Physics - Sound Wave Question with Solution | TestHub

Original frequency of the whistle is $f$.

Since the pitch appears to drop by $30\%$, the apparent frequency is $f^{\prime }=f-0.30f=0.70f$.

The engine is receding from a stationary observer. According to the Doppler effect, the apparent frequency is given by:

$f^{\prime }=f\left(\frac{v}{v+v_s}\right)$

where $v$ is the speed of sound and $v_s$ is the speed of the engine.

Substituting the given values:

$0.70f=f\left(\frac{350}{350+v_s}\right)$

$0.70=\frac{350}{350+v_s}$

$350+v_s=\frac{350}{0.70}$

$350+v_s=500$

$v_s=500-350=150{\text{ m s}}^{-1}$

Answer: 150