Two trains `A` and `B` are moving with speeds `20 m//s` respectively in the same direction on the same stright track, with `B` ahead of `A`. The engines are at the front ends. The engines 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 figure. The speed in the frequency (highest frequency - lowest frequency) is thus `320 Hz`. The speed of sound in still air is `340 m//s`.

The spread of frequency as observed by the passengers in train `B` is

Options

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

Answer

A

Explanation

As seen from `B`
`f'_(min) = ((340 - 30)/(340 - 20))(800)`
`f'_(max) = ((340 - 30)/(340 - 20))(1120)` ltbr. `f'_(max) - f'_(min) = 310`