Why do sound waves not bounce off of each other?

[yosimba2000]

If air is made up real little particles, then why would the waves made up of these particles not bounce off?

Here's my attempt at an explanation for the principle of superposition for soundwaves.

The wave is transferred by the air molecules hitting the ones adjacent to it. But because air is of low density, some of the original wave's particles do not collide with the next packet of air because there is a lot of empty space. For a reflected soundwave interacting with the original wave, although the waves are of higher density compared to the surrounding air, it's still not dense enough such that some of the particles from each wave just pass each other by. The passing of the gas molecules would seem to explain the super-position principle. We can also say that gas molecules are moving too fast to be appreciably affected by the passing-by of another gas molecule.

But this will explain why collisions of soundwaves appear differently than collisions of solids because every molecule in a solid is bound to a neighbor molecule, and pushing one solid molecule causes that to pull against the solid neighbor molecule while collisions in a soundwave are made of some collisions at the meeting point, but also a lot of passing-bys.

From experimentation we know that two sound waves 180 degrees out of phase but of same amplitude will cancel each other out, so that means probably most of the air molecules in a wave are going to pass-by the oncoming wave and preserve the amount of amplitude needed to cancel out. Otherwise if say 50% molecules collided and 50% passed-by, we'd only get 50% net reduction even if the soundwaves were of same initial amplitude. Then I guess you could come up with a formula describing the probability of a certain air molecule colliding or passing by.

What do you think?

 

[russ_watters]

This isn't correct. think more about the fact that waves of *anything* do not collide with each other.

 

[yosimba2000]

Is there an explanation of the principle of superposition in a sound wave? I know it works for waves in general but I'm trying to understand it in a physical way.

 

[russ_watters]

Is there an explanation of the principle of superposition in a sound wave? I know it works for waves in general but I'm trying to understand it in a physical way.

Superposition applies, yes, but you're looking for why. Another nudge: waves are made up of physical objects, but waves themselves are not physical objects.

Also, just in case; you need to get it totally out of your head that the particles in opposite traveling waves might luckily miss each other. In fact they must collide.

 

[yosimba2000]

I know they have to collide to create the next pressure wave, but I don't see why a wave is suddenly a new construct diferent from what it's made of.

 

[russ_watters]

I know they have to collide to create the next pressure wave, but I don't see why a wave is suddenly a new construct diferent from what it's made of.

A wave is just a description of a type of motion. Just like not every object that moves forward is a car, not every wave is made of water.

Physical objects can't pass through each other. Waves are not physical objects, so they can.

 

[olivermsun]

This isn't correct. think more about the fact that waves of *anything* do not collide with each other.

This is of course not true. Look at large amplitude surface waves on the ocean or in most other media I can think of for that matter.

Small amplitude waves do "mostly" not interact with one another. The OP's explanation is not bad for this. There's lots of empty space in the medium at rest, and there's not a huge disturbance from that state due to the wave(s).

 

[russ_watters]

This is of course not true. Look at large amplitude surface waves on the ocean or in most other media I can think of for that matter.

Small amplitude waves do "mostly" not interact with one another.

Perhaps we're using different definitions of the word "collide". I do indeed mean "interact". E.G., When two cars are on opposing velocity vectors and their paths intersect, they interact violently, radically altering their physical structure and motion. That's a collision. When two waves moving in opposite directions, they pass right through each other without interacting. They might interfere, but that's really just the temporary addition of their properties that happen to be in the same place at the same time. The waves themselves are still separate.

Please explain what you mean.

 

[DrClaude]

@russ_watters: I don't know if this is what @olivermsun had in mind, but what you say only holds if the medium is linear. In the nonlinear case, waves will interact, but this goes beyond the OP's question.

 

[A.T.]

But this will explain why collisions of soundwaves appear differently than collisions of solids because every molecule in a solid is bound to a neighbor molecule,

What about sound waves in solids?

 

[olivermsun]

@russ_watters: I don't know if this is what @olivermsun had in mind, but what you say only holds if the medium is linear. In the nonlinear case, waves will interact, but this goes beyond the OP's question.

