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A train standing a the outer signal of a...

A train standing a the outer signal of a railway station blows a whistle of frequency 400Hz in still air .
What is the frequency of the whistle for a platform observer when the train
(i) approaches the platform with a speed of `10ms^(-1)` ?
(ii) recedes from the platform with a speed of `10 ms^(-1)` ?

Text Solution

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(i) given `f=400 Hz, v_s=10 ms^(-1).`
(a) For a source approaching the stationary observer, on the platform, apparent frequency
`f'=f((v)/(v-v_s)),v-v_s=340-10=330 ms^(-1)`.
`& v+v_3=340+10=350 ms^(-1). = (400xx340)/(330)`
`f=412.1 Hz` ie apparent frequency `=412 Hz`
(b) For a source receding away from the stationary observer apparent frequency
`f'=f((v)/(f+v_s))=(400xx340)/(350)=388.6 Hz`
i.e. `f'=387 Hz.`
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