Is the energy of the electromagnetic wave proportional to the amplitude or to the amplitude squared of the wave?

Question

I've read that in mechanical waves that it's(energy) is proportional to the amplitude squared but in electromagnetic waves it's only proportional to the amplitude, is that really true?

Answer 1

Seems wrong then. The energy density of an electromagnetic wave is

$$u=\frac{\varepsilon_{0}|E|^2}{2}+\frac{|B|^2}{2\mu_{0}}$$

which is certainty proportional to its amplitude squared. For example, a plane wave of amplitude $\vec{E}_{0}$ also satisfies $|\vec{E}_{0}|=c|\vec{B}_{0}|$ such that

$$u=\frac{\varepsilon_{0}|\vec{E}_{0}|^2}{2}+\frac{|\vec{E}_{0}|^2}{2\mu_{0}c^2}=\varepsilon_{0}|\vec{E}_{0}|^2$$

since $c^2=\frac{1}{\varepsilon_{0}\mu_{0}}$.