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 .
A) 1300 Hz
B) 1320 Hz
C) 1270 Hz
D) 1360 Hz
E) 1370 Hz

Question

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  .
A) 1300 Hz 
B) 1320 Hz 
C) 1270 Hz 
D) 1360 Hz 
E) 1370 Hz

Quizplus · Accepted Answer

Since the police car is moving towards you, the effective speed of the sound wave is increased by the speed of the car, and when it moves away from you, the effective speed of the sound wave is decreased by the speed of the car. Using the formula for Doppler Effect, we can find the speed of the police car:

Δf/f0 = ±v/c
where Δf is the change in frequency, f0 is the original frequency, v is the speed of the car and c is the speed of sound.

When the car is approaching you, the frequency you hear is higher than the original frequency, so we have:

(1310 Hz - f0)/f0 = v/c

When the car is moving away from you, the frequency you hear is lower than the original frequency, so we have:

(1240 Hz - f0)/f0 = -v/c

Now we can solve for f0 by adding the two equations together:

(1310 Hz - f0)/f0 + (1240 Hz - f0)/f0 = 0

Simplifying the equation, we get:

f0 = 1270 Hz

Therefore, the frequency of the siren in the police car is 1270 Hz. Hence, the correct answer is C) 1270 Hz.

You Are Driving Along a Highway at 35