Why Does Sound Propagate?

[dknguyen]

I can see serious problems with this approach and it's also the parts of chconnor's dissertation that I tend to...I wont say, "disagree with" but, rather question the completeness of. It's obvious, both from a thought excersise view and from known physics, that the molecules are both moving and interacting. We agree there, right?

The problem is having molecules that are vibrating at random speeds somehow imparting a very specific sound propagation rate and, worse, a rate that is much faster than the proverbial speaker cone is traveling. In your analysis, why doesn't the sound propagate at different speeds depending on the rate the speaker cone is moving? Why does it, in fact, always move away from the cone at Mach 1, regardless of the rate of the air disturber?

You answer almost matches mine in that you conclude that the speaker is moving the molecules at some specific rate but, in your answer, at the rate of the speaker cone. But, then the effect sort of magically (through some undefined process) zips away at Mach 1. I'm saying that the mechanism for the sound wavefront to move away at Mach 1 is the crux of the issue of sound propagation, not the local movement of the molecules by the speaker cone...or the displacement of the rulers.

(add on) To put it perhaps more succinctly, it's not how the speaker cone moves the air molecules at that interface but, rather how the air molecules then move each other to propagate the effect.

I think that's where the usual science teaching falls down and why everyone here seems to be so hung up on the wave nature of sound rather than those instantaneous effects that cause it to propagate.

Just like flight, there is a point very early on where you CANNOT view air molecules as particles or else misconceptions start arising. It has to be viewed as a fluid. If you're looking at why the molecules interact with each other the way they do- look to general fluid dynamics (not just sound) which will deal with fun things like inertia, elasticity, compressibility, and friction. *weakly cheers "yaay"*

I seem to be at a similar dead end trying to understand flight- attempting to to reconcile the circulation of bound/trailing vortexes and how they use the bernoulli effect with the how a mass of air with equal momentum is diverted downards are all actually the same thing.

Because it's not the velocity of the cone that produces the speed of sound per say it's the pressure that builds up from the speakers displacement of the medium, the pressure wave itself is what travels. The speaker compresses the air in front of it and then releases that pressure very fast, because it does this relatively quickly high pressure pulses are created, it's those pressure waves that are actually propagating and that's only limited by the speed of sound in that medium.

You're saying that it's not so much that the cone is pushing or "pulling" (for lack of a better term) against the air, as it is the cone is moving out of or into the way of the air to compess to producing a pressure difference so the air can push against itself? Air pushing against itself would seem to remove much of the influence that the cone has regarding the actual velocity of the cone on individual air molecules. However, this view treats air as a collection of macro-particles rather than the fluid it actually is which would invalidate it.

I am visualizing the nearby air the cone is pushing against is being used as a "buffer" by the cone so that, as far as most of the air is concerned, it is just air pushing against air. That puts all the focus on the fluid nature of the air and how the inertia, compressiability, and elasticity, and friction produces pressure waves which might go a long way to explaining the consistent behaviour of sound regardless of the cone since it's air interacting with air. But the concept of an "air buffer" is making me start to wonder if there are both far and near field effects with sound like with EM radiation, with the near field effects that Crashsite is so concerned about being really unintuitive because it deals with the nitty gritty of fluid dynamics. THe buffer being kind of like a shock absorber in a car- "makes car's movement independent of the irregularities of the " - perfect shocks anyways.

 

[Sceadwian]

Air pushing against itself would seem to remove much of the influence that the cone has regarding the actual velocity of the cone on individual air molecules. However, this view treats air as a collection of macro-particles rather than the fluid it actually is which would invalidate it.

I don't follow DK, air as a fluid is exactly what I had in mind. I didn't mention anything about 'near field' effects as you say (which I think is perfectly applicable) because honestly my understanding of fluid dynamics is very poor. If you wanted to see what was really going on as far as near field effects go you'd have to look at sound waves being produced from a high speed camera using a field of smoke to try to make the flows visible. The actual interactions going on at the cone of a speaker are very complex.

 

[chconnor]

I think we're getting close, team.

While we're all calling crux, let me agree with crashsite that the crux is:

why doesn't the sound propagate at different speeds depending on the rate the speaker cone is moving? Why does it, in fact, always move away from the cone at Mach 1, regardless of the rate of the air disturber?

I think that's a great question.

First, regarding the jiggling mentioned earlier:

- Mach 1 is the speed of sound, not the speed of air, and there's no reason it would apply to the movement of individual particles. They move at all kinds of various speeds.

