Problem
A radar device emits microwaves with a frequency of 2.00 GHz. When the waves are reflected from a car moving directly away from the emitter, a frequency difference of 293 Hz is detected. Find the speed of the car.
1. The frequency f received by the car is given by f = f0 (1- ?)1/2/(1+ ?)1/2 ? = v/c
2. The car now acts as the source, sending signals of frequency f to the stationary radar receiver.
3. Consequently, frec = f (1- ?)1/2/(1+ ?)1/2 = f0 (1- ?)/(1+ ?) ? f0 (1- 2?) since v << c.
4. Solve for v: v/c = ?f/2f0 v = (3x108x 293/(4x109 ) m/s = 22 m/s = 79.2 km/h