two trains `Aand B` moving with speeds `20m//s` and `30m//s` respectively in the same direction on the same straight track, with `B` ahesd 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 spread of frequency as observed by the passenger in train `B` is

Options

A. (a) `310 Hz`
B. (b ) `330 Hz`
C. ( c ) `350 Hz`
D. (d) `290 Hz`

Answer

A

Explanation

(a) `v' = v_(1)[(v - v_(0))/(v - v_(s))] = 800[(340 - 30)/(340 - 20)] = 800 xx (31)/(32)`
`v" = v_(2)[(v - v_(0))/(v - v_(s))] = 1120 xx (31)/(32)`
:. `v" - v' = (1120 - 800) xx (31)/(32) = 320 xx (31)/(32) = 310 Hz`.