- The displacement of air from a speaker is many orders of magnitude larger than the jiggling, so the jiggling is kind of ignoreable for these purposes.

- so, to rephrase crashsite: why isn't the momentum inherent in the initial perturbation relevant to the speed of propagation? In rulers: if I push the first ruler very hard, it seems that the subsequent rulers would move quicker than if I pushed it less hard: the momentum of each would translate into the momentum of the next through the repulsive fields around them, right? But it doesn't work out that way. Similar to the question of "why doesn't a larger mass fall faster than a small mass in a gravitational field", or "why doesn't a larger-mass pendulum have a longer period than a smaller-mass pendulum", there are balances at play that counteract the (perhaps) more intuitive answer. In this case, I'm not sure how it plays out, but here's my guess: the higher momentum in the higher-pressure wave that results from a "fast" perturbation is balanced by the higher concentration of mass within that wave: more momentum, but more mass to move within that region, so it balances and the propagation speed is the same. Perhaps someone with more knowledge of kinetics can chime in, but that satisfies my brain.

Grab a slinky, stretch it out, and make some compression/rarefaction waves in it. With fast or slow initial perturbation, the waves should travel at the same rate. Even if that doesn't really explain anything, it might be useful to see.

To follow off dknguyen: hoping to run an accurate particle simulation of this kind in our limited human brains is probably a lost cause, or at least going to take more than the Internet's definition of a "dissertation", especially when we stop talking about idealized particles and start taking into account the vagaries of Real Air, which is why we start developing mathematical models that abstract things as waves so we don't have to hurt our brains.

-c

 

[crashsite]

Paging Dr. Schlieren...

If you wanted to see what was really going on as far as near field effects go you'd have to look at sound waves being produced from a high speed camera using a field of smoke to try to make the flows visible. The actual interactions going on at the cone of a speaker are very complex.

Probaby not smoke but, a Schlieren Photograph (which uses polarizing filters and the polarizing effects of gas pressure differences in a field to see such effects). Schlierin Photography has been around at least as long as supersonic flight and was used in early tests to see the shock waves. One would hope that the technology has advanced at least a little in the past 50+ years to be able to see the effect you talk about.

You're probably aware of all this but, they are interesting so, I've mentioned it in case there are those who are not.

(added on) http://www.efluids.com/efluids/pages/gallery.htm

 

[crashsite]

Just like flight, there is a point very early on where you CANNOT view air molecules as particles or else misconceptions start arising. It has to be viewed as a fluid.

Is that really just deferring the problem to another plane (no pun intended)? Saying that it can't be thought of on a Newtonian level (ie: actions and reactions and masses and inertia) but, rather must be elevated to the almost mystical zone of...(cue organ)..."fluid dynamics"?

I think speed-of-sound velocities can allow us to pretty much ignore relativistic effects and aren't what we are left with is Newtonian Physics?

I lustily add my voice to those here who proclaim themselves to have NO fluid dynamics expertise but, I have to wonder if there are not simplified analogies here, too that us common folk can understand...at least well enough to see thing on a "mechanical" level.

If air is made up of molecules of gasses, it makes sense to me that some reasonably elementary explanation of the interaction of the molecules of those gasses to propagate sound should be possible and practical. I mean, science classes don't have any trouble introducing Slinkies and steel balls separated by springs and longitudinal waves, etc. to supposedly teach us about sound propagation (even though those things don't really do it <== my opinion).

Anyway, sorry for getting off topic and going off on another rant there.

 

[crashsite]

Perhaps it's Elves at Work?

I don't even really question this. I was questioning 3v0's analysis about it. There are lots of things that are, self-limiting so it isn't unusual to me that something like the speed of sound propagation might be one of them. I accept it. What I don't accept is that I don't understand the mechanism of it.

I can see one of those centrifugal governors on an old stationary engine and pretty easily see how the weights move to add apparent mass to the system to keep the engine speed constant. If there is a similar level of explanation for the balancing mechanism for the speed of sound propagation, I'd like to see that, too.

I guess, I'm not yet convinced that there isn't one.

 

[crashsite]

Oh?

- Mach 1 is the speed of sound, not the speed of air, and there's no reason it would apply to the movement of individual particles. They move at all kinds of various speeds.

Do they?

I don't think I'd go so far as to say that they are so well matched in speed as to be coherent but, if they all have the same temperature (same energy), why wouldn't they all be moving at the same speed?

