Can two waves (like sound or electromagnetic waves) interfere head on? If yes, and suppose they are out of phase with each other and thus interfere destructively, where does the energy of the waves go?
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2Related: Why do travelling waves continue after amplitude sum = 0? – Ilmari Karonen Jul 21 '19 at 23:39
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Yes but it is only temporary, waves reemerge after the collision as if they have just passed thru each other. 2 water waves (one up and one down) show a flat line surface when they meet, the energy is stored in the elasticity of the water temporarily. – PhysicsDave Jul 22 '19 at 00:18
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@PhysicsDave Is water that elastic? – BioPhysicist Jul 22 '19 at 03:37
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1Water is about 80 times more compressible that steel, water hammer is another phenomenon of water elasticity. – PhysicsDave Jul 22 '19 at 10:54
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@PhysicsDave True... but I don't see how that means when waves destructively interfere that means that the energy is stored in the elasticity of the water. – BioPhysicist Jul 22 '19 at 17:27
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Wave motion is a very complex subject and elasticity of the medium is a fundamental requirement for waves in matter. At full interference the kinetic energy is zero and fully converted to potential energy of which the only form that is possible in elastic potential. – PhysicsDave Jul 23 '19 at 01:43
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@PhysicsDave Do you have any references? I'm just not sure I buy it. – BioPhysicist Jul 23 '19 at 04:20
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Another approach; in the LucasVB gif below we have a wave traveling to right from energy created at the right side and we have a wave traveling left from energy created at the left side, yet we have points of zero velocity in the pattern (red dots). How does the energy travel thru these points when there is zero velocity, must be potential. I.e. if you were an observer in the middle of a pond at a null point (with blinders on) for say 10 wave pulses approaching from 2 sides you would observe nothing yet the energy has passed on in both directions thru the point where you observed nothing! – PhysicsDave Jul 23 '19 at 12:40
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There are many references to wave action due to elasticity in google or wikipedia: "Mechanical waves can be produced only in media which possess elasticity and inertia." – PhysicsDave Jul 23 '19 at 12:49
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@PhysicsDave I'm not saying elasticity isn't important for waves. I just don't see how destructive interference requires potential energy storage. The the gif there is no net energy transfer in any direction at all. As for the references, I meant a reference showing how when waves destructively interfere that energy is temporarily stored in the elasticity of the medium. If you want me to see your comments please tag me. – BioPhysicist Jul 23 '19 at 23:06
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@AaronStevens For light (EM) waves we know these waves pass thru each other like water waves do, and we never have violation of energy conservation. We could say an electron in an atom would not get excited when intersected by 2 photons of opposite phase though. For matter waves we can have complete interference for a short time, all kinetic energy is zero, although for the standing waves I agree there is constant motion but in travelling waves this is not the case. – PhysicsDave Jul 24 '19 at 02:46
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@PhysicsDave I don't think that's the case for matter waves. For example, imagine that the gif is showing waves on a string. At the times where the black line is completely flat this does not mean there is no kinetic energy. Each part of the string not at a node still has a kinetic energy. – BioPhysicist Jul 24 '19 at 03:24
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@AaronStevens Good point but as I think about it, even in the gif there is a point of zero kinetic energy when at max amplitude. At this point (say guitar string) the velocity of the string reverses, i.e. it goes thru 0 velocity and at this point and all the energy is stored as tension in the string. For water standing waves we also have potential in the height. – PhysicsDave Jul 24 '19 at 11:53
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@PhysicsDave So then you are saying the opposite of what you were saying before – BioPhysicist Jul 24 '19 at 12:57
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@AaronStevens I think I'm also saying the opposite of what you said before too. So travelling waves show inertia and elasticity differently than standing waves but both can store 100% of the energy elastically when the kinetic energy is zero. ( and with water we also have a potential energy component in addition to the elastic). – PhysicsDave Jul 25 '19 at 01:12
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Can two waves (like sound or electromagnetic waves) interfere head-on?
Yes. When waves add in a superposition it is called interference. Two waves heading towards each other with have interference.
suppose they are out of phase with each other and thus interfere destructively, where does the energy of the waves go?
It depends on what you mean by "interfere destructively". If you mean at some point in time the amplitude is $0$ for all points in space, then there isn't a problem. The wave equation is a second-order equation, so the wave is not only determined by its amplitude. A simple example is seen with waves on a string. Send one pulse to the right and another opposite pulse to the left on the string. When they meet the amplitude of the superposition is $0$ at all points on the string for that instant in time. But the various parts of the string still have a velocity, and hence the two pulses will then move past each other. No energy is lost.
