Two trains `A and B` moving with speeds `20m//s` and `30m//s` respectively in the same direction on the same straight track, with `B` ahead of `A`. The engines are at the front ends. The engine of train `A` blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from `f_(1) = 800 Hz` to `f_(2) = 1120 Hz`, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus `320 Hz`. The speed of sound in still air is `340 m//s`.
(4) The speed of sound of the whistle is

Options

A. 340 m/s for passengers in A and 310 m/s for passengers in B
B. 360 m/s for passengers in A and 310 m/s for passengers in B
C. 310 m/s for passengers in A and 360 m/s for passengers in B
D. 340 m/s for passengers in both the trains.

Answer

B

Explanation

Sound is mechanical wave and hence it will be relative velocity as observed by passengers in both the trains.
For A sound is moving opposite to motion of train hence relative velocity becomes 340 + 20 = 360 m/s. Whereas in case of B sound and train both are moving in the same direction hence speed of sound as observed by the passenger in train B will be 340 - 30 = 310 m/s. Hence option (b) is correct.