# Why isn't energy created by the superposition of waves? [duplicate]

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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?

## marked as duplicate by Community♦Apr 20 '17 at 9:10

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