Question

A police siren emits a sinusoidal wave with frequency $f_s=300Hz$. The speed of sound is 340 m/s.If the siren is moving at 30 m/s, find the wavelength of the waves ahead of and behind the source.

Answer 1

Given - $f_s=300Hz,v=340m/s,v_s=30m/s$ ,

Doppler's effect gives the apparent wavelength of waves , when source is approaching the stationary listener (wavelength ahead the source) ,

${\lambda }^{\prime }=(v-v_s)/f_s=(340-30)/300=310/300=1.03m$ ,

the apparent wavelength of waves , when source is moving away from the stationary listener (wavelength behind the source) ,

${\lambda }^{\prime }=(v+v_s)/f_s=(340+30)/300=370/300=1.23m$