Deep-Water Wave Speed

This formula gives the speed of a surface gravity wave in deep water, where the seabed is far below the wave base and does not affect the motion. It comes from the deep-water dispersion relation, which shows that longer waves travel faster than shorter ones because their orbital motion penetrates more deeply into the water. The result depends only on wavelength and gravity, not on water depth, as long as the water is deep enough for the approximation to hold.

Use this for ocean swell, open-sea wave analysis, and problems involving surface gravity waves in water deeper than about half the wavelength. It is useful in marine navigation, coastal engineering, and any physics problem asking for wave speed from wavelength in deep water.

• Using the formula for shallow water, where speed depends on depth instead of wavelength
• Forgetting that λ must be in metres and g in m/s², which breaks the units
• Using π instead of 2π in the denominator, which gives a speed that is too large