Thermal Energy in Almost Normal Modes

A mode of motion that consists of a standing wave is usually assigned the thermal energy of a Planck oscillator in thermal equilibrium at the temperature of the medium carrying the standing wave. For a real standing wave which will be damped in time if it is excited beyond the thermal level, the energy of a Planck oscillator $E_{p0\mathrm{}}$ is not necessarily the correct energy to assign this mode at thermal equilibrium.