Regarding destructive interference of light waves, here's an interesting bit I found:
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ArcticMyst Security by Avery
How can I understand Light as a Wave?
- Thread starter Yawy
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As long as the headphones are well-designed. Wouldn't be very useful to design noise-canceling headphones that amplify the noise, now would it? It's not a coincidence, it's part of the design.
My shooting earplugs are really cool like that though: they lessen loud noises and amplify quiet noises, bringing everything to the same volume. Very cool stuff, well engineered.
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Ok, here's a question:let's say you have perfect sound-canceling headphones. In your ear, the volume is always zero. Now, people make it sound like wherever the sound constructively interfered, it would be twice as loud as normal. But if there is a second source of equal amplitude, what happened to all that extra energy from the second source? Shouldn't there be twice the total energy as before, not just twice the energy as before in the places where it constructively interferes? I would think that there would be 4x the energy density as there is twice the total energy but in a smaller area. Grr, this is kind of hard to explain...
Bluefan
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If we have a source with power 1 and we want to cancel that source, you can add a source also with power 1 next to it. The total power is then 2. This is then distributed over 2 places.
If they interfere there will be 0 power at the first place and the total power (a power of 2) at the other place. Without the interference there would be a power of 1 at both places.
You can add the area dependence yourself, because the noise gets less when youre far away. If headphones need to cancel noise, they only need to cancel the bit of noise that would reach your ear. For the outside world you headphones would actually add sound, because there's destuctive interference where your ears are there's constructive interference somewhere else. And there goes the energy the headphones add.
If they interfere there will be 0 power at the first place and the total power (a power of 2) at the other place. Without the interference there would be a power of 1 at both places.
You can add the area dependence yourself, because the noise gets less when youre far away. If headphones need to cancel noise, they only need to cancel the bit of noise that would reach your ear. For the outside world you headphones would actually add sound, because there's destuctive interference where your ears are there's constructive interference somewhere else. And there goes the energy the headphones add.
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Bluefan-if the power is now zero in some places, shouldn't the power that used to be there now all exist in a smaller area?
HIMNL9
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^ that's one of the principle of the sound stun-cannon ..... trying to obtain a constructive interference with high frequency and ultrasound in front of the device (unfortunately for the designers, there's still no way for produce a straight "beam of sound" 
)
But some of these principles are already applied to some high-end "cannon" speakers (aka LRAD) for techno/rock concerts ..... for concentrate the sound pressure in the public area and try to reduce (not cancel, just reduce) the surrounding noise outside the public zone ..... by the way, some military and police departments also copied this idea and made some device for riot control, from this same principle.
)But some of these principles are already applied to some high-end "cannon" speakers (aka LRAD) for techno/rock concerts ..... for concentrate the sound pressure in the public area and try to reduce (not cancel, just reduce) the surrounding noise outside the public zone ..... by the way, some military and police departments also copied this idea and made some device for riot control, from this same principle.
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I don't quite understand what you're asking. In case of no interference there is an equal power level everywhere, interference redistributes the power, making 0 power in one spot, but double power in the other.
Where there in the first case was power flowing to both places, with interference there is no power going to one of the places. Power that used to be there is then long gone, it's a traveling wave after all.
Sound has a large wavelength, a 1kHz tone has a 33cm wavelength. You can imagine it has a terrible divergence.
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This is really hard to explain...
OK, so if you add energy from a second source, it only redistributes the energy from the first source, it doesn't add to it? That is what confuses me. The energy from the second source has to end up somewhere.
It seems to me, from the animations I've seen, that the average power stays the same while the power in certain areas increases or decreases. This doesn't seem right to me.
OK, so if you add energy from a second source, it only redistributes the energy from the first source, it doesn't add to it? That is what confuses me. The energy from the second source has to end up somewhere.
It seems to me, from the animations I've seen, that the average power stays the same while the power in certain areas increases or decreases. This doesn't seem right to me.
Bluefan
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We have places A and B. With one source, a power of 1/2 ends up in both places. Add a second non-coherent source, and a power of 2* 1/2 = 1 end up in both places.
The second source does add to the total power, and interference won't change the total power. The sources add the power, interference is the phenomenon of a fixed phase relationship that sort of steers where both sources emit to, the don't change the sources or the total emitted power.
If you take away one source in the animation there will be a spherical wave left, covering all the area. But as it is just one source, there will be half of the power of the two sources combined.
In mathmatical terms: Both sources are of equal frequency, and the addition is completely linear. Add to oscillating term together of the same frequency and the output will be the same frequency but at a different amplitude, depending on the phase.
The second source does add to the total power, and interference won't change the total power. The sources add the power, interference is the phenomenon of a fixed phase relationship that sort of steers where both sources emit to, the don't change the sources or the total emitted power.
If you take away one source in the animation there will be a spherical wave left, covering all the area. But as it is just one source, there will be half of the power of the two sources combined.
In mathmatical terms: Both sources are of equal frequency, and the addition is completely linear. Add to oscillating term together of the same frequency and the output will be the same frequency but at a different amplitude, depending on the phase.
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So then it's four times the max power density, as I said? Because if the second source cancels out the other in place A, the power at place B would be 2 (instead of the original 1/2).
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No. The power adds in one place. 1/2 plus 1/2 = 1.
Black is the resulting wave of the addition of two others.
Black is the resulting wave of the addition of two others.
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OK, now hold on-let's say the brown/green wave peaks at 1. During the constructive period, it has twice the energy (peaks at 2). This makes sense as there are twice as many sources. However, for just as much time, it has zero energy! So the total energy stays exactly the same, it's just that it's lumped together into periods (or physical places) of all or nothing (but with the same average amplitude as before). That doesn't make any sense.
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csshih
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earplugs or full over ear headphone type earplugs?
HIMNL9
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@ossumguywill: remember that you can't destroy energy, no matter what you do, but you can, anyway, convert it in something other.
Acoustic energy "cancelled", in reality, is simply converted in something different (it can be heat, mechanical force on the parts of the earplugs and earphones, kinetic energy, material stress, and so on ..... the analyzation of all the variables involved can take a day), not "destroyed", or cancelled.
Acoustic energy "cancelled", in reality, is simply converted in something different (it can be heat, mechanical force on the parts of the earplugs and earphones, kinetic energy, material stress, and so on ..... the analyzation of all the variables involved can take a day), not "destroyed", or cancelled.
Bluefan
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The sound is locally cancelled not dissipated (in case of interference), but somewhere else amplified, you just divert the power. Practically all hearing protection is passive and dissipates the energy, but that's not interference.
What you are looking at is the field, and the power goes with the field squared, so that peak is 4 times as high in power than a single source, or double the power of the two sources combined. Average the 4 times higher peak with the periods of 0, and you end up with 2, the combined power of two sources.
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