The energy of an electromagnetic wave contained in a small volume oscillates with

$$\text{Let the electric field of the wave be given by: } E = E_0 \sin(\omega t - kx)$$

$$\text{The instantaneous energy density } u \text{ contained in a small volume is given by: } u = \varepsilon_0 E^2$$

$$u = \varepsilon_0 E_0^2 \sin^2(\omega t - kx)$$

$$\text{Using the trigonometric identity } \sin^2\theta = \frac{1 - \cos(2\theta)}{2}:$$

$$u = \frac{\varepsilon_0 E_0^2}{2} [1 - \cos(2\omega t - 2kx)]$$

The term $$cos(2\omega t - 2kx)$$ reveals that the instantaneous energy density oscillates with an angular frequency of $$2\omega$$ 

$$\nu_{\text{energy}} = 2\nu_{\text{wave}} \implies \text{Double the frequency of the wave}$$