Does constructive interfence violates the Principle of conservation of energy?

[Wen]

During constructive interfence of 2 equal amplitude wave, the amplitude of resultant wave doubles, hence the intensity increased by four times. Does this violates the Principle of conservation of energy?
Also what happen during destructive interfence, where has the energy lost?
Please enlighten me on this!

 

[Hootenanny]

The amplutude will double assuming that the waves are in phase. There is no energy change if you consider the whole system. When there are two waves in phase of equal amplitude they share half the total energy of the system. When they interfere constructively, yes the resulting wave has double the energy but there is only one of them! So the net amount of energy has not changed.

 

[dfx]

While we're on this topic, I had a theory that I thought I'd share and then have you efficient dispose of the weaknesses in it. Anyhow, say we had a beam of light/sound entering a setup of mirrors such that it is reflected around and then eventually ends up in line with the incident ray of light. Say we assume the reflected ray is exactly in phase with the incident ray of light. Then, the resultant wave should interfere constructively to produce a wave with much larger amplitude, right? Now isn't this a violation of the conservation of energy?

 

[Hootenanny]

I am not aware of any system of mirrors that could reflect it back in phase with the origonal wave. As far as I know it is only possible to reflect a wave back by pi radians in anti-phase, resulting in a standing wave, in which case, again energy would be conserved because energy is being transferred in opposite directions at the same rate and therefore the net transfer is zero.