Question

A train is moving with constant speed along a circular track. If length of the train is one fourth of the length of circular track then which of the following is/are correct options ? (Assume that source of the sound is at engine)

• A. Frequency observed by a passenger who is sitting in the middle of train (equidistant from front and rear end) will continuously increase.
• B. Frequency observed by a passenger who is sitting in the middle of train (equidistant from front and rear end) will remain constant but more than actual frequency.
• C. Frequency observed by a passenger who is sitting in the middle of train (equidistant from front and rear end) will remains constant and equal to actual frequency.
• D. Wavelength observed by the person who is on the rear end of train is more than the actual wavelength of sound wave.

Answer 1

Answer: (C), (D)

The correct options are
C Frequency observed by a passenger who is sitting in the middle of train (equidistant from front and rear end) will remains constant and equal to actual frequency.
D Wavelength observed by the person who is on the rear end of train is more than the actual wavelength of sound wave.


$f_{obs}=\frac{f(V_s+V\cos \theta )}{(V_s+V\cos \theta )}=f{\lambda }_{obs}=\frac{(V_s+V\cos \theta )}{f}$
For any observer in train frequency observed is equal to original frequency but observed wavelength is more.