English: The phase velocity c_p (blue line) and group velocity c_g (red line) as a function of water depth h, for surface gravity waves of constant period according to Airy wave theory.
Quantities have been made dimensionless using the gravitational acceleration g and period T. The deep-water wavelength is L₀ = g/(2π)T² and the deep-water phase speed is c₀ = L₀/T.
The grey line corresponds with the shallow-water limit c_p =c_g = √(gh). The phase velocity c_p is related to the wavelength L through c_p = L/T. Consequently, for fixed period T, L/L₀ varies identical to c_p/c₀ with depth changes.