Question

You are driving along a highway at 27.7 m/s when you hear a siren. You look in the rear-view mirror and see a police car approaching you from behind with a constant speed. The frequency of the siren that you hear is 1830. Hz. Right after the police car passes you, the frequency of the siren that you hear is 1760. Hz.

a) How fast was the police car moving?

b) You are so nervous after the police car passes you that you pull off the road and stop. Then you hear another siren, this time from an ambulance approaching from behind. The frequency of its siren that you hear is 1880. Hz. Once it passes, the frequency is 1680. Hz. What is the actual frequency of the ambulance’s siren?

Answer 1

((V+Vr)/(V+Vs))*Fs = 1760 Hz.

V = 343m/s = Velocity of sound in air.
Vr=27.7m/s=Velocity of receiver(motorist).
Vs = Velocity of source(Police car).

a. ((343+27.7)/(343+Vs))1830 = 1760
((370.7)/(343+Vs))1830 = 1760
678381/(343+Vs) = 1760
Cross multiply:
1760((343+Vs) = 678,381
343 + Vs = 385.44
Vs = 385.44 - 343 = 42.4 m/s = Velocity
of police car.

b. F = (1880+1680) /2 = 1780 Hz.