PHYSICS 231 Lecture 35 Sound Hello Darkness my

PHYSICS 231 Lecture 35: Sound Hello Darkness, my old friend I’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 brain Still remains, Within the sound of silence. Paul Simon-1964 Remco Zegers Question hours: Thursday 12: 00 -13: 00 & 17: 15 -18: 15 Helproom 1 PHY 231

Sound: longitudinal waves PHY 231 2

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: v=331 (T/273 K) so v=343 m/s at room temperature PHY 231 3

Quick quiz The speed of sound in air is affected in changes in: (more than one possible) a) wavelength b) frequency c) temperature d) amplitude e) none of the above answer c) PHY 231 4

Intensity: rate of energy flow through an area Power (P) J/s A (m 2) I=P/A (J/m 2 s=W/m 2) 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 231 5

Intensity Faintest sound we can hear: I~1 x 10 -12 W/m 2 (1000 Hz) Loudest sound we can stand: I~1 W/m 2 (1000 Hz) Factor of 1012? Loudness works logarithmic… PHY 231 6

decibel level =10 log(I/I 0) y=log 10 x log(ab) log(a/b) log(an) I 0=10 -12 W/m 2 inverse of x=10 y =log(a)+log(b) =log(a)-log(b) =nlog(a) PHY 231 (y=ln(x) x=ey) 7

decibels =10 log(I/I 0) I 0=10 -12 W/m 2 An increase of 10 d. B: intensity of the sound is multiplied by a factor of 10. 2 - 1=10 10=10 log(I 2/I 0)-10 log(I 1/I 0) 10=10 log(I 2/I 1) 1=log(I 2/I 1) 10=I 2/I 1 I 2=10 I 1 PHY 231 8

example A machine produces sound with a level of 80 d. B. How many machines can you add before exceeding 100 d. B? 1 machine 80 d. B=10 log(I/I 0) 8=log(I/I 0)=log(I/1 E-12) 108=I/1 E-12 I 1=10 -4 W/m 2 ? ? machines 100 d. B=10 log(I/I 0) 10=log(I/I 0)=log(I/1 E-12) 1010=I/1 E-12 I? ? =10 -2 W/m 2 I 1/I? ? =10 -4/10 -2=1/100 The intensity must increase by a factor of 100; one needs to add 99 machines. PHY 231 9

Frequency vs intensity 1000 Hz PHY 231 10

Relation between amplitude and intensity A x xharmonic(t)=Acos( t) -A time (s) For sound, the intensity I goes linear with the amplitude of the longitudinal wave squared I~A 2 PHY 231 11

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? PHY 231 12

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. I=Power/Surface=P/A=P/(4 r 2) r=1 r=2 r=3 I=P/(4 r 2)=P/(4 ) I=P/(4 r 2)=P/(16 ) I=P/(4 r 2)=P/(36 ) 1 4 9 I 1/I 2=r 22/r 12 PHY 231 13

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 70 d. B (vacuum cleaner), what is the sound level at Abbott? Cherry Lane: 70 d. B=10 log(I/I 0) I=1010 I 0=10 -5 W/m 2 ICherry. Lane/IAbbott=r. Abbott 2/r. Cherry. Lane 2 Iabbott=Icherrylanercherrylane 2/rabbott 2=7. 3 x 10 -8 W/m 2 Sound level: 49 d. B (normal conversation) PHY 231 14

Wave fronts PHY 231 15

Doppler effect: a non-moving source vsound source f=vsound/ you PHY 231 16

doppler effect: a source moving towards you the distance between the wave front is shortened vsource you prime’: heard observable The frequency becomes larger: higher tone PHY 231 17

doppler effect: a source moving away from you the distance between the wave front becomes longer vsource you source The frequency becomes lower: lower tone PHY 231 18

doppler effect: you moving towards the source vsound source you PHY 231 19

doppler effect: you moving away from the source vsound source you PHY 231 20

doppler effect: general source you vobserver: positive if moving towards to source vsource: positive if moving towards the observer PHY 231 21

example A police car using its siren (frequency 1200 Hz) is driving west over Grand River with a velocity of 25 m/s. You are driving east over grand river, also with 25 m/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? vsound=343 m/s a) b) PHY 231 22