Physics - Sound Wave Question with Solution | TestHub

The apparent frequency $F^{\prime }$ heard by the observer is given by the Doppler effect formula:

$F^{\prime }=F\left(\frac{V-v_o}{V-v_s}\right)$

where $V$ is the velocity of sound, $v_o$ is the velocity of the observer, and $v_s$ is the velocity of the source.

Since the observer is moving away from the source, the relative velocity of sound with respect to the observer decreases, so we use $V-v_o$ in the numerator. Here, $v_o=\frac{V}{4}$.

Since the source is moving towards the observer, the apparent wavelength decreases, so we use $V-v_s$ in the denominator. Here, $v_s=\frac{V}{3}$.

Substituting the given values into the formula:

$F^{\prime }=F\left(\frac{V-\frac{V}{4}}{V-\frac{V}{3}}\right)$

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

$F^{\prime }=F\left(\frac{3}{4}\times \frac{3}{2}\right)$

$F^{\prime }=\frac{9}{8}F$

Answer: $\frac{9}{8}\mathrm{F}$