Post on 25-Feb-2016
description
PHY 2311
PHYSICS 231Lecture 35: Sound
Remco ZegersQuestion hours: Thursday 12:00-13:00 & 17:15-
18:15Helproom
Hello Darkness, my old friendI’ve 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 brainStill remains,Within the sound of silence.
Paul Simon-1964
PHY 2312
Sound: longitudinal waves
PHY 2313
The speed of soundDepends on the how easy the material is compressed (elastic property) and how much the material resistsacceleration (inertial property)
v=(elastic property/inertial property)
v=(B/) B: bulk modulus : density
The velocity also depends ontemperature. In air:
v=331(T/273 K)
so v=343 m/s at room temperature
PHY 2314
Quick quizThe speed of sound in air is affected in changes in:(more than one possible)a) wavelengthb) frequencyc) temperatured) amplitudee) none of the above
answer c)
PHY 2315
Intensity
Intensity: rate of energy flow through an area
Power (P) J/s A (m2)
I=P/A (J/m2s=W/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.
PHY 2316
IntensityFaintest sound wecan hear: I~1x10-12 W/m2
(1000 Hz)Loudest sound we canstand: I~1 W/m2
(1000 Hz)
Factor of 1012? Loudness works logarithmic…
PHY 2317
decibel level =10log(I/I0) I0=10-12 W/m2
y=log10x inverse of x=10y (y=ln(x) x=ey) log(ab) =log(a)+log(b)log(a/b) =log(a)-log(b)log(an) =nlog(a)
PHY 2318
decibels=10log(I/I0) I0=10-12 W/m2
An increase of 10 dB:intensity of the sound is multiplied by a factor of 10.
2-1=10 10=10log(I2/I0)-10log(I1/I0) 10=10log(I2/I1) 1=log(I2/I1) 10=I2/I1 I2=10I1
PHY 2319
exampleA machine produces sound with a level of 80dB. Howmany machines can you add before exceeding 100dB?1 machine80 dB=10log(I/I0)8=log(I/I0)=log(I/1E-12)108=I/1E-12I1=10-4 W/m2
?? machines100 dB=10log(I/I0)10=log(I/I0)=log(I/1E-12)1010=I/1E-12I??=10-2 W/m2
I1/I??=10-4/10-2=1/100The intensity must increase by a factor of 100;one needs to add 99 machines.
PHY 23110
Frequency vs intensity
1000 Hz
PHY 23111
Relation between amplitude and intensity
time (s)
A
-A
x xharmonic(t)=Acos(t)
For sound, the intensity I goes linear with theamplitude of the longitudinal wave squared
I~A2
PHY 23112
Intensity and distance from the source
Sound from a point source produces a spherical wave.Why does the sound get fainter further away fromthe source?
PHY 23113
Intensity and distanceThe amount of energy passingthrough a spherical surfaceat distance r from the sourceis constant, but the surfacebecomes larger.
I=Power/Surface=P/A=P/(4r2)
r=1 I=P/(4r2)=P/(4) 1r=2 I=P/(4r2)=P/(16) 4r=3 I=P/(4r2)=P/(36) 9
I1/I2=r22/r1
2
PHY 23114
ExampleA person living at Cherry Lane (300 m from the rail track)is tired of the noise of the passing trains and decides tomove to Abbott (3.5 km from the rail track). If the soundlevel of the trains was originally 70dB (vacuum cleaner), what is the sound level at Abbott?
Cherry Lane: 70dB=10log(I/I0) I=1010I0=10-5 W/m2
ICherryLane/IAbbott=rAbbott2/rCherryLane
2
Iabbott=Icherrylanercherrylane2/rabbott
2=7.3x10-8 W/m2
Sound level: 49dB (normal conversation)
PHY 23115
Wave fronts
PHY 23116
Doppler effect: a non-moving source
source you
vsoundf=vsound/
PHY 23117
doppler effect: a source moving towards you
source you
the distance betweenthe wave front is shortened
sourcesound
sound
sourcesoundsource
vvvfvf
fv
fv
fv
The frequency becomes larger: higher tone
vsource
prime’: heard observable
PHY 23118
doppler effect: a source moving away from you
sourceyou
the distance betweenthe wave front becomes longer
!!!: negativevvv
vfvf
fv
fv
fv
source
sourcesound
sound
sourcesoundsource
The frequency becomes lower: lower tone
vsource
PHY 23119
doppler effect: you moving towards the source
source you
vsound
sound
soundobserverobserver
vvvfvff
observerv
:secondper detected s wavefrontadditional
PHY 23120
doppler effect: you moving away from the source
source you
vsound
negativev
vvvfvff
observer
sound
soundobserverobserver
:
v:secondper
detected s wavefrontadditional
observer
PHY 23121
doppler effect: general
source you
source
observer
vvvvff
vobserver: positive if moving towards to sourcevsource: positive if moving towards the observer
PHY 23122
exampleA police car using its siren (frequency 1200Hz) is drivingwest over Grand River with a velocity of 25m/s. Youare driving east over grand river, also with 25m/s.a)What is the frequency of the sound from the siren thatyou hear? b) What would happen if you were also driving west?vsound=343 m/s
Hz
f
vvvvffsource
observer
138916.1120025343253431200
a) b)
Hz
f
vvvvffsource
observer
1200.11200)25(343
253431200