Attached Link: https://en.wikipedia.org/wiki/Cycloid#Related_curves

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If the complete water wave pattern could be split (by a method somewhat like Fourier analysis) into various wave trains (each with its own one frequency), then the speed of each wave train is proportionate to the square root of its wavelength. That is why on the sea, big long waves roll on fast and overtake small overlying ripples.

If amplitude * 2 * pi / wavelength is small, the curve is nearly a sine wave, but the tops are curved slightly sharper then the bottoms. If amplitude * 2 * pi < wavelength, the curve is a curtate cycloid; the tops are curved sharper then the bottoms.

If amplitude * 2 * pi = wavelength, the curve is a cycloid; the tops are sharp.

If amplitude * 2 * pi > wavelength, the curve is a prolate cycloid; the tops are loops, and on the surface water tries to go through other water, but cannot, and breaks into foam.

For curtate and prolate cycloids, see the image at is link.

It is not the same with light waves and sound waves.