A train stands at a platform blowing a whistle of frequency 400Hz in still air. What is the frequency of the whistle heard by a man running (a) towards the engine at `10ms^(-1)` (b) away from the engine at `10m//s` ?
What is the wavelength of sound received by the running man in each case ?

Explanation

Here, `v=400Hz, v^(')=?upsilon_(L)=10m//s`
`v^('')=?`
(a) When man is running towards the engine,
`v^(')=((upsilon+upsilon_(L))v)/(upsilon)=((340+10)400)/(340)=411.8Hz`
(b) When man is running away from engine,
`v^('')=((upsilon-upsilon_(L))v)/(upsilon)=((340-10)400)/(340)=388.2Hz`
The wavelength of sound is not affected by the motion of the listener. Therefore,
`lambda=(upsilon)/(v)=(340)/(400)=0.85m`