Final answer:
Wave dispersion is the process where waves of different wavelengths travel at varying speeds, causing the waves to spread out. In deep water waves, this dispersion occurs because the propagation speed is dependent on the wavelength of the wave, resulting in longer wavelengths moving faster than shorter ones.
Step-by-step explanation:
Wave Dispersion
Wave dispersion is a phenomenon wherein waves of different wavelengths travel at different velocities, leading to the spreading out of a wave over distance. It occurs when the speed of propagation varies with the wavelength. This is observable in various types of waves, including sound waves, electromagnetic waves, and water waves. Specifically, for deep water waves, the wave celerity or propagation speed depends on the wavelength, where longer wavelengths travel faster than shorter ones.
In deep water, the celerity (or wave speed) is proportional to the square root of the wavelength, and thus, waves with different wavelengths will move at different speeds. This wavelength-dependent speed causes waves to spread out or disperse over time. This is why, in deep water, wave dispersion can be particularly notable, and it is responsible for the sorting of waves by their size and speed, with the result that waves don't arrive as a jumbled mix but rather in a sequence according to wavelength.