Q: Why is it that photographs of wire mesh things, like window screens and grates, have waves in them?
In the case of pictures, the smaller the pattern, the higher its “frequency”, and the higher the pixel count the higher the “sampling frequency”. The standard 24 frames per second (a sampling frequency of 24 Hz) means that things that repeat faster than 12 times per second will be aliased. The “π-ϕ” is different from “ϕ”, however this new phase doesn’t impact the frequency (frequency is what you see and hear). Otherwise, what you see between 0 and may be an alias of a different, higher frequency. But that doesn’t really matter, since you can write a signal out as a bunch of sine waves added together, and the same math applies to each of those.