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