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**Where does "extra" energy come from in superposed waves?**

**1. I am needing to understand how, when two identical waves are superposed in phase, and the amplitude doubles, how is it that the energy of the resulting wave is greater than the sum of the two superposed waves.**

**2. Given that E = A^2, and my example waves are measured in meters and use this formula: E=100 J/m^2, then,**

a wave with an amplitude of 2m therefore has an energy of E = 100 J/m^2 * 2^2 = 400 J

Two 2m waves are superposed in phase and the amplitude is now 4m. The new wave now has an energy of E = 100 J/m^2 * 4^2 = 1600 J

Where did the extra 800J come from? It seems to have come out of thin air, which violates the conservation of energy.

a wave with an amplitude of 2m therefore has an energy of E = 100 J/m^2 * 2^2 = 400 J

Two 2m waves are superposed in phase and the amplitude is now 4m. The new wave now has an energy of E = 100 J/m^2 * 4^2 = 1600 J

Where did the extra 800J come from? It seems to have come out of thin air, which violates the conservation of energy.