Question

A train whistling at constant frequency 'n' is moving towards a station at a constant speed V. The train goes past a stationary observer on the station. The frequency 'n' of the sound as heard by the observer is plotted as a function of time 't'. Identify the correct curve

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is D

The problem involves the Doppler Effect, which describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

When the source (train) is moving towards the observer, the sound waves are compressed, which leads to an increase in the frequency heard by the observer. When the train passes the observer and starts moving away, the sound waves are stretched, and the frequency decreases.

- As the train approaches the observer, the observed frequency will increase.
- When the train passes the observer, the frequency will suddenly drop and become lower than the initial frequency as the train moves away.

The graph that represents this situation will show:
- An increasing frequency as the train approaches the observer.
- A sharp drop in frequency once the train moves past the observer.

This is accurately represented by option (D), where the frequency increases as the train gets closer and drops immediately after it passes.

Answer 2

This problem involves the Doppler effect, where the frequency of sound is perceived differently by an observer depending on the motion of the source and the observer.

• When the train is approaching the observer, the sound frequency increases due to the Doppler effect. As the source moves towards the observer, the observed frequency is higher than the emitted frequency.
• When the train passes the observer, the observed frequency suddenly drops to a lower value as the train moves away.

Thus, the graph of the observed frequency \( n(t) \) with respect to time \( t \) should show an increase in frequency as the train approaches and a decrease as the train moves away.

Option (D) correctly represents this scenario, where the frequency increases as the train approaches and then decreases once it passes the observer.