The siren of a police car at rest emits a sound at a frequency of 1500 Hz. What frequency will you hear if you are at rest and the police car is moving at 30 m/s
a. toward you,
b. away from you?
Take the speed of air to be 340 m/s.

a. The detected frequency is   Hz.

a. In this case the detector is a rest and the source is moving toward the detector. The detected frequency is                         

     
where v_s is the speed of the car and v is the speed of sound.

    Thus, the detected frequency is

As expected, the detected frequency is higher than the emitted frequency.

b. In this case the detector also at rest but the source is moving away from the detector.

Therefore the detected frequency is

The observed frequency is less that the emitted frequency.

b. The detected frequency is Hz.