Intensity and amplitude
The intensity of a wave is defined as the amount of energy that passes though unit area perpendicular to the wave direction in unit time.
The amplitude of a wave varies in a sinusoidal manner with time whereas the intensity of the wave varies as sine squared. These two variations are shown in Figure 1 below.
The intensity of a wave depends on its energy and the energy varies in a different way from the amplitude.
Since the variation in amplitude is simple harmonic (or a sum of simple harmonic oscillations) the energy variation with time is proportional to sine squared.
The units of intensity are Wm-2.
(See: 16-19/Mechanics/Simple harmonic motion/Text/Energy in shm)
Energy in waves - tsunamis
One of the most frightening demonstrations of the energy carried by a wave is shown by the tsunami. One such series of waves was generated by the undersea earthquake off the coasty of Sumatra in Indonesia on 26th December 2004. The earthquake reached 9.0 on the Richter scale and the resulting tsunamis devastated coastal regions of eleven countries from Indonesia to Africa – killing over 120 000 people.
In deep water such as the Pacific Ocean a tsunami might travel at about 200 m/s, or nearly 450 miles/hr. The rate at which a wave loses its energy is inversely related to its wave length, and since tsunamis have very long wavelengths and travel at high speeds, they can also travel very large distances across the ocean with only limited energy losses.
As a tsunami leaves the deep water of the open ocean and travels into the shallower water near the coast, it changes. A tsunami travels at a speed that is related to the water depth - therefore as the water depth in which it is moving decreases, the tsunami slows down. However the energy content of the tsunami is more or less constant and so as the tsunami slows down it increases in height reaching a height of many metres or even tens of metres as it hits the coast.