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.

For a one-dimensional standing wave where a characteristic impedance for the medium $Z_0=R_0+i{X}_0$ exists, the correct thermal energy (average stored thermal energy) to assign a standing wave $E_{\mathrm{sw}}$ is related to the energy of a Planck oscillator by $\frac{E_{p0\mathrm{}}}{E_{\mathrm{sw}}}=1+\frac{{X_0}^2}{{R_0}^2}.$

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