1. PHY 231 1 PHYSICS 231 Lecture 33: Sound, Doppler and Shock Remco Zegers Question hours:Tue 4:00-5:00 Helproom

2. PHY 231 2 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

3. PHY 231 3 Frequency vs intensity 1000 Hz

4. PHY 231 4 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.

5. PHY 231 5 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

6. PHY 231 6 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?

7. PHY 231 7 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

8. PHY 231 8 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?

9. PHY 231 9 Wave fronts

10. PHY 231 10 Doppler effect: a non-moving source source you v sound f=v sound /

11. PHY 231 11 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

12. PHY 231 12 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

13. PHY 231 13 doppler effect: you moving towards the source source you v sound

14. PHY 231 14 doppler effect: you moving away from the source source you v sound

15. PHY 231 15 doppler effect: general source you v observer : positive if moving towards to source v source : positive if moving towards the observer

16. PHY 231 16 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)

17. PHY 231 17 applications of the doppler effect: speed radar

18. PHY 231 18 applications of doppler effect: weather radar Both humidity (reflected intensity) and speed of clouds (doppler effect) are measured.

19. PHY 231 19 shock waves what happens if v source  v sound ?

20. PHY 231 20 shock waves II high-pressure wave a lot of energy is stored in the wave (loud bang, vibrations, broken windows) sin  =v sound /v source v source /v sound : Mach Mach 1: speed of sound. Mach 2: 2x speed of sound etc

21. PHY 231 21 shock waves: passing jet

22. PHY 231 22 example you jet A low-flying jet passes by at 300m away from you. When it is 1 km further, you hear the sonic shock-wave. What was the speed of the jet in mach? 300m 1000m