How does super position not violate conservation of energy?

AI Thread Summary
The principle of superposition states that when two waves of the same amplitude are perfectly in phase, their resultant amplitude doubles, leading to a wave with four times the original energy. This raises concerns about energy conservation, as the combined energy appears to exceed the sum of the individual waves. However, the energy increase is not a violation of conservation laws because it results from the constructive interference of the waves, not from an external energy source. The discussion clarifies that energy conservation holds true when considering the entire system and the conditions under which superposition occurs. Understanding wave interactions is crucial to resolving these apparent contradictions in energy conservation.
Michio Cuckoo
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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?
 
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hmmm... is there something wrong with my phrasing of the question?
 
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
 

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