Can someone please explain the concept behind this wave properties moving plates problem/solution

Question

The problem talks about microwaves from a microwave transmitter that are reflected from two parallel sheets A and B.

Sheet A partially reflects microwave energy while allowing some to pass through. All of the microwave energy incident on sheet B is reflected. Sheet A is fixed and sheet B is moved towards it. While sheet B is moving, the intensity of the signal detected at the receiver goes through a series of maximum and minimum values.

I don't understand how the speed of the moving plate will affect the frequency at which the intensity maxima of the received signal will vary. Let's say sheet B is moving at 0.75 m/s and microwaves are of wavelength 32mm. The formula used to calculate this is $$\text{frequency} = \frac{\text{speed of the plate}}{\text{distance between successive maxima}}.$$ Can someone help me explain the concepts here? I tried looking at the path difference, but still not clear.

Answer 1

Assume that on reflection there is no phase change at each of the sheets and that the change in frequency on reflection from sheet $B$ due to the Doppler effect is negligible because the speed of sheet $B$ is so much less than the speed of the microwaves.

If the distance between sheets $A$ and $B$ is a whole number of half wavelengths then the waves reflected from sheet $A$ and the waves reflected from sheet $B$ arrive at the receiver in phase.
So successive maxima occur when the sheet $B$ has travelled a distance $\frac{\rm wavelength}{2}$.

Suppose the time taken for sheet $B$, moving at speed $v$, to travel a distance $s$ between successive maxima is $t$ then $t = \frac s v $

So the frequency at which successive maxima a received is $\frac 1 t = \frac v s = \frac{\text{speed of the plate}}{\text{distance between successive maxima}}$