While standing at a crosswalk,you hear a frequency of 560 Hz from an approaching police car.After the police car passes,its frequency is 480 Hz.What is the speed of the police car? (speed of sound = 340 m/s)
A)13.1 m/s
B)17.4 m/s
C)21.1 m/s
D)26.2 m/s

Question

Quizplus · Accepted Answer

We can use the formula for Doppler Effect:

(f_observed - f_source) / f_source = v / v_sound

where: 
f_observed = 480 Hz 
f_source = 560 Hz 
v_sound = 340 m/s (speed of sound)

Solve for v (speed of the police car):

(480 - 560) / 560 = v / 340

-0.1429 = v / 340

v = -0.1429 x 340

v = -48.572 m/s

Note that the negative sign indicates that the police car is moving away from the observer.

To get the speed of the police car in the direction of the observer, we can take the absolute value:

v = 48.572 m/s

Therefore, the speed of the police car is approximately 26.2 m/s (to two significant figures).

The answer is D) 26.2 m/s.

While Standing at a Crosswalk,you Hear a Frequency of 560