Question

A train with a frequency '2f'. What will be the frequency heard by a person sitting in the train? Speed of the train is V.

• A. fv/(330+v)
• B. f(330+v)/330
• C. fv/(330-v)
• D. 2f

Answer 1

Answer: (D)

2f

Answer 2

Explanation of the Solution:

The Doppler effect describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. For a Doppler shift to occur, there must be a non-zero relative velocity between the source and the observer.

In this scenario:

1. Source: The train (or something on it) is emitting sound with a frequency of '2f'.
2. Observer: A person is sitting inside the train.

Since the person is sitting in the train, they are moving at the same velocity 'V' as the source of the sound (the train). Therefore, the relative velocity between the sound source and the observer is zero ($V_{relative} = V_{source} - V_{observer} = V - V = 0$).

When there is no relative motion between the source and the observer, there is no Doppler shift. The frequency heard by the observer will be exactly the same as the frequency emitted by the source.

Thus, the frequency heard by the person sitting in the train is '2f'.