Question

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

• 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)

Wavelength observed by the person who is on the rear end of train is more than the actual wavelength of sound wave.


$f_{\text{obs}}=\frac{f[v_s+v\cos \theta ]}{[v_s+v\cos \theta ]}=f$
${\lambda }_{obs}=\frac{v_s+v\cos \theta }{f}$
For any observer in train, frequency observed is equal to original frequency but observed wavelength is more.