A siren on the top of the police car emits sound at frequency of 823 Hz. The car is approaching a bystander on a sidewalk at speed 39.5 m/s. What is the freguency the bystander hears? Assume the speed of sound in air to be 340 m/s.

The bystander will hear a frequency of 931.18 Hz.

Explanation:

let V = 39.5 m/s be velocity of the police car and Fs be the frequency a siren of the police car emits. let v = 0 m/s be the velocity of the bystander and Vs = 340 m/s is the velocity of sound in air.

then, we know that the bystander has to hear a higher frequency than the one emitted and the frequency that the bystander hears is given by the doppler relation:

Fo = [ (Vs) / (Vs - V) ]*Fs

= [ (Vs) / (Vs - V) ]*Fs

= [ (340) / (340 - 39.5) ] * (823)

= 931.18 Hz

Therefore, the bystander will hear a frequency of 931.18 Hz.