 

[chconnor]

I can see one of those centrifugal governors on an old stationary engine and pretty easily see how the weights move to add apparent mass to the system to keep the engine speed constant. If there is a similar level of explanation for the balancing mechanism for the speed of sound propagation, I'd like to see that, too.

I guess, I'm not yet convinced that there isn't one.

I hear you. I understand if my explanation didn't satisfy you, but I did provide a sort-of-answer to that:

here's my guess: the higher momentum in the higher-pressure wave that results from a "fast" perturbation is balanced by the higher concentration of mass within that wave: more momentum, but more mass to move within that region, so it balances and the propagation speed is the same. Perhaps someone with more knowledge of kinetics can chime in, but that satisfies my brain.

...yeah, not exactly authoritative . As I said, that makes sense in my head as an explanation of why it balances, but it obviously wouldn't suffice as a "proof" of why.

If one looks at centrifugal governor and is told that the forces balance, one can say "I'm satisfied, that seems right" even if one doesn't know the differential equations behind it all. Hopefully someone can provide a clearer explanation than mine for you about the propagation, if mine doesn't satisfy. I fear that the complexity of the forces involved may be an interplay that is beyond mere mortals' psychic reach without some mathematical abstraction: as opposed to objects of the same mass falling at the same rate, this subject may not be intuitive. I think you'd agree that there are plenty of things in the world, even limiting our perception to Newtonian physics, that are beyond grasp without abstractions like math to aid us? So maybe sound propagation, beyond however far we've come in this thread, is one of those things? Otherwise I'm hoping some mechanical engineer can do a better job than I on this important point of "balancing".

I don't think I'd go so far as to say that they are so well matched in speed as to be coherent but, if they all have the same temperature (same energy), why wouldn't they all be moving at the same speed?

They don't have the same temperature/energy. They have different kinetic energies, and the average is called the "temperature" of the air in question. See the helpful animation at: Temperature - Wikipedia, the free encyclopedia

-c

 

[dknguyen]

Is that really just deferring the problem to another plane (no pun intended)? Saying that it can't be thought of on a Newtonian level (ie: actions and reactions and masses and inertia) but, rather must be elevated to the almost mystical zone of...(cue organ)..."fluid dynamics"?

I think speed-of-sound velocities can allow us to pretty much ignore relativistic effects and aren't what we are left with is Newtonian Physics?

It probably can be approached a Newtonian level since a fluid is just of particles, but the particles are much much smaller than we are used to thinking about. The Newtonian might be too low level in this case because it's a fluid with many more much smaller particles with a lot more interactions to keep track of that manifest as higher level phenomena. For macro-particles, Newton might be a high-level explanation, bUt for fluids Newton might be too low level. There are too many interactions going on in a fluid to keep track of using Newton. Kind of like trying to do all biology soley by working at the chemistry level, or doing all chemistry by working at the physics level.

I lustily add my voice to those here who proclaim themselves to have NO fluid dynamics expertise but, I have to wonder if there are not simplified analogies here, too that us common folk can understand...at least well enough to see thing on a "mechanical" level.

If air is made up of molecules of gasses, it makes sense to me that some reasonably elementary explanation of the interaction of the molecules of those gasses to propagate sound should be possible and practical. I mean, science classes don't have any trouble introducing Slinkies and steel balls separated by springs and longitudinal waves, etc. to supposedly teach us about sound propagation (even though those things don't really do it <== my opinion).

From what I've been seeing so far about flight, there is aren't any elementary Newtonian or fluid dynamic explanations that are satisfactory at the kind of level you are searching for. Just like with your case about sound, it seems that for every elementary or simplified explanation that one can come up with, all you have to do is look into it just a little bit deeper before everything falls apart (that's the reason I don't think you actually figured out how wings work at an early age, but think you did, and I think you are trying to do the same thing with sound that you think you did with flight). THere is such a thing as irreducible complexity and I don't think that my problem with flight and your problem with sound are coincidental since they both involve fluid dynamics, which neither of us understands very well.

From the sounds of it, you would also be really perplexed as to why tapping the end of a slinky with a higher or lower speed does not affect the speed that the wave propogates at or what actually decides the speed of the transverse wave when you wave the end of the rope up and down (since you aren't actually pushing longitudinally at all). Maybe it would be easier to figure out one or two of these macro examples first before moving onto the complexities of a fluid.

 

[Sceadwian]

Don't Schlieren Photographs require really bright light?

