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Power Input

The damping force is characterized by saying that it dissipates or absorbs energy. In case of wave motion in a perfectly elastic (i.e. non-dissipative) medium, the energy is not dissipated as heat but gets absorbed in the medium in the form of kinetic energy of motion and elastic potential energy. We calculated the power input by the driving force for transverse waves on the string, we can rewrite that expression in terms of impedance as following.

The instantaneous power input by driving force, by definition, is driving force times velocity of motion of the particles of the medium (at x = 0):

For example, in case of transverse waves on string, instantaneous power point

= ρ A² ω² v cos² ω t

The average power per cycle is therefore