The wave speeds are greater in deep water than in shallow water due to the influence of water depth on wave propagation. This phenomenon can be explained by considering the basic principles of wave theory.
In deep water, the depth of the water is significantly greater than the wavelength of the waves. As a result, the wave's motion is primarily influenced by the depth of the water rather than the ocean floor or seabed. In this case, the key factor determining wave speed is the water's inertia and the restoring force of gravity.
The speed of a deep-water wave is determined by the wavelength (λ) and the acceleration due to gravity (g) according to the formula:
v = √(gλ/2π)
Since both gravity and wavelength remain constant, the wave speed in deep water is proportional to the square root of the wavelength.
In shallow water, on the other hand, the depth of the water is comparable to or smaller than the wavelength of the waves. In this case, the interaction with the ocean floor becomes significant, affecting wave propagation. The presence of the seabed causes the waves to interact with the bottom, resulting in reduced wave speeds.
The speed of a shallow-water wave is determined by the water depth (d) and the acceleration due to gravity (g) according to the formula:
v = √(gd)
Since water depth is a factor, the wave speed in shallow water is proportional to the square root of the water depth.
Therefore, in deep water, where the depth is significantly greater than the wavelength, the wave speeds are greater. In shallow water, where the depth is comparable to or smaller than the wavelength, the wave speeds are lower due to interactions with the ocean floor.