I think the example of the moon kinda sucks, I agree. but it doesn't mean that this is totally irrelevant. To measure the speed of a wave, you find the length

I think the example of the moon kinda sucks, I agree. but it doesn't mean that this is totally irrelevant. To measure the speed of a wave, you find the length between peaks, the wavelength, and then the time it takes to go from peak to peak, the period. Wavelength / period = speed, which has nothing to do with the motion of the particle. But the interesting thing about waves is that it can stack without disturbing each other, and if you can stack different waves just right, you can make create something that looks periodic, but travels faster than any of the combined waves. Shining light on the moon or motion on a LCD screen uses a similar idea where the peak intensity is moving much faster than the components (pixels don't move at all in lcd screens). If this is periodic, you can call it a wave, whether it makes sense or not to call it as such.