Does constructive interfence violates the Principle of conservation of energy?

In summary, when two equal amplitude waves interfere constructively, the resulting wave has double the amplitude and four times the intensity, but there is no violation of the Principle of Conservation of Energy as the total energy remains the same. When there is destructive interference, the energy is not lost but rather redistributed within the system. The proposed theory of using mirrors to reflect a wave back in phase with the original wave is not possible and does not violate the principle of energy conservation as energy is being transferred in opposite directions at the same rate.
  • #1
Wen
44
0
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!
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

1. Does constructive interference violate the Principle of Conservation of Energy?

No, constructive interference does not violate the Principle of Conservation of Energy. This principle states that energy cannot be created or destroyed, only transformed from one form to another. Constructive interference simply adds together the energies of two or more waves, resulting in a larger amplitude.

2. How does constructive interference affect the energy of a system?

Constructive interference increases the energy of a system by adding together the energies of two or more waves. This can be seen in phenomena such as standing waves and resonance.

3. Can constructive interference create energy out of nothing?

No, constructive interference does not create energy out of nothing. The energy present in the system is simply being redistributed and combined in a way that results in a larger amplitude.

4. Is the Principle of Conservation of Energy relevant to all forms of interference?

Yes, the Principle of Conservation of Energy applies to all forms of interference, including constructive interference. This principle is a fundamental concept in physics and applies to all systems and processes.

5. How does the Principle of Conservation of Energy relate to the superposition of waves?

The Principle of Conservation of Energy is closely related to the superposition of waves, which is the combination of two or more waves to form a resultant wave. This principle ensures that the energy of the system is conserved, even when waves interfere with each other.

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