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      \[v={{v}_{0}}={{v}_{s}}\] and        \[f=f\left( \frac{v+{{v}_{0}}\cos \theta }{v+{{v}_{s}}\cos \theta } \right)\]                 \[=f\left( \frac{v+v\cos \theta }{v+v\cos \theta } \right)=f\]