Physics - Sound Wave Question with Solution | TestHub

Let the original frequency of the sound be $n$ and the apparent frequency be $n^{\prime }$.

Given that $n^{\prime }=\frac{n}{2}$.

Since the apparent frequency is less than the original frequency, the source must be moving away from the stationary observer.

The formula for apparent frequency when the source moves away from a stationary observer is:

$n^{\prime }=n\left(\frac{V}{V+v_s}\right)$

Substituting $n^{\prime }=\frac{n}{2}$:

$\frac{n}{2}=n\left(\frac{V}{V+v_s}\right)$

$\frac{1}{2}=\frac{V}{V+v_s}$

$V+v_s=2V$

$v_s=V$

The source should move with a speed equal to the speed of sound $V$.

Answer: V