A police car moving at 36.0 m/s is chasing a speeding motorist traveling at 30.0 m/s. The police car has a siren that emits sound at 3550 Hz. What is the frequency that the motorist hears?

The frequency heard by the motorist is 4313.2 Hz.

Explanation:

let f1 be the frequency emited by the police car and f2 be the frequency heard by the motorist, let v1 be the speed of the police car and v2 be the speed of the motorist and v = 343 m/s be the speed of sound.

because the police car is moving towards the motorist at a higher speed, then the motorist will hear a increasing frequency and according to Dopper effect, that frequency is given by:

f1 = [ (v + v2 / (v - v1)) ] * (f2)

= [ (343 + 30) / (343 - 36) ] * (3550)

= 4313.2 Hz

Therefore, the frequency heard by the motorist is 4313.2 Hz.