A stationary police car emits a sound of frequency 1200 Hz that bounces off of a car on the highway and returns to the police car with a frequency of 1250 Hz. The police car is right next to the highway, so the moving car is traveling either directly towards or directly away from the parked officer. Determine the car’s velocity, and whether the car was traveling towards or away from the police car.

Question

A stationary police car emits a sound of frequency 1200 Hz that bounces off of a car on the highway and returns to the police car with a frequency of 1250 Hz.  The police car is right next to the highway, so the moving car is traveling either directly towards or directly away from the parked officer.  Determine the car’s velocity, and whether the car was traveling towards or away from the police car.

Brit · Accepted Answer

The answer said it was 7.02 m/s and not 14.3 m/s

Henry · Answer

F = ((V + Vr) / (V + Vs)) * Fo = 1250.
((343 + Vr) / (343 + 0)) * 1200 = 1250,
Divide both sides by 1200:
(343 + Vr) / 343 = 1.0417,
Multiply both sides by 343:
343 + Vr = 357.29,
Vr = 357.29 - 343 = 14.3m/s Toward the
police car.

Vr = Velocity of the receiver(car).
Vs = Velocity of the source(police car.