Physics - Sound Wave Question with Solution | TestHub

The actual frequency of the whistle is $f_0=256\text{ Hz}$.

The velocity of the source is $v_s=\frac{v}{3}$, where $v$ is the velocity of sound in air.

Since the observer is stationary and the source is approaching, the apparent frequency $f^{\prime }$ is given by the Doppler effect formula:

$f^{\prime }=f_0\left(\frac{v}{v-v_s}\right)$

Substituting the given values:

$f^{\prime }=256\left(\frac{v}{v-\frac{v}{3}}\right)$

$f^{\prime }=256\left(\frac{v}{\frac{2v}{3}}\right)$

$f^{\prime }=256\times \frac{3}{2}$

$f^{\prime }=128\times 3=384\text{ Hz}$

The number of waves per second the observer will receive is $384$.

Answer: $384$