Editing Dispersion relation (section)

===Deep water waves===
{{Further|Dispersion (water waves)|Airy wave theory}}
[[Image:Wave group.gif|frame|right|Frequency dispersion of surface gravity waves on deep water. The {{colorbull|red|square}} red square moves with the phase velocity, and the {{colorbull|limegreen|circle}} green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The {{colorbull|red|square}} red square traverses the figure in the time it takes the {{colorbull|limegreen|circle}} green dot to traverse half.]]

The dispersion relation for deep [[ocean surface wave|water waves]] is often written as

: <math>\omega = \sqrt{gk},</math>

where ''g'' is the acceleration due to gravity. Deep water, in this respect, is commonly denoted as the case where the water depth is larger than half the wavelength.<ref>{{cite book | title=Water wave mechanics for engineers and scientists | author=R. G. Dean and R. A. Dalrymple | year=1991 | series=Advanced Series on Ocean Engineering | volume=2 | publisher=World Scientific, Singapore | isbn=978-981-02-0420-4 }} See page 64–66.</ref> In this case the phase velocity is

: <math>v_p = \frac{\omega}{k} = \sqrt{\frac{g}{k}},</math>

and the group velocity is

: <math>v_g = \frac{d\omega}{dk} = \frac{1}{2} v_p.</math>