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Two trains A and B moving with speeds 20...

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

A

310 Hz

B

330 Hz

C

350 Hz

D

290 Hz

Text Solution

Verified by Experts

The correct Answer is:
A
For the 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))=775 Hz`
`f_(2) =1120 ((340-30)/(340-20))=1085 Hz`
Therefore, spread of frequency, `f_(2)' = f_(1)' = 310 Hz`.
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