A car approaching a crossing at a speed of 20 ms -1 sounds a horn of frequency 500 Hz when it is at a…
A car approaching a crossing at a speed of 20 ms -1 sounds a horn of frequency 500 Hz when it is at a distance of 80 m from the crossing. Speed of sound in air is 330 ms -1. What frequency is heard by an observer 60 m from the crossing on the straight road which crosses car road at right angles?
Solution
Sol. The given situation is as shown in figure.
$\cos\theta = \frac{80}{100} = \frac{4}{5}$
$\therefore$ Apparent frequency,
$f_a = \left(\frac{v}{v - v_s\cos\theta}\right) f = \left(\frac{330}{330 - 20 \times \frac{4}{5}}\right) 500$
$= 525.5\ \mathrm{Hz}$
Answer: $525.5$ Hz