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)` ?

Explanation

given f =400 Hz, `v_(s) = 10 ms^(-1)`
(i) 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) = ( 400 xx 340)/( 330)`
`f' = 412.1 Hz` ie apparent frequency = 412 Hz
(ii) For a source receding away from the stationary observer apparent frequency
`f' = f (( v)/( v+v_(s))) = ( 400 xx 340)/( 350) = 388.6 Hz`