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PHYSICS 231 Lecture 35: Sound

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

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PHYSICS 231 Lecture 35: Sound

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  1. PHYSICS 231Lecture 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 PHY 231

  2. Sound: longitudinal waves PHY 231

  3. 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

  4. 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) PHY 231

  5. 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 231

  6. Intensity Faintest sound we can hear: I~1x10-12 W/m2 (1000 Hz) Loudest sound we can stand: I~1 W/m2 (1000 Hz) Factor of 1012? Loudness works logarithmic… PHY 231

  7. 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 231

  8. 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 231

  9. example A machine produces sound with a level of 80dB. How many machines can you add before exceeding 100dB? 1 machine 80 dB=10log(I/I0) 8=log(I/I0)=log(I/1E-12) 108=I/1E-12 I1=10-4 W/m2 ?? machines 100 dB=10log(I/I0) 10=log(I/I0)=log(I/1E-12) 1010=I/1E-12 I??=10-2 W/m2 I1/I??=10-4/10-2=1/100 The intensity must increase by a factor of 100; one needs to add 99 machines. PHY 231

  10. Frequency vs intensity 1000 Hz PHY 231

  11. 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 I~A2 PHY 231

  12. 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

  13. 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r2) r=1 I=P/(4r2)=P/(4) 1 r=2 I=P/(4r2)=P/(16) 4 r=3 I=P/(4r2)=P/(36) 9 I1/I2=r22/r12 PHY 231

  14. 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: 70dB=10log(I/I0) I=1010I0=10-5 W/m2 ICherryLane/IAbbott=rAbbott2/rCherryLane2 Iabbott=Icherrylanercherrylane2/rabbott2=7.3x10-8 W/m2 Sound level: 49dB (normal conversation) PHY 231

  15. Wave fronts PHY 231

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

  17. 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 PHY 231

  18. 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 PHY 231

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

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

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

  22. 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? vsound=343 m/s a) b) PHY 231

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