The engine of a train sound a whistle at frequency `v`, the frequency heard by a passenger is

Options

A. `gtv`
B. `ltv`
C. `=1/v`
D. `=v`

Answer

To solve the problem of determining the frequency heard by a passenger on a train when the engine sounds a whistle at frequency \( \nu \), we can apply the principles of the Doppler effect.

### Step-by-Step Solution:

1. **Understanding the Doppler Effect**: The Doppler effect describes how the frequency of a wave changes for an observer moving relative to the source of the wave. If the observer is moving towards the source, they perceive a higher frequency, and if they are moving away, they perceive a lower frequency.

2. **Identifying the Observer and Source**: In this scenario, the source of the sound is the train's whistle, which emits a sound at frequency \( \nu \). The observer is the passenger on the train.

3. **Analyzing the Relative Motion**: Since the passenger is traveling with the train, there is no relative motion between the passenger (observer) and the train (source). This means that the passenger is not moving towards or away from the source of the sound.

4. **Determining the Frequency Heard by the Passenger**: Because there is no relative motion, the frequency of the sound heard by the passenger will be the same as the frequency emitted by the source. Therefore, the frequency heard by the passenger is \( \nu \).

5. **Conclusion**: The frequency heard by the passenger is \( \nu \).

### Final Answer:
The frequency heard by the passenger is \( \nu \).