The Energy in an Electromagnetic Wave and the shape of the Wave

[fizzyfiz]

no need of equations

 

[BvU]

I met a statement that the energy of EM wave is proportional to the amplitude square

Don't keep us in the dark: tell us where you encountered this statement. In a dark alley or in broad daylight ?

the shape of EM wave is sinusoidal

The wave equation is linear: any sum of sinusoidals is also a solution.

Does shape of EM wave change when it travels through medium

Depends on the dispersion relation.

no need of equations

Totally disagree

 

[Nugatory]

The wave equation is linear: any sum of sinusoidals is also a solution.

Any sum of sinusoidals that are themselves solutions is also a solution, and these sums are not necessarily sinusoidal

BvU already knows this of course; I'm just adding footnotes for other people who may be reading the thread.

 

[vanhees71]

Though you forbid me to use the adequate language, which are formulae, I answer, because maybe it can help you to understand the issue. No matter which specific electromagnetic field you have (of course it must obey the Maxwell equations for the given charge-current distribution) the energy density of the electromagnetic field in a vacuum is (in SI units)
$$u_{\text{em}}(t,\vec{x})=\frac{\epsilon_0}{2} \vec{E}^2(t,\vec{x}) + \frac{1}{2 \mu_0} \vec{B}^2(t,\vec{x}).$$