The amplitude of water waves can increase in shallow water due to a phenomenon known as wave shoaling. When a wave propagates from deep water to shallow water, the wave encounters a change in the depth of the water. This change in depth affects the wave's characteristics, including its amplitude.
In shallow water, the depth of the water is comparable to or smaller than the wavelength of the wave. As the wave approaches shallow water, the wavefronts become compressed and the distance between successive wave crests decreases. However, the wave's frequency remains constant because it is determined by the source that generates the wave.
As a result of this compression of wavefronts, the same amount of energy carried by the wave is now concentrated over a smaller distance. This leads to an increase in the wave's amplitude. In other words, the wave becomes steeper and more peaked as it moves into shallower water.
The increase in wave amplitude in shallow water is a consequence of the conservation of energy. Since the total energy of the wave remains constant, the reduction in the distance between wave crests results in a higher concentration of energy in a smaller area, leading to a larger wave height or amplitude.
It's important to note that wave shoaling and the resulting increase in wave amplitude in shallow water are specific to water waves, which are governed by fluid dynamics. The behavior of waves in other media, such as electromagnetic waves or sound waves, may differ.