That's exactly what I mean. Many waves are commonly observed with finite amplitude behavior — they visibly interact beyond simple superposition. It's relevant because the OP is trying to formulate a physical explanation for why sound waves do not seem to interact. (FWIW, I don't know that it's necessary to try and explain what the individual gas particles are doing.)

 

[Andy Resnick]

If air is made up real little particles, then why would the waves made up of these particles not bounce off?

There is such a thing as phonon-phonon scattering:
http://solidstate.mines.edu/videonotes/VN_6_4.pdf
http://www.iue.tuwien.ac.at/phd/karamitaheri/node59.html

Classically, in the linear approximation, sound waves don't interact- this is the principle of superposition.

 

[russ_watters]

@russ_watters: I don't know if this is what @olivermsun had in mind, but what you say only holds if the medium is linear. In the nonlinear case, waves will interact, but this goes beyond the OP's question.

Thanks.

That's exactly what I mean. Many waves are commonly observed with finite amplitude behavior — they visibly interact beyond simple superposition. It's relevant because the OP is trying to formulate a physical explanation for why sound waves do not seem to interact. (FWIW, I don't know that it's necessary to try and explain what the individual gas particles are doing.)

So "this of course is not true" except it is "mostly" true and in particular is true for the case described in the OP? How is saying this at all helpful to the OP? Given that you still haven't explained at all how this counterexample is useful for understanding the OP's case, I don't see that this provides anything helpful and is confusing in that it is vague and substantially over-stated in importance.

Further, the OP's statement about empty space is not in fact "not bad for this", it's completely wrong. The atoms/molecules themselves must collide, otherwise the wave isn't being transferred. You'd end up with two fluid streams in bulk motion, moving through each other, not a wave traveling through a medium. Or to say it another way: the collissions between the particles are what transfers the wave through the medium.

Please: it's bad form in general to tell someone they are wrong when in fact they are mostly right and more to the point are right as it applies to the question they are answering. If you want to extend beyond the scenario given, start by acknowleding that what has already been said works and that you wish to move past it to some additional effect/more precise forumlation/works differently for a different case, etc.

 

[olivermsun]

Thanks.

So "this of course is not true" except it is "mostly" true and in particular is true for the case described in the OP?

What was "of course not true" was your statement:

This isn't correct. think more about the fact that waves of *anything* do not collide with each other.

In fact, lots of waves of *lots of things* do collide with each other in observable ways under non-exotic conditions.

How is saying this at all helpful to the OP? Given that you still haven't explained at all how this counterexample is useful for understanding the OP's case, I don't see that this provides anything helpful and is confusing in that it is vague and substantially over-stated in importance.

Well, since the OP is trying to understand why acoustic waves seem to pass through each other unimpeded, it doesn't seem a very good explanation to say "because linear superposition works."

Further, the OP's statement about empty space is not in fact "not bad for this", it's completely wrong. The atoms/molecules themselves must collide, otherwise the wave isn't being transferred. You'd end up with two fluid streams in bulk motion, moving through each other, not a wave traveling through a medium. Or to say it another way: the collissions between the particles are what transfers the wave through the medium.

The molecules within each wave must collide for each wave to propagate. That fact by itself doesn't necessitate that the particles belonging to the two waves must interact with each other. On other hand, since we observe that waves do in fact interact nonlinearly (beyond superposition of quantities like local density, pressure, and parcel velocity), the idea of the particles "belonging" to the two waves just happening to pass through one another must not be quite correct. However, as I said before, it's probably not necessary to figure out what actually happens with the particles to answer the OP. (One can think about the wave motions at the fluid level.)

Please: it's bad form in general to tell someone they are wrong when in fact they are mostly right and more to the point are right as it applies to the question they are answering. If you want to extend beyond the scenario given, start by acknowleding that what has already been said works and that you wish to move past it to some additional effect/more precise forumlation/works differently for a different case, etc.

I'm not even sure what you think you are mostly right about.

 

[A.T.]

