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

Answer: (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 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, $v^{\prime }=f\times \lambda$

$C+u=f\lambda ⟹\lambda =\frac{C+u}{f}$