1. PHY 102: Waves & Quanta Topic 5 Sound John Cockburn (j.cockburn@... Room E15)

2. Sound Waves Speed of sound in fluids in fluids, gases and solids Doppler Effect Beats

3. Sound waves Unlike waves on a string (transverse waves), sound waves are longitudinal waves Particles undergo SHM about equilibrium positions PARALLEL to direction of wave propagation Compression/rarefaction of the medium through which the sound wave travels……………………………………………… Wave travelling from left to right/right to left still described by: But this time, y is in same direction as x……

4. Sound waves (Ear, for example is sensitive to pressure, not dislacement Fluctuations)

5. Speed of sound In a fluid: Bulk modulus density In a solid rod: Young’s modulus

6. Speed of sound

7. The Doppler Effect If we stand still near a source of sound, and the source is also not moving we hear sound of a certain frequency f 0 If either, or both, the listener and the source are moving relative to one another, then a different frequency f L is heard by the listener. In general, if the listener and the source are moving towards each other, f L > f 0, ie a higher pitch is heard. If the listener and the source are moving away from each other, f L <f 0, ie a lower pitch is heard. This is known as the Doppler Effect Ambulance sirens, car horns, etc. etc.

8. Explanation of the Doppler Effect Listener moving towards stationary source with velocity v L

9. Explanation of the Doppler Effect Effective velocity of sound heard by listener = v L +v: Moving listener, stationary source

10. Moving Source It takes a time T for one complete cycle of the wave to be emitted. (T = 1/f 0 ) During this time, the wavefront has moved a distance vT, and the source has moved a distance v s T The wavelength is: In front of source Behind source

11. Moving listener approaching moving source (Stationary source, earlier slide) (Modified λ, due to moving source)

12. And now the good news…………………… Works for ALL relative motions of source and listener in acoustic Doppler shift calculations, PROVIDED you DEFINE the positive direction as the listener to source direction, and set the signs of v L and v s accordingly…………………………………………………………………………… ………

13. Example calculations Two train whistles A and B each have a frequency of 392 Hz. A is stationary, while B is moving to the right, away from A, at a speed of 35ms -1. A listener is between the 2 trains and is also moving to the right, with a speed of 15ms -1. What frequencies does the listener hear from whistles A and B? (speed of sound in air = 340ms -1 )

14. Whistle A Positive direction

15. Whistle B Positive direction

16. A police car (whose driver has clearly been watching too much Starsky and Hutch), with a 300Hz siren is approaching a warehouse at 30ms -1 with the intention of crashing through the door. What frequency does the driver hear reflected from the warehouse? (speed of sound in air = 340ms -1 ) Two part question………………………..

17. In the first part, treat the warehouse door as the “listener”….. Sound at this frequency is reflected back towards the police car. This becomes the “new” f 0 for the 2 nd part of the question…………………..

18. Now, the warehouse door is the stationary source of the reflected sound……..

19. Beats These occur from the superposition of 2 waves of close, but different frequency: