I When is a water surface not dispersive?

[Daniel Petka]

TL;DR Summary

Shallow water waves => high freqs faster, deep water waves => low freqs faster. When are low freqs and high freqs equally fast = no dispersion?

For my project, I need water waves of all frequencies to move at the same speed. I read this article, but struggled to grasp some concepts. The key idea of the article is that a raindrop hitting a water surface basically creates a pulse containing all the frequencies, and since the water is very shallow, the high frequencies move faster, which creates the chirp. There is something I am confusing, since according to wikipedia, shallow waves should have no dispersion, but the raindrop clearly shows otherwise.

Then, there is another part in the article which I don't get:

" Raindrops may react differently in other situations. Imagine that rain is hitting a lake or ocean – or those deep pothole puddles that require galoshes. Here, the raindrop hits the water, but the force due to gravity becomes more important. It moves waves of all sizes at the same speed which may overpower the rippling effect due to the surface force. "

But don't deep water waves disperse too? Low frequencies move faster in deep water.. The only thing that makes sense to me rn, is that there has to be some sweet spot where the effects of shallow water (high freq faster) and deep water (low freq faster) cancel out?.The article shows a perfect non-dispersive wave when the force of gravity goes up, but, of course the model is incomplete. The math here is a bit over my head, I would highly appreciate any help!

 

[Arjan82]

So, the ripple effect that the article is talking about are not gravitational waves, but capillary waves. They are dominated by surface tension. These waves are much faster apparently.

Gravity waves in shallow water (depth much less than wave length) indeed do not disperse, so all frequencies move indeed at the same speed.

Gravity waves in deep water do disperse, there the higher wavelength (lower frequency) waves are fastest.