Surface Waves

Find the velocity of propagation of small waves in shallow water. The water is considered shallow if the wavelength is considerably larger than the depth of the water $H$ . Thanks to this we can assume that along a vertical cross-section the horizontal velocity of all particles $v_{h}$ is the same and that the vertical velocity of water particles is significantly smaller than the horizontal velocity. The smallness of the waves means that their height is significantly smaller than the depth of the water. This allows us to assume that the horizontal velocity of the water particles is significantly smaller than the wave velocity, $u$ .

So, we need to find $u$ .

$Given Information :$

$g = 10$ $\frac{m}{s^{2}}$

$H = 2.5m$