ?
?10log(I/I0) I010-12 W/m2
ylog10x inverse of x10y (yln(x) xey)
log(ab) log(a)log(b) log(a/b) log(a)-log(b) lo
g(an) nlog(a)
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decibels
?10log(I/I0) I010-12 W/m2
An increase of 10 dB intensity of the sound is
multiplied by a factor of 10.
?2-?110 1010log(I2/I0)-10log(I1/I0)
1010log(I2/I1) 1log(I2/I1)
10I2/I1 I210I1
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example
A machine produces sound with a level of 80dB.
How many machines can you add before exceeding
100dB?
1 machine 80 dB10log(I/I0) 8log(I/I0)log(I/1E-1
2) 108I/1E-12 I110-4 W/m2
?? machines 100 dB10log(I/I0) 10log(I/I0)log(I/
1E-12) 1010I/1E-12 I??10-2 W/m2
I1/I??10-4/10-21/100 The intensity must
increase by a factor of 100 one needs to add 99
machines.
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Frequency vs intensity
1000 Hz
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Relation between amplitude and intensity
A
xharmonic(t)Acos(?t)
x
time (s)
-A
For sound, the intensity I goes linear with
the amplitude of the longitudinal wave
squared IA2
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Intensity and distance from the source
Sound from a point source produces a spherical
wave. Why does the sound get fainter further away
from the source?
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Intensity and distance
The amount of energy passing through a spherical
surface at distance r from the source is
constant, but the surface becomes
larger. IPower/SurfaceP/AP/(4?r2)
r1 IP/(4?r2)P/(4?) 1 r2
IP/(4?r2)P/(16?) 4 r3 IP/(4?r2)P/(36?)
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I1/I2r22/r12
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Example
A person living at Cherry Lane (300 m from the
rail track) is tired of the noise of the passing
trains and decides to move to Abbott (3.5 km from
the rail track). If the sound level of the trains
was originally 70dB (vacuum cleaner), what is
the sound level at Abbott?
Cherry Lane 70dB10log(I/I0) I1010I010-5
W/m2 ICherryLane/IAbbottrAbbott2/rCherryLane2 Iab
bottIcherrylanercherrylane2/rabbott27.3x10-8
W/m2 Sound level 49dB (normal conversation)
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Wave fronts
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Doppler effect a non-moving source
fvsound/?
vsound
source
you
?
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doppler effect a source moving towards you
the distance between the wave front is shortened
vsource
source
you
prime heard observable
The frequency becomes larger higher tone
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doppler effect a source moving away from you
the distance between the wave front becomes longer
vsource
source
you
The frequency becomes lower lower tone
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doppler effect you moving towards the source
vsound
source
you
?
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doppler effect you moving away from the source
vsound
source
you
?
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doppler effect general
source
you
vobserver positive if moving towards to
source vsource positive if moving towards the
observer
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example
A police car using its siren (frequency 1200Hz)
is driving west over Grand River with a velocity
of 25m/s. You are driving east over grand river,
also with 25m/s. a)What is the frequency of the
sound from the siren that you hear? b) What would
happen if you were also driving west? vsound343
m/s
a)
b)