Physics - Sound Wave Question with Solution | TestHub

The apparent frequency heard by the listener is given by the Doppler effect formula:

$n^{\prime }=n\left(\frac{V+v_L}{V-v_S}\right)$

Since both the source and the listener are moving towards each other with speed $\frac{V}{3}$:

$v_L=\frac{V}{3}$

$v_S=\frac{V}{3}$

Substituting these values into the formula:

$n^{\prime }=n\left(\frac{V+\frac{V}{3}}{V-\frac{V}{3}}\right)$

$n^{\prime }=n\left(\frac{\frac{4V}{3}}{\frac{2V}{3}}\right)$

$n^{\prime }=2n$

Answer: $2n$