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. enter image description here

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.


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 $\frac 1 t = \frac v s = \frac{\text{speed of the plate}}{\text{distance between successive maxima}}$


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