Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 19

A Doppler radar is used to determine the speed of a moving vehicle by measuring the frequency shift of the wave reflected from the vehicle.
(a) Assuming that the reflecting surface of the vehicle can be represented by a perfectly conducting plane and that the transmitted signal is a time-harmonic uniform plane wave of a frequency f incident normally on the reflecting surface, find the relation between the frequency shift f and the speed u of the vehicle.
(b) Determine u both in (km/hr) and in (miles/hr) if f = 2.33 (kHz) with f = 10.5 (GHz).