The energy of an electromagnetic (EM) wave depends on both its frequency and its amplitude. The energy carried by an EM wave is proportional to the square of its amplitude and is directly proportional to its frequency.
The energy of an EM wave is described by the Poynting vector, which represents the rate of energy flow per unit area in the direction of wave propagation. The formula for the Poynting vector (S) is given by:
S = (1/μ₀) * E x B
where: S is the Poynting vector (energy flow per unit area), E is the electric field vector, B is the magnetic field vector, and μ₀ is the permeability of free space (a physical constant).
The energy density (u) of an EM wave is obtained from the magnitude of the Poynting vector:
u = |S|
The intensity (I) of the EM wave, which is the energy flux per unit area, is given by the time-averaged value of the Poynting vector:
I = <|S|> = (1/2μ₀) * E₀ * B₀
where E₀ is the peak electric field amplitude and B₀ is the peak magnetic field amplitude.
So, as you can see, the energy of an EM wave is directly related to both the amplitude (E₀ and B₀) and frequency (ω) of the wave. Higher frequencies and larger amplitudes both contribute to a higher energy content in the wave.