91Ó°ÊÓ

Given data:

Given that the stationary car's sound frequency is 520 Hz and the frequency detected by the moving listener is 490 Hz, the velocity at which the listener is moving away from the car must be determined in order to detect that frequency.

Therefore, the formula to detect frequency by the listener;

$f_L=f_s\left(\frac{vÂ\pm v_L}{v+v_S}\right)$

Here,

The speed of sound in air $v=344m/s$

Speed listener $v_L$

The source is stationary $v_S=0m/s$

Frequency of the sound emitted by the car localid="1664339995390" $f_S=520\mathrm{Hz}$

Frequency of the sound detected by the listener $f_L=490Hz$

Minus sign will be used in the numerator as the listener is moving away from the car.

$$\begin{gathered} \frac{f_L}{f_S}=\left(\frac{v-v_L}{v+0}\right) \\ v-v_L=\frac{v×f_L}{f_S} \\ {v}_L=v-\frac{v×f_L}{f_S} \end{gathered}$$

Putting the values;

$$\begin{gathered} {\mathrm{v}}_{\mathrm{L}}=\left(344\mathrm{m}/\mathrm{s}\right)-\frac{\left(344\mathrm{m}/\mathrm{s}\right)×\left(490\mathrm{Hz}\right)}{520\mathrm{Hz}} \\ {\mathrm{v}}_{\mathrm{L}}=19.8\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the velocity will be 19.8m/s.