Doppler effect and Shock waves

1. Lecture 10 Doppler effectandShock waves Pre-reading: §16.8–16.9 Please take a clicker and an evaluation form

2. Doppler Effect • Change in perceived frequency due to relative motion of a source (S) and listener (L) Stationary Source Moving Source

4. Doppler Effect • Change in perceived frequency due to relative motion of a source (S) and listener (L) • Case 1: Source at rest, Listener movingfL = (1 + vL/v) × fS • Case 2: Source and Listener moving • Pay attention to sign of vL, vS ! (positive from L to S) • For light wavesfL = √[ (c–v) / (c+v) ] × fS c = 3.0 × 108 ms–1

6. Doppler Effect • Change in perceived frequency due to relative motion of a source (S) and listener (L) • Case 1: Source at rest, Listener movingfL = (1 + vL/v) × fS • Case 2: Source and Listener moving • Pay attention to sign of vL, vS ! (positive from L to S) • For light wavesfL = √[ (c–v) / (c+v) ] × fS c = 3.0 × 108 ms–1

7. Stationary Source Moving Source

8. Clicker questions A bird flies in a circle centred on a person’s head and emits a continuous sinusoidal sound wave with frequency of f = 1000 Hz.

9. d A bird flies in a circle centred on a person’s head and emits a continuous sinusoidal sound wave with frequency of f = 1000 Hz. Now there is another person standing a large distance away.

10. Shock Waves • What if speed of source is equal to or greater than the speed of sound? vS = vsound vS > vsound

11. This is exactly analogous to the bow wave produced by a swimmer moving faster than the speed of the waves on water. Bow wave produced by a platypus swimming

12. Shock Waves F/A-18 “Hornet”

13. Shock Waves • What if speed of source is equal to or greater than the speed of sound? vS = vsound vS > vsound

14. Shock Waves • The waves ‘pile up’ at surface • When that surface hits your ears, you hear very loud sound: sonic boom • If vS > v(sound), the surface has the shape of a cone with an opening angle α where • vS/vis called the Mach number

15. Clicker questions The diagram shows the wavefronts generated by an airplane flying past an observer A at a speed greater than that of sound.

16. The carillon in the Quad is ringing. You are so excited to have finished your Physics lecture and get to lunch that you run towards the Quad at twice the speed of sound. As you approach the bells, they sound • higher pitched than normal • lower pitched than normal • like a sonic boom

17. That’s all, folks!