Question

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 :

• A. $\frac{C+u}{f}$
• B. $\frac{C-u}{f}$
• C. $\frac{C(C+u)}{(C-u)f}$
• D. $\frac{C}{f}$

Answer 1

The correct option is A $\frac{C+u}{f}$

Net velocity of sound w.r.t. ground,
$v^{\prime }=v_s+v_m$
where $v_s$ is the velocity of sound with respect to 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, $v^{\prime }=f\times \lambda$
$C+u=f\lambda \Rightarrow \lambda =\frac{C+u}{f}$