16.9:
Energy and Power of a Wave
The total energy of a wave is the sum of its kinetic energy and potential energy.
The potential energy associated with a wave is observed to be equal to its kinetic energy. Adding them, we see that the total energy of a wave depends on its amplitude, angular frequency, and wavelength.
A wave having high amplitude and frequency will deliver more energy than a wave having low amplitude and frequency. The average energy transfer is proportional to the square of both amplitude and frequency of the wave.
The power of a mechanical wave is the energy associated with the wavelength divided by the wave’s period.
Using the expression–wavelength divided by period equals the wave velocity–the equation of power is obtained as the product of the square of the wave amplitude and the square of its frequency.
16.9:
Energy and Power of a Wave
The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated with a wave is called its power, which is total energy divided by the time it takes to transfer the energy. For a sinusoidal wave, energy and power are proportional to the square of both the amplitude and the angular frequency.
Waves can also be concentrated or spread out, as characterized by the intensity of the wave. Intensity is directly proportional to the power of the wave and inversely proportional to the area covered by the wave. The more area a wave covers, the lower the intensity. For example, in an earthquake, waves spread out over a large area. As they move away from the source, the severity of damage reduces. The SI unit of intensity is watts per square meter.
In the case of spherical waves, like the kind produced by a sound speaker, intensity also decreases the farther we are from the source. When a spherical wave moves out from a source, the surface area of the wave increases as the radius increases. The intensity for a spherical wave, therefore, decreases while the energy remains constant.
This text is adapted from Openstax, University Physics Volume 1, Section 16.4: Energy and Power of a Wave.