Question

A car moving at 108 km h⁻¹ finds another car in front it going in the same direction at 72 km h⁻¹. The first car sounds a horn that has a dominant frequency of 800 Hz. What will be the apparent frequency heard by the driver in the front car? Speed of sound in air = 330 m s⁻¹.

Answer 1

Given:
Velocity of car sounding a horn $v_s$ = 108 km/h = $108\times \frac{5}{18}\mathrm{m}/\mathrm{s}$ = 30 m/s
Velocity of front car $v_0$ = 72 kmh⁻¹ = $72\times \frac{5}{18}=20\mathrm{m}/\mathrm{s}$
Frequency of sound emitted by horn $f_0$ = 800 Hz
Velocity of air v = 330 ms⁻¹
Apparent frequency of sound heard by driver in the front car ($f$) is given by:

$f=\left(\frac{v-v_0}{v-v_s}\right)f_0$

On substituting the values in the above equation, we get:

$$\begin{gathered} f=\left(\frac{330-20}{330-30}\right)\times 800=826.67 \\ \simeq 827\mathrm{Hz} \end{gathered}$$