A train, standing at the outer signal of a railway station blows a whistle of frequency 400Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of `10ms^(-1)` , (b) receeds from the platform with a speed of `10ms^(-1)`? (ii) What is the speed of sound in each case ? The speed of sound in still air can be taken as `340ms^(-1)`

Explanation

(i) (a)Frequency of the whistle, ν = 400 Hz
Speed of the train,` v_(T)= 10` m/s
Speed of sound, v = 340 m/s
The apparent frequency ,`(v')` of the whistle as the train approaches the platform is given by the relation:
`v'=((v)/(v-v_(T)))v`
`=((340)/(340-10))xx400=412.12 Hz`
(b) The apparent frequency `(v^(n))`of the whistle as the train recedes from the platform is given by the relation:
`v^(n)=((v)/(v+v_(T)))v`
`((340)/(340+10))xx400=388.57 Hz`