A train at rest blows a whistle of frequency 600 Hz in still air. What is the frequency of whistle for a platform observer when the train.(a) approaches the platform with a speed of `15 ms^(-1)` (b) recedes from the platform with a speed of 15 ms-l? What is the speed of sound in each case? Speed of sound in air is `345 ms^(-1)` .

Explanation

Given, `f_0. = 600 Hz, f= ?, V_s = 15 ms^(-1)`
(a) Source approaching the observer at rest:
` f = f_0 ((V - 0)/(V - V_s) ) , `
i.e., apparent frequency` f= (600 xx 345)/(345 - 15)`
i.e., ` f = (600 xx 345)/(330)`
i.e., ` f = 627.27 Hz`
Hence the apparent frequency increases with the approach of the source of sound. The relative speed of sound w.r.t observer `= 330 ms^(-1)`
(b) Source receding the observer:
` f^1 = (f_0 V)/(V + V_s)`
i.e., ` f' = (600 xx 345)/(345 + 15)`
i.e., ` f'= (600 xx 345)/(360) `
i.e., ` f' = 575.00 Hz`
Hence the apparent frequency decreases when the source of sound recodes the observer The relative speed of sound w.r.t observer `= 360 ms^(-1)`