How does super position not violate conservation of energy?

[Michio Cuckoo]

according the principle of superposition, a wave with a certain amplitude superposed with a similar wave will yield a wave with 4 times the amount of energy.

This would be double the combined energy of the original 2 waves. Assuming 2 point wave sources are perfectly in phase; and there is no destructive interference, wouldn't this violate energy conservation?

 

[Michio Cuckoo]

hmmm... is there something wrong with my phrasing of the question?

 

[Michio Cuckoo]

according the principle of superposition, a wave with a certain amplitude superposed with a similar wave will yield a wave with 4 times the amount of energy.

Original waves energy: A^2 Superposed waves energy: (2A)^2 = 4A^2

 

[A.T.]

https://www.physicsforums.com/showthread.php?t=610551