A stationary source emits sound of frequency
`upsilon=1200Hz`. If a wind blows at the speed of 0.1c deduce (i) the percentage change in the wavelength and (ii) the change in the frequency for a stationary observer on the wind side of the source. What happens when there is no wind, but the observer moves at speed 0.1c towards the source?

Explanation

If there is no wind n waves emitted by the source in each second will form a train of waves of length equal to speed c of the sound. When the wind blows at speed w, the same number of waves will form a train of length `c+w` on the windside.
`lamda'=(c+w)/(n)=(c+w)/(c )lamda`
`implies((lamda^(1)-lamda))/(lamda)=(w)/(c)`
`%` increase in wavelength
`=(w)/(c )xx100=(0.1c)/(c )xx100=0`
let `n'` be the apparent frequency Then `n'lamda'=c+w` (since speed of sound on the wind side is `c+w`)
or `n'=(c+w)/(lamda')=n`
so, there is no change in the frequency of the wave. When the source moves, the wavelength is not changed but the frequency appears to change. The apparent frequency is given by
`n'=(c-v_0)/(c-v_S)xxn`
Here `v_S=0`, `v_0=-0.1c`, therefore
`n'=(c-(-0.1c))/(c )xxn=1.1n`
`%` increase`=(n'-n)/(n)xx100=10`