Wave propagation

Definition of Wave propagation: Progression and transformation of waves in time and space. This is the common definition for Wave propagation, other definitions can be discussed in the article

The speed [math]c[/math] of a wave propagating without frictional losses in deep water is given by [math]c \approx \sqrt{g/k} = g/\omega[/math] where [math]g[/math] is the gravitational acceleration, [math]k=2 \pi / \lambda[/math] the wave number, [math]\lambda[/math] the wavelength and [math]\omega=kc[/math] the angular frequency. Deep water means: depths [math]h[/math] much larger than [math]1/k[/math]. The dependency of the propagation speed on frequency causes wave dispersion. In shallow water (depth [math]h[/math] much smaller than [math]1/k[/math]) the wave propagation speed is proportional to the square root of the water depth [math]h[/math] (formula: [math]c \approx \sqrt{gh}[/math]). A wave group propagates at a smaller speed [math]c_g[/math] than the constituent short waves. Wave energy propagates at the speed of the wave group. See: Shallow-water wave theory.