 

[tresca]

There has certaintly been alot of discussion on this and i have not read all 11 pages of this thread.

So, some questions may have already been answered, but I will try and give my understanding to it.



Sound is a pressure wave. Something pushes against a medium at certain frequencies and our ears detect this change and produce sound.

Molecules cannot occupy the same place at the same time. Just like how no two cars can occupy the same parking spot at the same time. As mentioned before, sound is a pressure wave, which means, something is pushing molecules around. Lets pretend its my voice and the medium is air. As I say a word, I am causing the air around my mouth to move. Those molecules then move outwards, and essentially push the other molecules away. There is a transfer of energy. Since molecules cannot occupy the same location and there was a transfer of energy, new molecules are pushing out. Each successive collision with other molecules causes loss. That is why for a given amplitude, someone can only hear you so far away because our ears will not be able to detect the difference in air movement. That is why there is no build up of sound at a node.


There are somethings in the world that intuition alone cannot explain. For that, we need to turn our eyes towards math to help us understand what we cannot see.


Did that answer the original question on page 1 ?

 

[Sceadwian]

Viewing waves on water explains it pretty well for me =)

 

[dknguyen]

Actually...I just came up this analogy. I think it's quite good...

First let's outline a few basic things:
Propogation of sound is NOT the movement of the air molecules. It is the propogation of energy due to the movement of the pressure wave which is where the molecules transfer their kinetic energy to other molecules when they collide. THe molecules themselves are just vibrating back and forth- one one extreme of the oscillatory motion (closest to the source) they are impacted by other air molecules and receive momentum from them. On the other extreme of the oscillatory motion they impact other air molecules transferring their momentum to those molecules.

Now, why is the motion of the air molecules is not directly tied to the motion of the diaphram? And why is the speed of sound always the same for the same medium regardless of what the diaphram is actually doing? I am proposing that the compressibility of air (which is dependent on the vibration of the air molecules due to kinetic/thermal energy, inertia, friction, and elasticity) is the key. Regardless of how fast you compress the air, the rate at which it decompresses is dependent on the medium and not how the medium was compressed to begin with. The initial compression produces the high pressure front, but the decompression causes the medium to push against itself moving the high pressure front through the medium thus propogating the sound.

Now the analogy...air molecules are moving VERY quickly all over the place. Much more quickly than the diaphram is. So from the diaphram's perspective, each air molecule and the empty space surrounding it is actually like mass of foam (sort of like an electron cloud in an atom). THe molecule moves around this empty space so fast that as far as the diaphram is concerned, the molecule is everywhere in this empty space even though it's not. So you can push against this empty space and come into contact with the molecule, but since there is also empty space around the molecule, it will give way if you push. Sort of like a block of foam. Now... if you have an infinite row of foam blocks sitting against each other (large air mass), and you apply momentary pressure to a block of foam sitting at the end of the row (like a diaphram) by hitting it hard enough so the compresses (forming a high pressure front) causing a subsequent decompression towards the far side of the foam block thus transferring the compression to the next foam chunk(ie. propogation of the pressure wave to areas of lower pressure- the speed of sound). Does the speed at which the foam decompresses and the subsequent application of pressure to the next foam block which compresses it and so forth, vary with how how hard you smacked it? No, it does not. Now if you smack the end of the foam column periodicially, multiple peaks of maximum compression would appear with a new one being formed with every smack as the older peak rippled down the row. The higher frequency you smacked the end of the foam row, the closer the distance between peaks (higher frequency sound). THe harder you smacked them, the more higher these peaks would be (higher pressure, higher amplitude so louder sound).

So what determines the speed the pressure fronts, max compression peaks, or waves (whatever you want to call it)? The compressibility of the foam (and how fast it decompresses) which is dependent on things like inertia, elasticity, and friction. Just like air particles.

 

[crashsite]

Square One

They don't have the same temperature/energy. They have different kinetic energies, and the average is called the "temperature" of the air in question. See the helpful animation at: Temperature - Wikipedia, the free encyclopedia

Well, let's see. If this animation is slowed 2 trillion fold, that would put the action on the order of pico-seconds. So even if you're down to angstrom units of distance, the vibrational speed of the atoms would be much greater than Mach 1. So, that part of my theory falls apart and I must go pretty much back to square one.

But, we know that sound does propagate at Mach 1 (by definition), so there must be some mechanism by which it does it.

