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}.

#### Solution

Given:

Velocity of car sounding a horn \[v_s\]= 108 km/h =\[108 \times \frac{5}{18} \text { m/s }\]= 30 m/s

Velocity of front car* *\[v_0\]= 72 kmh^{−1} =\[72 \times \frac{5}{18} = 20 \text { m/s }\]

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:

\[f = \left( \frac{330 - 20}{330 - 30} \right) \times 800 = 826 . 67\]

\[ \simeq 827 \text{ Hz }\]