Two dimensional water (surface) waves travel along the boundary between air and water. The restoring forces for wave motion are surface tension and gravity. Most characteristics of the waves depends on the wavelength and water depth; as these forces acts differently at different water depths -

1. If the depth is shallower than ½ of the original wavelength, they are called shallow water waves. The speed of shallow water wave is described by : $$v = \sqrt{qd}$$

   where, \(d\)= depth of the water (in meters)

2. For deep water waves, the equation for speed will be : $$v = \frac{\lambda}{T} = \lambda f$$

   Where,

   \(\lambda\) = wavelength

   \(T\) = time period

   \(f\) = frequency of the wave

   Speed of deep water wave will n=be approx given by: $$v = \sqrt{\frac{g\lambda}{2\pi}}$$

   [NOTE:speed is directly proportional to the square root of wavelength]