Well, since the OP is trying to understand why acoustic waves seem to pass through each other unimpeded,

OP compares waves in gas meeting vs. solid bodies colliding.
OP thinks it's a matter of solid vs. gas.
Yet waves in solids don't behave like solid bodies colliding.
So it's mainly a matter of wave vs. body, as Russ explained.

How much interaction there actually is between waves is not that relevant here, because it's usually much less than between solid bodies colliding, which was the comparison here.

 

[Orodruin]

The wave is transferred by the air molecules hitting the ones adjacent to it. But because air is of low density, some of the original wave's particles do not collide with the next packet of air because there is a lot of empty space. For a reflected soundwave interacting with the original wave, although the waves are of higher density compared to the surrounding air, it's still not dense enough such that some of the particles from each wave just pass each other by. The passing of the gas molecules would seem to explain the super-position principle. We can also say that gas molecules are moving too fast to be appreciably affected by the passing-by of another gas molecule.

This is not an appropriate way of thinking about what a wave is. The propagation of a wave is not due to "some particles passing by". By the very nature of mechanical waves, the average position of each particle does not change. In fact, in the typical derivation of the wave equation for pressure waves, the medium is considered a continuum and not made up of particles (even if that is what you come down to if you take a more fine-grained look). In fact, you can derive the wave equation by linearising the mass and continuity equations for a gas that satisfies the adiabatic gas law $pV^\gamma = \mbox{constant}$.

As others have pointed out, a key concept in obtaining the wave equation in many cases is linearisation, i.e., assuming that perturbations are small and keeping only the linear correction to a constant solution. The solutions to linear PDEs satisfy the superposition principle, which is why the waves approximately do not interact. Any interaction terms would be described by higher order corrections to the linearisation that can usually be ignored as long as the wave amplitudes are small. However, the non-linear terms do exist for most wave phenomena and will be observable whenever the amplitudes are large enough. The most striking example where the wave equation is exact and not based on a linearisation is classical electromagnetic waves. The resulting wave equation for the electric and magnetic fields are exactly what comes out from Maxwell's equations. This should not come as a surprise as Maxwell's equations in themselves are already linear. (It should be noted that although classical electromagnetic waves do not interact with each other, light-by-light scattering is a prediction of QED recently observed by ATLAS.)

 

[olivermsun]

OP compares waves in gas meeting vs. solid bodies colliding.
OP thinks it's a matter of solid vs. gas.
Yet waves in solids don't behave like solid bodies colliding.
So it's mainly a matter of wave vs. body, as Russ explained.

Again this seems to be "explaining the phenomenon by assuming it." Wave and solid bodies obviously behave differently. The OP seems to be trying to understand why they behave differently.

How much interaction there actually is between waves is not that relevant here, because it's usually much less than between solid bodies colliding, which was the comparison here.

I pointed out that Russ' earlier statement that waves in *anything* don't collide, period, was incorrect. That's all. It might or might not be relevant, depending on how one is trying to explain this.

In fact, it might be useful for the OP to consider what it means (physically) for two (acoustic) waves to pass through one another. Orodruin's discussion in the post above sets this up nicely.

 

[yosimba2000]

Again this seems to be "explaining the phenomenon by assuming it." Wave and solid bodies obviously behave differently. The OP seems to be trying to understand why they behave differently.

In fact, it might be useful for the OP to consider what it means (physically) for two (acoustic) waves to pass through one another. Orodruin's discussion in the post above sets this up nicely.

Yes, this is exactly the mentality that I had when asking this question. Unfortunately, Orodruin's answer went a bit over my head. So here's my thought experiment.

We have a sound source producing a soundwave every second (1 Hz), the soundwave travels at 1 m/s, and there is a perfectly reflecting wall 1 meter away from the source. At t=0, we produce a wave. At t=1, the wave hits the reflecting wall and is about to come back. Also at t=1, a new wave is just generated. As the first wave comes back and the second wave goes forward, they will meet in the middle at 0.5 meters at t=1.5. At this point, let's assume the soundwaves collide and squish against each other within negligible time, but then reflect back again. So at t=1.5, the pressure amplitudes have added up for a small moment (like superposition would predict), then start reflecting.

