Doppler effect: 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 1310 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 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

Using the Doppler Effect equation:

f' = f(v ± vd) / (v ± vs)

where 
f = frequency emitted by the source (unknown in this problem) 
v = velocity of sound in air = 343 m/s 
vd = velocity of the detector (you) = 35.0 m/s 
vs = velocity of the source (police car)

First, let's calculate vs using the first perception of the frequency:

1310 Hz = f(343 m/s) / (343 m/s - vs)

1310 Hz(343 m/s - vs) = f(343 m/s) 
vs = 343 m/s - (f/f')343 m/s = 343 m/s - (1310/1240)343 m/s = 27.3 m/s

Now, we can use vs to calculate the frequency f emitted by the source when the siren is receding:

1240 Hz = f(343 m/s) / (343 m/s + 27.3 m/s) 
1240 Hz(343 m/s + 27.3 m/s) = f(343 m/s) 
f = 1270 Hz

Therefore, the frequency of the siren in the police car is 1270 Hz (choice C).

Doppler Effect: You Are Driving Along a Highway at 35