A train, standing in a stationyard, blows a whistle of frequency 400Hz in still air. The wind starts blowing in the direction from the yard to the station at a speed of `10ms^(-1)`. What are the frequency, wavelength, and speed of sound for an observer standing on the station's platform ? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of `10ms^(-1)` ? Th speed of sound in still air can be taken as `340ms^(-1)`.

Explanation

v = 400 Hz, `V_(m) = 10 ms^(-1)`
V = 340 m/s
(a) As the wind is blowing in the direction of sound therefore, effective speed of sound `V' = V + V_(m)` = 340 + 10 = 350 m/s
As there is no relative motion between source and listener, therefore frequency of sound will remain unchanged. `therefore` v = 400 Hz
Wavelength `lambda = (V')/(v) = (350)/(400) = 0.875` m
(b) When observer is moving towards the stationary source in still air
`V_(m) = 0, V_(L) = - 10 ms^(-1), V_(s) = 0`
`v' = (V - V_(L))/(V - V_(S)) v = (340 - (-10))/(340 - 0) v`
`= (340 + 10)/(340) xx 400` = 411.76 Hz
As the source of sound is at rest.
Therefore, wavelength of sound remains unaffected. As the air is still, therefore, effective speed of sound = 340 + 0 = 340 m/s