• E_x(z,t) signal produced by a 1 MHz source f(t)=sin(wt)u(t) located on z=-900 m plane propagates to the right and gets reflected from an PEC plate located at z=vt on the right.
  • For v=0 the incident and reflected fields superpose to produce the standing wave field shown by the green curve.
    • The frequency w'' of the reflected wave is the same as w since v=0 and the reflector is fixed at z=0.
  • For v=(3/5)c the incident and reflected fields superpose to produce the field variation shown by the red curve.
    • The red curve is a superposition of two plane waves of different frequencies (caused by Doppler shift) propagating in opposite directions.
    • Doppler shifted frequency of the reflected wave is w''=w/4 (and also k''=k/4 since w/k=w''/k''=c).

The above waveforms should help you understand how a police Doppler radar works --- a ticket is issued when a signal waveform like the red curve is detected at the radar site!!