I think dknguyen may be on the right track a couple of posts further down. Sort of an extension of your rulers but, with the rulers being squishy and elastic. I'm definitely going to have to mull what he says over but, it's a concept that I know I never heard in science class.

The question now is did I not hear it because it's all bunk or because the teacher was....?

 

[crashsite]

Much More Involved Than Your Usual Home Movies...

Don't Schlieren Photographs require really bright light?

They sure did 50+ years ago when running celuloid through a high-speed movie camera at 1000 frames a second. I don't know about now but, I would guess not particularly.

It would be interesting to see if a Schlieren movie sequence could capture the air pressure patterns around something like a piezo emitter (such as my digitape unit, which I pictured in an earlier post in this thread, back on page 5...which BTW was also the way some the old Polaroid and home video cameras used to autofocus). It would be especially interesting if the sequence could capture and show the sound wavefront propagating away from the face of the piezo element.

 

[crashsite]

Near Field vs. Far Field

Molecules cannot occupy the same place at the same time. Just like how no two cars can occupy the same parking spot at the same time. As mentioned before, sound is a pressure wave, which means, something is pushing molecules around. Lets pretend its my voice and the medium is air. As I say a word, I am causing the air around my mouth to move. Those molecules then move outwards, and essentially push the other molecules away. There is a transfer of energy. Since molecules cannot occupy the same location and there was a transfer of energy, new molecules are pushing out. Each successive collision with other molecules causes loss. That is why for a given amplitude, someone can only hear you so far away because our ears will not be able to detect the difference in air movement. That is why there is no build up of sound at a node.

That does a good job of explaining what may happen at the interface between the emitter (vocal cords in your example) and the immediately surrounding air. Not so much why the words you say, remain essentially intact, 110 feet away a tenth of a second later. Or why 110 feet in air but some 13,000 feet in steel.

That's pretty much where the explanation also seems to stop in science class. Maybe dknguyen is right that the next step is so...esoteric...that it's beyond the minds of mere mortals. I sure hope not!

Actually, I'm kind of intrigued with his "foam blocks" analysis...gee, on the previous page already. But, I'm going to have to think about that one for awhile for it to sink in.

 

[tresca]

Or why 110 feet in air but some 13,000 feet in steel.

The more dense a medium is, the closer the molecules are together. The closer they are together the greater chance, a collision will occur. More energy, the greater the vibration.
However, in a gas, the molecules are much farther apart, and thus have a harder time transfering this energy and so.

I guess one way to maybe look at it is, say you are going to punch someone in the face. If you are really close to him, you hit him smack on and he'll fall back. But what if he steps back, your follow through no longer hits him in the face, now maybe his shoulder. The furthur he steps back, the lower on his body you hit him until you are not hitting him at all. Assuming your punch is a right/left cross with a follow through at a slightly downward angle.

So the denser(closer) something is, sound propogates(lands the punch on target) better because you can transfer the energy much better. The less dense(farther ), such as a gas, the harder it becomes to propogate (land a punch on target).

Analogy might be a little off

 

[chconnor]

Is this one of those sociology-class experiments about the Internet? To see how long you can keep a thread going? You picked the right forum.

Well, let's see. If this animation is slowed 2 trillion fold, that would put the action on the order of pico-seconds. So even if you're down to angstrom units of distance, the vibrational speed of the atoms would be much greater than Mach 1. So, that part of my theory falls apart and I must go pretty much back to square one.

But, we know that sound does propagate at Mach 1 (by definition), so there must be some mechanism by which it does it.

Indeed you are right about the average particle speed; I did some research, and one estimate is **broken link removed**

But again, for the purposes of understanding why and how the pressure wave propagates, the speed of air molecules' at-rest random movements seems moot: just forget that they are jiggling; I think your previous notion of the averaged velocity vectors being a wash is right on: it's the average movement of aggregates of particles that really counts. Consider that the wavelength for a 20kHz tone (the smallest audible wavelength, at the outer edge of human hearing) is ~0.68 inches. That's a lot of molecules, even if some seem to violate the movement of a wave by going the opposite direction at > Mach 1.

Maybe it's easier if, instead of seeing my "rulers" or idealized particles as individual molecules zipping around all crazy at 500 m/s, we let each idealized particle represent an aggregate of molecules who have an average nature.

So, in terms of sound moving at Mach 1, yes, the "mechanism by which is does it" is the combination of the intra-molecular forces and the rate at which they rebalance themselves in reaction to a disturbance. Are we agreed that the remaining issue is why the rebalancing is agnostic to the initial disturbance?

