Question

17. An ambulance at rest blows a siren of frequency 700 Hz. A vertical reflecting board

which is moving at constant velocity 4 ms¹ towards the ambulance. How many beats
per 5 seconds can be heard by the driver in the ambulance?
(The speed of sound is 350 ms ¹)

Answer 1

In this case the board is moving towards the observer so the board will receive the frequency as a moving observer

The board then emits the sound received and becomes a moving source according to the driver in the ambulance

f' = f (V + Vo) / V where V is the speed of sound and f' is the frequency received by the moving board

Now the board becomes a moving source and

f' = f (V / (V - Vs) and V is again the speed of sound

Combining these equations we get

f = (V + Vo) / (V - Vs) = 700 (350 + 4) / (350 - 4) = 716 / s

The driver would hear 16 beats / sec

Note: one can do these separately

f' = 700 * (350 + 4) / 350 = 708 frequency received for moving observer

f' = 708 * 350 / (350 - 4) = 716 / sec moving source stationary observer

Every 5 sec one would hear 5 * 16 = 80 beats