Question

A factory siren has a frequency of 990 Hz. Calculate the frequency heard by a person sitting in a car moving at 72 kmh-1 (i) away from the siren and (ii) towards the siren. Take the speed of sound in air as 330 ms-1.

Answer 1

The Doppler shift is given by equation

$$f=\left(1\pm \frac{v}{c}\right)f_0$$

(i)

$$f=\left(1- \frac{v}{c}\right)f_0=\left(1- \frac{20\:\rm{m/s}}{330\:\rm{m/s}}\right)\times 990\:\rm{Hz}$$

$$=930\:\rm{Hz}$$

(ii)

$$f=\left(1+ \frac{v}{c}\right)f_0=\left(1+ \frac{20\:\rm{m/s}}{330\:\rm{m/s}}\right)\times 990\:\rm{Hz}$$

$$=1050\:\rm{Hz}$$