A buildup of a pressure-front in air takes just so long to transfer that energy into the next group of molecules that the resulting propagation of the wave moves at Mach 1. The rate at which that energy transfers doesn't correlate with the intensity of that pressure front (aka the "amplitude of the wave", which is what the speed of the initial disturbance determines) because of a "self-balancing" effect of the forces involved.

Earlier, I threw out a theory for why that is. Here's a variation:

A pendulum swinging.... it takes the same amount of time for the pendulum to swing back to center whether you give it a strong initial push or a weak one because of the "self-balancing" effect: if the mass swings way out the side, the gravity vector pulls very efficiently down on the mass and thus exerts a strong "restoring force". If the mass swings a little bit out to the side, gravity is less efficient at expressing this "restoring force". A long travel of the pendulum is associated with high restoring force, a small travel is associated with low restoring force, and it balances. This explanation may not intuitively prove that it would balance exactly, but it's maybe good enough, right? It follows, obviously, that it takes the pendulum an equal amount of time to swing out, slow down, and stop (before it starts to head back to center) whether given a hard or soft push.

Imagine again a wave traveling through a line of particles stretching to the horizon. Since the particles themselves don't have a net movement when a wave passes through them, how do we even know where this "wave" is, in order to accurately measure its speed and name that "Mach 1"?

We track the "peak" of the wave, which in this case can be detected as the point of highest pressure, or, put another way, the point at which the particles stop moving forward, and can even start moving backwards (especially in a cyclical wave; see the handy image from page 2).

In the "fast version", after the initial push, the first particle is moving very fast, but its high speed eventually slows to a stop as it pushes up against the second particle. The same thing happens in the "slow version": initial movement, then stopping (and with both, a potential reversing of direction). Like a pendulum given a push, the particle in the fast version moves quickly over a greater distance but meets a higher restoring force. The slower particle moves a short distance and meets a lower restoring force. The forces "balance". The speed of the initial push determines how far the first particle will move before stopping due to proximity with its neighbor, but not how long that will take. As with pendulums, it comes out the same. We are reducing out a lot of mechanics, here, of course, but that's the gist. Again, these "particles" are standing in for aggregates of molecules.

The principle is the same as the particle is imparting its energy into the next particle in line: higher speed = greater acceleration and distance but higher repelling force. The fact that the initial push was fast or slow isn't forgotten by the wave, it just manifests as the intensity of the pressure instead of the speed of the propagation; that speed, like a pendulum system, is dependent on the mass of the particles, the restoring forces at play, etc etc (aka the "medium") by the principles suggested above.

There's a ton of simplification in all this, to be sure, but it gets the point across. Or does it.

Someone smack me down if i'm off-base, here.

I think dknguyen may be on the right track a couple of posts further down. Sort of an extension of your rulers but, with the rulers being squishy and elastic. I'm definitely going to have to mull what he says over but, it's a concept that I know I never heard in science class.

Hey, whatever works. The rulers were made squishy and elastic by virtue of their repulsive and attractive fields at the end, but it's just semantics.

-c

 

[crashsite]

Too Many Variables....Yikes!

The more dense a medium is, the closer the molecules are together. The closer they are together the greater chance, a collision will occur. More energy, the greater the vibration.
However, in a gas, the molecules are much farther apart, and thus have a harder time transfering this energy and so.

I had thought of this but, then hit a snag when colder, denser air gives a slower speed of sound. That's when I started thinking about the relationship between temperature and the vibrational speed of the molecules and how that might explain the temperature vs. Mach speed.

 

[crashsite]

I think I'll buy some Excedrin...

Indeed you are right about the average particle speed; I did some research, and one estimate is **broken link removed**

Actually, I'm a little surprised that the number comes out so close to the known speed of sound.

An issue I've thought about but, have been deliberately avoiding is the business about air being a mixture of gasses and how that mix affects the speed of sound. But, if one must think about averages anyway, maybe the average vibrational rate of the whole mass of air is what has the velocity of Mach 1?

What I am sure of is that I'm getting a headache! My mind is not as nimble as it never used to be.

It does seem like you and dknguyen really are pretty much saying the same thing, just in slightly different ways with different analogies when you describe your respective thoughts on how the sound wavefront may propagate.

I'm going to have to do some mulling on all of this. But, I feel like I'm getting some views that are leading to some modicum of understanding in my feeble brain. At least I hope so.