1. PHY 231 1 PHYSICS 231 Lecture 35: Sound Remco Zegers Question hours: Thursday 12:00-13:00 & 17:15-18:15 Helproom 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

2. PHY 231 2 Sound: longitudinal waves

3. 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

4. PHY 231 4 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)

5. PHY 231 5 Intensity 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.

6. PHY 231 6 Intensity Faintest sound we can hear: I~1x10 -12 W/m 2 (1000 Hz) Loudest sound we can stand: I~1 W/m 2 (1000 Hz) Factor of 10 12 ? Loudness works logarithmic…

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

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

9. 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/I 0 ) 8=log(I/I 0 )=log(I/1E-12) 10 8 =I/1E-12 I 1 =10 -4 W/m 2 ?? machines 100 dB=10log(I/I 0 ) 10=log(I/I 0 )=log(I/1E-12) 10 10 =I/1E-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.

10. PHY 231 10 Frequency vs intensity 1000 Hz

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

12. 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?

13. 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  r 2 ) r=1 I=P/(4  r 2 )=P/(4  )1 r=2 I=P/(4  r 2 )=P/(16  )4 r=3 I=P/(4  r 2 )=P/(36  )9 I 1 /I 2 =r 2 2 /r 1 2

14. 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/I 0 ) I=10 10 I 0 =10 -5 W/m 2 I CherryLane /I Abbott =r Abbott 2 /r CherryLane 2 I abbott =I cherrylane r cherrylane 2 /r abbott 2 =7.3x10 -8 W/m 2 Sound level: 49dB (normal conversation)

15. PHY 231 15 Wave fronts

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

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

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

19. PHY 231 19 doppler effect: you moving towards the source source you v sound

20. PHY 231 20 doppler effect: you moving away from the source source you v sound

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

22. 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? v sound =343 m/s a)b)