1. For an electromagnetic wave, the electric and magnetic fields vary sinusoidally:

$E = E_0 \cos(\omega t - kx), \qquad B = B_0 \cos(\omega t - kx)$

2. The energy density of the electromagnetic wave is the sum of electric and magnetic energy densities:

$u = \frac{1}{2}\varepsilon_0 E^2 + \frac{1}{2\mu_0} B^2$

Since for an electromagnetic wave, $B = \dfrac{E}{c}$, both terms vary as $\cos^2(\omega t-kx)$.

So,

$u \propto \cos^2(\omega t-kx)$

3. Use the identity:

$\cos^2\theta = \frac{1+\cos 2\theta}{2}$

Thus,

$u \propto \frac{1+\cos 2(\omega t-kx)}{2}$

This shows that the energy density oscillates with angular frequency $2\omega$.

4. Since frequency is proportional to angular frequency, the energy oscillates with frequency:

$2f$

That is, double the frequency of the wave.

5. Checking options:

• A: double the frequency of the wave ✅
• B: the frequency of the wave ❌
• C: half the frequency of the wave ❌
• D: zero frequency ❌

Therefore, the correct answer is A.