Physics - Sound Wave Question with Solution | TestHub

Let the speed of the car be $v_s$.

Frequency heard by the stationary observer when the car is approaching is given by:

$f_1=f_0\left(\frac{V}{V-v_s}\right)$

Frequency heard by the stationary observer when the car is receding is given by:

$f_2=f_0\left(\frac{V}{V+v_s}\right)$

Given the ratio of frequencies is $7:5$:

$\frac{f_1}{f_2}=\frac{7}{5}$

$\frac{\frac{V}{V-v_s}}{\frac{V}{V+v_s}}=\frac{7}{5}$

$\frac{V+v_s}{V-v_s}=\frac{7}{5}$

$5(V+v_s)=7(V-v_s)$

$5V+5v_s=7V-7v_s$

$12v_s=2V$

$v_s=\frac{V}{6}$

Answer: $\frac{\mathrm{V}}{6}$