2. 1© Manhattan Press (H.K.) Ltd. Source moving Observer moving Observer moving 11.5 Doppler effect Both source and observer moving Both source and observer moving

3. 2 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 180) Doppler effect The apparent change in the pitch or frequency of a source of sound when there is relative motion between the source and the observer is known as the Doppler effect. E.g. - Siren of ambulance or police car appears to change its pitch

4. 3 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 181) Doppler effect Image swimmer treading water Swimmer towards A (speed < wave speed) more waves (higher f) less waves (lower f)

5. 4 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 182) Source moving 1. Source approaching observer (A) When the source is approaching the observer, the frequency encountered by the observer is higher.

6. 5 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 183) Source moving 2. Source moving away from observer (B) When the source is moving away from the observer, the frequency encountered by the observer is lower. Go to Example 5 Example 5

7. 6 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 184) Observer moving 1. Observer approaching a stationary source (O) Irrespective of whether the observer or the source is moving towards the other, the apparent frequency is higher.

8. 7 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 185) Observer moving 2. Observer moving away from source (S) Irrespective of whether the observer or the source is moving away from the other, the apparent frequency is smaller. Go to Example 6 Example 6

9. 8 © Manhattan Press (H.K.) Ltd. 11.5 Doppler effect (SB p. 186) Both source and observer moving Go to Example 7 Example 7 If the source and observer approach each other, the apparent frequency is higher. Conversely, the apparent frequency is lower if they are moving away from each other. uouo usus ObserverTo source+ Away from source- SourceTo observer- Away from observer+

10. 9 © Manhattan Press (H.K.) Ltd. End

11. 10 © Manhattan Press (H.K.) Ltd. Q: Q: The frequency of a police car siren is 400 Hz. Calculate the apparent frequency received by a stationary observer when (a) the car approaches him with a speed of 30 m s −1, and (b) the car moves away from him with a speed of 30 m s −1. (Speed of sound = 330 m s −1 ) Solution 11.5 Doppler effect (SB p. 183)

12. 11 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 11.5 Doppler effect (SB p. 183)

13. 12 © Manhattan Press (H.K.) Ltd. Q: Q: A whistle emits sound of frequency 440 Hz. If the speed of sound is 340 m s –1, what are the frequencies of the sounds detected by an observer inside a car which is moving with a velocity of 20 m s –1 (a) towards the whistle, and (b) away from the whistle? Solution 11.5 Doppler effect (SB p. 186)

14. 13 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 11.5 Doppler effect (SB p. 186)

15. 14 © Manhattan Press (H.K.) Ltd. Q: Q: A whistle producing sound of frequency 1 000 Hz moves with a velocity of 50 m s −1. An observer also moves in the same direction with a velocity of 25 m s −1. If the speed of sound in air is 350 m s −1, what is the frequency of the sound heard by the observer? Solution 11.5 Doppler effect (SB p. 187)

16. 15 © Manhattan Press (H.K.) Ltd. Solution: 11.5 Doppler effect (SB p. 187) Situation 1: The source is in front of the observer. Using the sign convention discussed earlier: 1. Since the observer is approaching the source, the velocity of the observer is +u o. 2. Since the source is moving away from the observer, the velocity of the source is +u s.

17. 16 © Manhattan Press (H.K.) Ltd. Solution (cont’d): Return to Text 11.5 Doppler effect (SB p. 187) Situation 2: The source is behind the observer. 1. Since the observer is moving away from the source, hence use -u o. 2. Since the source is moving towards the observer, hence use -u s.