You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind at constant speed and you perceive the frequency as 1310 Hz.You are relieved that he is in pursuit of a different driver when he continues past you,but now you perceive the frequency as 1240 Hz.What is the frequency of the siren in the police car? The speed of sound in air is 343 m/s.
A)1300 Hz
B)1320 Hz
C)1270 Hz
D)1360 Hz
E)1370 Hz

Question

Quizplus · Accepted Answer

We can use the Doppler effect equation to solve the problem:

f' = f(v +/- vd) / (v +/- vs)

where f is the actual frequency of the siren, v is the speed of sound, vd is the speed of the observer relative to the air, vs is the speed of the source relative to the air, and f' is the perceived frequency.

In this case, the observer (you) is stationary relative to the ground, so vd = 0. The police car is moving towards you when you first hear the siren, so vs is negative. When the police car passes you, it is moving away from you, so vs is positive. We can set up two equations and solve for the frequency of the siren:

1310 = f(343 - 35) / (343 - vs)
1240 = f(343 + 35) / (343 + vs)

Solving these equations simultaneously gives us vs = 62 m/s and f = 1270 Hz. Therefore, the answer is C) 1270 Hz.

You Are Driving Along a Highway at 35