A source of sound $S$ having frequency $f.$ Wind is blowing from source to observer $O$ with velocity $u$. If speed of sound with respect to air is $C,$ the wavelength of sound detected by $O$ is:
Medium
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Net velocity of sound $w.r.t$ ground, $v^{\prime}=v_{s}+v_{m}$
where $v_{s}$ is the velocity of sound $w.r.t$ medium and $v_{m}$ is the velocity of the medium.
Thus $v^{\prime}=C+u$
As both the source as well as the observer are at rest, so frequency will remain the same as $f$ irrespective of the velocity of medium.
Let $\lambda$ be the wavelength of the sound wave detected by observer.
using, $v^{\prime}=f \times \lambda$
$C+u=f \lambda \Longrightarrow \lambda=\frac{C+u}{f}$
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