If instead, you mean can we have two waves approach each other so that for all times larger than some finite time the superposition is $0$, then this is impossible? This assumes that we have two non-zero waves with some sort of localization in space. These waves will eventually move past each other. Even if you had a continuously oscillating source you couldn't cancel everything out. Of course, your energy conservation argument is sufficient as well in my opinion.
xray0
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BioPhysicist
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1Yes, moving past each other like this: https://commons.wikimedia.org/wiki/File:Standing_waves1.gif – Jul 21 '19 at 18:45
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Re. "still have a velocity, and hence the two pulses will then move past each other. No energy is lost", during the time the string displacement is zero where is the energy stored--in the momentum? – user45664 Jul 21 '19 at 19:17
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@user45664 There parts of the string still in motion. That is where the energy is. Look at Pieter's animation. – BioPhysicist Jul 21 '19 at 21:15
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@Aaron Stevens I was thinking of two pulses of opposite polarity in two different directions approaching each other. Where is the energy when they pass each other and for an instant the net displacement is zero? – user45664 Jul 22 '19 at 01:53
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@user45664 Parts of the string have vertical velocities still... $0$ displacement doesn't mean all parts of the string are not moving. Please look at the black line in Pieter's animation. His is for a standing wave, but you can still see this happening. – BioPhysicist Jul 22 '19 at 01:58
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What will happen if, instead of travelling in opposite directions, the two out-of-phase waves travel in the same direction with the same speed? Is that even possible? Is it possible to generate two continuous waves, travelling in the same direction with equal speeds but out of phase, that completely overlap? – Visal Jul 22 '19 at 16:49
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@Visal if they are the same exact periodic waveform, then you can only get them to exactly overlap if they are in phase. – BioPhysicist Jul 22 '19 at 16:58
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@AaronStevens Right. Actually, by ‘completely overlap’ I meant that the angle between the axes(are they called that in case of 1-D waves?) of the two waves is zero(that is they have the same axis) – Visal Jul 22 '19 at 17:11
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@Visal Yes. Any time waves "overlap" it is called interference. This is what the first part of my answer is saying – BioPhysicist Jul 22 '19 at 17:24
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I don’t think I am able to ask the question clearly. In the case of the two waves travelling in the opposite directions, the two waves interfere to produce a standing wave. What will happen if the two waves( with the same exact periodic waveform), travelling in the same direction with the same speed, interfere destructively? Will the amplitude of the resultant wave be zero at all times? – Visal Jul 22 '19 at 17:45
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@Visal Yes. Imagine having two regular combs. Moving the combs to the right is like a wave traveling to the right. Now align the combs so that the teeth of one comb up with the space between the teeth of the other comb. In this way you cannot see through the combs any more (destructive interference). Now move the combs to the right at the same speed. You still can't see through the combs. You are just translating the $0$ amplitude, which still gives you $0$ amplitude. – BioPhysicist Jul 22 '19 at 17:48
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Yes, right. So it means, essentially, no energy is being transferred by such combination of waves. Right? – Visal Jul 22 '19 at 18:00
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@Visal Yes that is right, although if I can see where you are heading with this I don't think energy conservation is at risk of being violated here. I am not sure how you could actually create two waves like this with a source that is providing a net energy transfer. – BioPhysicist Jul 22 '19 at 18:03
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Yes @AaronStevens. That’s why I asked if it is even possible to create such waves. – Visal Jul 23 '19 at 02:41
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@AaronStevens How about a sheet of transparent material that is emitting a wave as another identical wave is passing through it, such that the two waves moving in the same direction dovetail like the two combs? – Visal Jul 23 '19 at 03:29
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Two waves of the same frequency and oppposite direction of propagation will produce a standing wave.
Like this figure by LucasVB:
Edit: In a standing wave, the energy oscillates back and forth between different forms. For a mechanical wave (transverse wave on a string for example), that is elastic potential energy and kinetic energy. At instances when the string is straight (minimal potential energy), the kinetic energy is at its maximum.
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... in which case it is important to remark that the energy doesn't "go" anywhere. The details depend on the medium, though: (i) for sound, the energy is not the square of the function being plotted, whereas (ii) for light, the electric energy density is the square of the black line, which does fluctuate -- out of sync in space and time from the magnetic energy density, so that the total energy density stays constant. – Emilio Pisanty Jul 21 '19 at 18:48
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Why not? Superposition is superposition. Standing waves result from interference of waves of opposite propagation direction.
my2cts
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For sound waves and other waves that depend on the motion of atoms and molecules, destructive interference will eventually disperse the energy to the atoms and molecules finally ending up in heat (motion of matter).
