Question

A police radar gun operates at an emitted frequency of 10 GHz (10 x 109 Hz). The police officer aims his radar toward a speeding car moving directly away from him at v = 0.2c. The signal reflects off the car and travels back to the police officer where he detects it.

1. What frequency does he detect?

2. Instead the police officer aims the radar at an airplane flying directly overhead at an

   altitude of 10,000 m with v=0.2c in a direction perpendicular to the officer. Again the radar reflects off the plane and comes back. Do you need to account for gravitational time dilation to get the frequency detected? Why or why not?

3. For the setup in part b, what is the frequency detected by the police officer?

Answer 1

The frequency formula is given by,

Answer 1:

Since,

Thus, we have,

On substituting,