A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.)
A) 220
B) 448
C) 526
D) 552
E) 383

Question

Quizplus · Accepted Answer

We can use the formula for Doppler Effect:

$f' = f\frac{v\pm v_o}{v\pm v_s}$

where:

$f$ is the frequency of the siren emitted by the police car

$v$ is the speed of sound in air

$v_o$ is the velocity of the observer (moving car)

$v_s$ is the velocity of the source (police car)

Since the observer (moving car) is approaching the police car, we use the plus sign for the velocity of the observer:

$f' = 500\frac{343+36}{343-0} = 552$ Hz

Therefore, the frequency heard by the observer in the moving car as he approaches the police car is 552 Hz.

The best choice is D.

A Car Approaches a Stationary Police Car at 36 M/s