You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1340 Hz. You are relieved that he is in pursuit of a different speeder when he continues past you, but now you perceive the frequency as 1300 Hz. What is the speed of the police car? The speed of sound in air is 343 m/s.
A) 38.4 m/s
B) 30 m/s
C) 39.2 m/s
D) 40.1 m/s
E) 41.7 m/s

Question

Quizplus · Accepted Answer

Assuming the police car is moving towards you when you hear the frequency as 1340 Hz, the frequency you hear is given by:
f1 = (v + vp) / λ
where, v is the speed of sound in air (343 m/s), vp is the speed of the police car, and λ is the wavelength of the sound waves.
Similarly, when the police car continues past you and you hear the frequency as 1300 Hz, the frequency you hear is given by:
f2 = (v - vp) / λ
Dividing the two equations, we get:
f1 / f2 = (v + vp) / (v - vp)
Solving for vp, we get:
vp = (v (f1 - f2)) / (f1 + f2)
Substituting the given values, we get:
vp = (343 (1340 - 1300)) / (1340 + 1300) = 40.1 m/s
Therefore, the speed of the police car is 40.1 m/s, which is closest to choice D) 40.1 m/s.

You Are Driving Along a Highway at 35