Question

The apparent frequency of the whistle of an engine changes in the ratio 6:5 as the engine passes a stationary observer. If the velocity of sound is 330ms^-1 what is the velocity of the engine?

Answer 1

Let f be frequency of the sound emitted by the engine and vs be its velocity. The apparent frequency f of the whistle as the engine is approaching the observer is, 

But v = 330 ms^-1

Let f” be the apparent frequency of the sound heard when the engine is moving away from the observer. Then But v = 330 ms^-1

Cross multiplying

6 × (330 – v_s) = 5 × (330 + v_s)

330 × 6 – 6V_s = 5 × 330 + 5 v_s

330 × 6 – 330 × 5 = 5v_s + 6v_s

330 (6 – 5) = 11v_s

330 × 1 = 11 v_s

∴ v_s = 330/11 = 30 ms^-1.