So we want to know how does the speed of a shallow water wave varies. If the wavelength is large enough in comparison to the depth of the water, meaning the wavelength is 20 times longer than the depth of water, the speed of a shallow water wave is the square root of gravity times water depth or: v=√(g*d), where v is speed of the wave, g=9.81 m/s^2 and d is water depth.