What Happens to the Energy in Destructive Wave Interference?

[Dale]

My GR knowledge is not sufficient to answer. I doubt it is possible in a static spacetime, and in a non-static spacetime energy is notoriously hard to even define, let alone conserve.

 

[|squeezed>]

Recall the Michelson interferometer:

...(c)...(d)

......BS2
-->..\...-->...\...| (a)
...BS1... __
......(b)

(a),(b) : mirrors

For convenience i placed an extra beam splitter (BS1) before the beam enters the interferometer. In this way you can see the overlap from the mirrors' back-reflections at (c). When you have a bright fringe (constructive interference) at (d) you get a dark fringe at (c) (destructive interference) and vice versa. You cannot have a dark fringe in both arms.

Hope that helps.

 

[carrotstien]

[cool un-allowed theory was here]

 

[Dale]

First, what you are describing is called a dipole, and it is well understood. The field is non-zero always, but it decays faster than a monopole field.

Second, this forum is not the appropriate place for personal theories. Please re-read the rules that you agreed to when you signed up.

 

[hangover]

I was wondering about this one day and perhaps someone here can supply an explanation. Let’s assume you can get two waves on the same frequency and amplitude perfectly aligned with each other but on opposite phase so they cancel each other out, which from what I understand is called destructive wave interference.

Since the energy from the two waves is canceled out, it can't be measured or used, correct? What happens to that energy? Doesn't that violate the law of conservation of energy?

sorry for posting my opinion. To my knowledge(General Physics),"energy" is not cancel out in destructive interference, is it?
In thin film interference(2 wave traveling in the same direction), the energy is redistributed to the wave involving in constructive interference.
In the case of 2 waves traveling in opposite direction, destructive interference occurs; when crest of 1 wave meets the the trough of another wave, the wave seems to be disappeared. However, when this process finishes, wave appears again and the 2 wave keeps on moving. Therefore, according to what i learnt, energy is conserved and, in my opinion, energy is stored in the moment of cancellation.
Sorry, it is only my explanation and may be misleading.

 

[Claude Bile]

Sorry to dig this thread back up but I have been thinking about this same issue a lot. I wanted to question something further.

The pulse example he gave was something I thought about in particular myself. What confused me is once the waves cancel each other out, what attributes of the system allow them to "know" where to continue after time T where they cancel.

Consider a standing wave on a string; at some time, then the displacement will be zero everywhere. Where has the energy gone? Nowhere, because while the displacement is zero, the velocity is not. You can make a similar argument for EM waves; while the E field may be zero at some time, dE/dt and d^2E/dt^2 are not zero, which is important. (Keep in mind too, that quantities like energy density and Poynting vector are time-averaged, which is why time derivatives do not appear in these expressions).

In other words if we could freeze a moment in time where they are cancelled, what can we observe to tell us that the two pulses' magnitudes would return and continue on as before? How could we tell the difference between this two pulse system and a system where there were never any pulses at all?

Another way a look at it... even if there was one pulse and I froze time, how could I tell if the pulse was moving in a positive or negative direction along the X axis. If I can't tell, how can the Universe?

The momentum of the wave will determine the direction that it propagates.

Is this all really a version of the Uncertainty Principal?

Nope, you don't need to resort to quantum physics!

Claude.

 

[Claude Bile]

sorry for posting my opinion. To my knowledge(General Physics),"energy" is not cancel out in destructive interference, is it?
In thin film interference(2 wave traveling in the same direction), the energy is redistributed to the wave involving in constructive interference.
In the case of 2 waves traveling in opposite direction, destructive interference occurs; when crest of 1 wave meets the the trough of another wave, the wave seems to be disappeared. However, when this process finishes, wave appears again and the 2 wave keeps on moving. Therefore, according to what i learnt, energy is conserved and, in my opinion, energy is stored in the moment of cancellation.
Sorry, it is only my explanation and may be misleading.

To add to this;

In the instance of thin-films, you can either suppress transmission or reflection but never both. Energy (and momentum) is always conserved.

Claude.

 

[Darmog]

Palladin would be interested to learn that I have noise cancelling headphones that work rather well to make listening to music much better in car, train, and plane. The background roar and rumble is much reduced. Air pilots use a similar article. I presume the energy is mostly absorbed in the shells and partly dissipated in all directions.
Darmog

 

[petelewis]

Palladin would be interested to learn that I have noise cancelling headphones that work rather well to make listening to music much better in car, train, and plane. The background roar and rumble is much reduced. Air pilots use a similar article. I presume the energy is mostly absorbed in the shells and partly dissipated in all directions.
Darmog

I'd be interested to hear more about this from someone in the know. I'm considering buying noise-cancelling headphones, but it seems to me that they would actually be sending more sound energy into my ears, even though they would sound quieter. Am I right?

Are there health implications of this?

 

[Darmog]

from Darmog to Petelewis and other interested in noise cancelling earphones.
I'm sure manufacturers of these phones would be pleased to reassure you that there is no extra energy entering the ears and may offer to send you a set on approval.