If we stop here and observe the region between 0 and 0.5 meters, we will see the second wave traveling this region back to the source. But if we assumed that soundwaves can travel through each other instead of reflecting, you would reason out that the soundwave you observe within this region is actually the first wave. But since both waves travel at the same speed and the point of collision is the same, any wave observed between 0 and 0.5m could plausibly be from a reflection or a pass-through of the waves.

But I am inclined to believe that, if gas molecules can interact, then it is actually a reflection of the waves rather than a pass-through, but the principle of superposition "works" in the sense that the results are correct, but its explanation is not.

 

[olivermsun]

yosimba,

Your belief in reflection vs. pass-through (superposition) can be tested. I would begin by asking two questions. First, what's the difference between reflection ("R") and superposition ("S") of the two waves? Second, what do "R" and "S" predict differently if the two waves are of different amplitude?

 

[yosimba2000]

yosimba,

Your belief in reflection vs. pass-through (superposition) can be tested. I would begin by asking two questions. First, what's the difference between reflection ("R") and superposition ("S") of the two waves? Second, what do "R" and "S" predict differently if the two waves are of different amplitude?

The reflection would be a wave bouncing off an incoming wave. S predicts you can add the two waves together to get the net wave, and that waves pass through each other.

For two different amplitudes, my R hypothesis says the colliding waves will reflect with their original amplitudes, while S says the waves will add and pass through each other so that where I would expect an R amplitude, it's actually an S amplitude.

But if what we observe matches the result of S (but let's still assume the explanation of S is still wrong), then we cannot get that result from the current R hypothesis. Therefore, if we must maintain R to be somewhat correct, then we can say when the two different amplitude waves collide, the waves DO reflect, but they carry on the other wave's amplitude. So the wave 1 will reflect back with amplitude of wave 2, and wave 2 will reflect back with amplitude of wave 1. So in this way, it seems the waves have passed-through when infact they transferred amplitudes.

I think it has to be this way because if waves transfer by collision and molecules don't pass-through the other wave's molecules, but we observe waves to be propagated as if they passed-through, then the colliding wave molecules had to have exchanged properties.

 

[olivermsun]

The reflection would be a wave bouncing off an incoming wave. S predicts you can add the two waves together to get the net wave, and that waves pass through each other.

Let's start with the definition of superposition ("S"). Strictly speaking, "S" simply says that the solution for two waves propagating through the medium is exactly the same as the sum of the solutions for the waves treated individually. It's usually convenient to think of the waves passing through one another unimpeded (since that's how the solution looks) but you could certainly label (and track) the waves however you wanted.

For two different amplitudes, my R hypothesis says the colliding waves will reflect with their original amplitudes, while S says the waves will add and pass through each other so that where I would expect an R amplitude, it's actually an S amplitude.

But if what we observe matches the result of S (but let's still assume the explanation of S is still wrong), then we cannot get that result from the current R hypothesis. Therefore, if we must maintain R to be somewhat correct, then we can say when the two different amplitude waves collide, the waves DO reflect, but they carry on the other wave's amplitude. So the wave 1 will reflect back with amplitude of wave 2, and wave 2 will reflect back with amplitude of wave 1. So in this way, it seems the waves have passed-through when infact they transferred amplitudes.

In both cases you have 2 waves emerging from the "collision," one that looks like a continuation of wave 1 and one that looks like wave 2. The difference is that "R" swaps the labels and calls the "wave that looks like a continuation of wave 1" a "reflection of wave 2 that has been modified by the collision to look like wave 1," and vice versa. Is there any difference between the solutions that the two "theories" give you?

I think it has to be this way because if waves transfer by collision and molecules don't pass-through the other wave's molecules, but we observe waves to be propagated as if they passed-through, then the colliding wave molecules had to have exchanged properties.

To go back to Oroduin's post, the waves are not propagating because there is some net motion of the molecules of air in the direction of wave propagation. But we can follow up on this after we sort out the part above.