Two identical waves, of amplitude $A$, have energy proportional to $A^2$. The sum of the energies of these two waves being proportional to $2A^2$.
If these two waves superimpose to form a wave of the same form with amplitude $2A$. The energy of this wave will now be proportional to $(2A)^2 = 4A^2$. This suggests an increase in energy by a factor of $2$, which is a contradiction to the conservation of energy.
How is this rectified please?
