question_answer

A train is moving with a constant speed along a circular track. The engine of the train emits a sound of frequency\[f\]. The frequency heard by the guard at rear end of the train is

A)  less than\[f\]

B)  equal to\[f\]

C)  is greater than\[f\]

D)  may be greater than, less than or equal to\[f\] depending on the factors like speed of train, length of train and radius of circular track

Correct Answer: B

Solution :

Suppose v be the speed of sound. Then        \[v={{v}_{o}}={{v}_{s}}\] and        \[f=f\left( \frac{v+{{v}_{o}}\cos \theta }{v+{{v}_{s}}\cos \theta } \right)\]                      \[=f\left( \frac{v+v\cos \theta }{v+v\cos \theta } \right)=f\]