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When depth of water remains constant and when frequency of water waves increases does wavelength and speed of water waves change too?

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In my understanding, if the depth of water remains constant, using the equation v= square root of gh, the velocity will remain constant as well since g is constant and h is unaltered. Then the relationship between frequency and wavelength are the ones that come into consideration using the equation v=f(lamda). So if the frequency increases, wavelength should decrease by the same ratio to keep the speed constant.

And also logically, if the speed increases as well as the wavelength, let's say by also the same ratio, this would make the frequency constant. Just imagine cars passing across a finish line, the number of cars passing being the frequency and the distance between one car and another being the wavelength, If speed increases as well as the wavelength, it would make not much of a difference in the number of cars passing the line per second.