Energy and Power of a Wave

The total energy of a wave is the sum of its kinetic energy and potential energy. These two energy forms are equal in magnitude for a wave. Together, they determine how much energy the wave carries and transfers through a medium.

A wave's total energy depends on its amplitude, angular frequency, and wavelength. Waves with high amplitude and frequency deliver more energy than those with low amplitude and frequency. The average energy transfer is proportional to the square of both amplitude and frequency.

Wave power is the average rate of energy transfer, calculated as total energy divided by the time required to transfer it. For mechanical waves, power equals the energy associated with one wavelength divided by the wave's period, expressed as the product of the square of amplitude and the square of frequency.

Intensity is directly proportional to wave power but inversely proportional to the area the wave covers. As a spherical wave spreads from a source, its surface area increases while total energy remains constant, causing intensity to decrease. This explains why earthquake damage reduces farther from the epicenter.

Wave intensity represents the concentration or spread of wave energy across an area. The SI unit of intensity is watts per square meter. Higher intensity indicates more energy concentrated in a smaller area, while lower intensity means energy is distributed over a larger region.

Intensity depends on both the power of the wave and the area it covers. A wave with greater power or concentrated over a smaller area produces higher intensity. Conversely, the same power spread over a larger area results in lower intensity, which is why sound from a speaker decreases with distance.

Wave velocity is derived from wavelength divided by period. This relationship is fundamental to calculating wave power, which uses velocity to express how energy propagates through a medium. Understanding this connection helps predict energy transfer rates in mechanical wave systems.