question_answer

A long train is moving on a circular track. The speed of train remains constant during motion. Engine of the train is emitting a sound of frequency \[{{f}_{0}}\]. The frequency observed by the guard at the rear end of the train is

A) is equal to \[{{f}_{0}}\]

B) is less than \[{{f}_{0}}\]

C) is more than \[{{f}_{0}}\]

D) may be greater than, less than or equal to \[{{f}_{0}}\]depending on speed and length of train.

Correct Answer: A

Solution :

[a] \[f={{f}_{0}}\left( \frac{v\pm {{v}_{0}}}{v\pm {{v}_{S}}} \right)={{f}_{0}}\left( \frac{v+u\cos \theta }{v+u\cos \theta } \right)={{f}_{0}}\] where 'u' is speed of train.