Suppose I have a wave pool with two sources, A and B. The two sources both produce sine waves of the same frequency, and the sources are separated by a distance of the period of the wave.
So they will make an interference pattern on the surface of the pond (or if they are light waves, an interference pattern of light).
Now I want to add another wave source - this one the product of A and B. The puzzle is how to do that. I can mathematically multiply a sine by another sine - it will give a wave of the same period, but the shape is different - however, I don't know that you could generate a wave like this with either water or light.
Is there any solution other than that one? My goal is to find the values of A and B such that a sum such as "A + B - AB" is maximized and I thought of using waves as a way to do this kind of math.