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

(a) If the observer be at rest and the source is movi g towards the observer, then
`v' = v.(upsilon)/(upsilon - upsilon_(s))`
`v' = 400 xx (340)/(340 - 10)`
`v' = (400 xx 340)/(330) = 412` Hz.
(b) If the observer be at rest and the source is moving away from the observer, then
`v' = v.(upsilon)/(upsilon + upsilon_(s)) = 400 xx (340)/(340 + 10)`
`v' = (400 xx 340)/(350) = 389` Hz
(c) The speed of sound in each case remains same and is equal to 340 `ms^(-1)`.