The energy of an electromagnetic wave contained in a small volume...

The formula to calculate the energy confined within the electric component of an electromagnetic wave can be written as

${u}_{E} = \dfrac{1}{2}{ε}_{0}{E}^{2}dV . . . \left(1\right)$

Let's assume that the equation of the electric component is given by

$E = {E}_{0}\sin \left(\omegat + ϕ\right) . . . \left(2\right)$

Substitute the expression for the electric field component from equation (2) into equation (1) and simplify to obtain the expression for the energy confined within the small volume $dV$.

$\begin{cases}{u}_{E} & = & \dfrac{1}{2}{ε}_{0}{\left[{E}_{0}\sin \left(\omegat + ϕ\right)\right]}^{2}dV \\ & = & \dfrac{1}{2}{ε}_{0}{{E}_{0}}^{2}\sin^{2}\left(\omegat + ϕ\right)dV \\ & = & \dfrac{1}{4}{ε}_{0}{{E}_{0}}^{2}\left[1 - \cos \left(2\omegat + 2ϕ\right)\right] . . . \left(3\right)\end{cases}$

From equation (3), it can be concluded that the frequency of oscillation of the energy confined within a small volume is double the frequency of the wave.