Elementary my dear, Watson...
Yes, I said to FULLY understand sound propagation, and I stand by that comment, admitting that I do not FULLY understand it (by fully I mean completely describe the continuous motion of individual particles and the forces between them).
I have to believe that a few concepts can be picked out of the complex world of physics and presented at a fairly elementary and mechanical (read that, "non-mathematical) manner. Otherwise it would make no sense to even try to discuss sound propagation except with the likes of Einstein and Hawking.
But, I have to be realistic that any elementary descriptions of what's happening will be open to lots of (well justified) criticism by people who are more astute in physics than myself. Still, I have to hope that my child-like models will give sufficient
conceptual information to allow the other math morons, out there in the world, at least a reasonably defensible model on which to base their understanding of sound propagation.
I believe that the molecular view is the correct one to gain that conceptual understanding.
As a side note, you keep using instant-by-instant, however to me this implies discrete time stepping and I believe you actually mean continuously. This is kind of a math term so I’m sorry, but I believe it much more accurately describes what you mean and what is going on.
I absolutely mean, "instant-by-instant" (regardless of mathematical definitions of the terminology). Instant, as defined by the time it takes for a molecule that's been bumped by another molecule to then bump another one. That seems like it's typically only a few picoseconds (which to me is pretty instant-like).
Conceptually that should be sufficient (for a gas), however I believe this is what the majority of the information presented here is trying to do and you are dismissing all of it. I would also like to mention that the spring mass model is very much a Newtonian system.
It just seems like the, spring mass model has more to do with the way the molecules themselves interact with each rather than how the molecules interact to move the sound along.
But, I'm open to why it's also germain to the actual sound propagation process.
I’m not sure whether your arguing against standing waves in general or just in sound/pressure....
Waves, in general are a phenomenon that happen over time. If one were to take an instantaneous snapshot of the positions of air molecules and examine it, would one see a wave? If the answer is "yes" then waves and standing waves can exist. If the answer is, "no" then the wave, or any wave structure, can only be thought of as the result of what happens to the molecules over time.
As I've said many times, I think this is the primary problem with the way schools teach sound and sound propagation. They start out with waves and then when it comes time for sound to propagate at 1100 feet per second...there's no reaons given except that, magically, somehow, it does.
I ask someone to tell me how longitudinal waves in the air manage to zip away from something like a speaker at 1100 feet per second. How can they? That's just not the right venue to try to do it.
I think you misunderstand thermal energy (I believe this is what you mean when you say “heat”, if not the speaker may be cooled so that it imparts zero or even negative heat into the air, and you may ignore the rest of this post). I said it in my original post and I will say it again: Sound is thermal energy (molecular energy relative to each other), therefore you cannot ignore the energy imparted by the speaker (otherwise there would be no sound).
I'm sure I do! So, I restrict myself to the very mechanical model of heat making molecules move and more heat making them move faster. I allow that different materials hold their molecules differently and so the motion of the molecules can be different in different materials.
I accept that heat transfer by conduction is from the energy exchanged as molecules, with different energies, bump each other. But, I have a virtually non-existent understanding of how radient heat is either absorbed by or radiated by a molecule.
I also assume that, when the subject is sound propagation, there is at least a tacit assumption that all the molelcules are about the same temperature and so they merely change directions when colliding rather than transfering energy to/from each other.