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`.
The speed of sound of the whistle is

Options

A. 310 Hz
B. 330 Hz
C. 350 Hz
D. 290 Hz

Answer

A

Explanation

For thr passengers in train B, observer is receding with velocity 30 m/s and source is approaching with velocity 20 m/s
`:. f_(1)=800((340-30)/(340-20))=775Hz`
and `f_(2)=1120((340-30)/(340-20))=1085Hz`
`:.` Spread of frequency
`= f_(2) - f_(1) = 310 Hz`