The engine of a train moving with speed 10 ms⁻¹ towards a platform sounds a whistle at frequency 400 Hz. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air =330 ms⁻¹ )

Solution

Physics sir · 3 steps

The whistle and the passenger ride the same train, so neither moves relative to the other. No Doppler shift.

1. Who moves. The engine (source) and the passenger (observer) both move forward at 10 m s⁻¹. The passenger sits behind the engine, so sound has to travel backwards along the train to reach them.
2. Doppler formula. The observer moves towards the source at 10 m s⁻¹, which adds 10 on top. The source moves away from the observer at 10 m s⁻¹, which adds 10 on the bottom.

   f' = f (v + u)/(v + u) = 400 × (330 + 10)/(330 + 10) = 400 Hz

3. So. The two effects cancel exactly, so the passenger hears the true frequency, 400 Hz, which is option (c). The platform is irrelevant here.

The idea to keep. A Doppler shift needs relative motion between source and observer. If both move with the same velocity in still air, the heard frequency equals the emitted one.

Answer from the NTA final answer key. Solution by PrepWiser.