For light, which does not depend on a medium to propagate, it is more complicated. Light only superimposes, does not interact. This MIT video shows what is happening in superposition interference of a laser beam split in two and made to interfere. The energy not appearing in the pattern goes back to the lazing mechanism!
In general for electromagnetic waves, when interference light patterns are seen, the energy goes from the dark regions to the bright regions, i.e.it is a function of at least two spatial dimensions, not the one-dimensional plots usually showing amplitudes interfering. In my answer here to an almost duplicate question, I go into more detail. Note that in order to see light, it has to interact with matter, so in the end, the energy will go into heating the screen material.
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1@AaronStevens total destructive interference raises the problem of energy conservation. In light, which is composed of photons yes, total interference as the video shows needs and explanation for where the energy goes. – anna v Jul 21 '19 at 14:24
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The linked by you video from MIT is so obvious, “This MIT video is instructive and a real experiment that shows that in destructive interference set up with interferometers there is a return beam, back to the source, as far as classical electromagnetic waves go. So the energy is balanced by going back to the source.” How ignorant someone could be and downvote the answer, than more doing this without explanation. – HolgerFiedler Jul 21 '19 at 19:53
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The MIT video does not explain where the energy goes because by setting up the strong interference the laser cavity actually lase less, i/e a current meter on the power supply would show a decrease. It is easy to recreate this type of interference with a laser diode for example, external mirrors can easily upset the wave function of the cavity and reduce lasing. – PhysicsDave Jul 23 '19 at 12:46
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@AaronStevens The MIT video does not explain where the energy goes because by setting up the strong interference the laser cavity actually laser less, i/e a current meter on the power supply would show a decrease. It is easy to recreate this type of interference with a laser diode for example, external mirrors can easily upset the wave function of the cavity and reduce lasing. – PhysicsDave Jul 24 '19 at 02:03
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@PhysicsDave your explanation is just another way of describing that a lasing system is one quantum mechanical entity.. And quantum mechanics has inherent energy conservation. I think the professor's explanation is correct. – anna v Jul 24 '19 at 04:06
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Of course annav's answer is right. Let me add a few things, because there are two basic theories:
in the double slit experiment, when we interpret the photon (shot one at a time) pass through both slits as partial waves, those waves interfere. They can interfere constructively (their in phase, create a dot on the screen) or destructively (out of phase and no dot on the screen). Of course the explanation here is that the photons, and the slits are entangled, and so the energy of the photons that interfere destructively, will give their energy to the slits as they scatter inelastically, or get absorbed by the slits. Energy is conserved. If they interfere constructively, the energy is in the dot on the screen. Energy is still conserved.
virtual particles and antiparticles, these are of course duo to wave-particle duality acting as waves too, and when they in your case interfere head on, they cancel out, and the energy goes to where it came from. Back to the vacuum energy density. Yes, photons are their own antiparticles. When you talk about elementary particles in the SM, particles can annihilate with their own antiparticles. This is what you are asking about, because in this case, when the particle antiparticle is created, it pops in and out of existence. From where? From the vacuum energy density (virtual particles).
Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron–positron pair near a nucleus. For pair production to occur, the incoming energy of the interaction must be above a threshold of at least the total rest mass energy of the two particles, and the situation must conserve both energy and momentum.
https://en.wikipedia.org/wiki/Pair_production
In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons.[1] The total energy and momentum of the initial pair are conserved in the process and distributed among a set of other particles in the final state.
https://en.wikipedia.org/wiki/Annihilation
Now it is very important to understand that virtual particles are not real particles, and they can pop in and out of existence from the energy density of quantum vacuum. Virtual particles are a mathematical model of describing the interaction of quantum fields, in this case the poping of in and out of virtual particles.
This is not the case in pair production and annihilation. These are real particles. In the case of pair production and annihilation, and this is what you are asking about, two particles (particle antiparticle pair) is created or annihilated. When the particle and anti particle, like an electron and a positron, traveling as waves, collide head on, both cease to exist as fermions (or when the photon ceases to exist and creates a electron and positron), and the energy (momentum) transforms into a photon. So energy is conserved.
Árpád Szendrei
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I don't agree with the double slit interpretation that a photon is cancelling "itself" out. All photons that enter the slits emerge and appear on the screen, no energy is lost. See Feynman path interpretation on the "pattern", the word interference is historical. – PhysicsDave Jul 23 '19 at 12:27