Finally some common sense...up to the "waves" anyway...
Well, you said quite a lot there and, I agree with all of it right down til you got to the "wave" part. So, rather than reiterate it all again, I'll just make a synopsis of each of your paragraphs and then more fully discuss the waves.
Crashsite. you are right about the velocity of the gas molecules being the key to the behaviour of a gas.
If you think I'm going to disagree with that, you're nuts...
...and, not just
gas molecules.
Any molecules whether they are moving around or merely vibrating in place.
This is where the theory (and facts) deviate from your proposals. Key to this theory is that the number of molecules is very large, in excess of 10^20 in any typical container. To understand what happens in this situation you need a theory that can track a large number of molecules, this is what statistical mechanics does. You haven't presented any theory apart from a picture of a handful of molecules (color coded as you point out!).
Of course there are a lot of molecules and you can
only consider them on a statisticaql basis. That's why I've been repeatedly saying that you have to deal with them on a statistical basis and no-one was agreeing. They were all still trying to deal with it as pressure waves. I even went so far as to try to equate the process with the development of actuary tables for the insurance industry and...still no believers.
So, I put it down to the level of three (count 'em 3)
color coded molecules to show the basic action and
still no-one "got it". I am considering contacting the
Fisher-Price Company to see if maybe they've developed a crib toy that might show the concept.
In air at normal conditions, the mean free path of a molecule is measured in tens of nanometers and the collision frequency in GHz.
Yes! That's why I've been pounding on the notion that you have to think of the process of sound propagation at the picosecond time scale.a Trying to deal with it on the macro, wave level has you pushing air around...
not propagating sound.
Now you seem to be either totally confused or paranoid about waves. When we are talking about wave propagation in air, we are almost never talking about sine waves! We are talking about disturbances (like your cricket's leg). When physicists talk about waves in air they mean that for small disturbances the air obeys the wave equation. Basically this is because if you push on a bit of air, it moves it's neighbour a bit and it tends to push back but also pushes on the next bit of air - so the disturbance propagates.
That does a really good job of describing how you get ripples on a pond and ripples of air in an air mass when you push on or displace them. It does
nothing to explain how the sonic shock wave takes off at Mach 1. The problem with invoking the wave equation is that the topic of this thread is not, "
How Do Ripples Propagate?".
Feynman did make a valiant effort to try to equate the wave equation with the speed of sound (with his tiny but arbitrarily sized air pressure packets, adjacent to other tiny but arbitrarily sized air pressure packets and a bunch of math to try to eventually come up with an approximation of the "right" answer that the speed of sound is actually related to the velocity of the molecules). Then, he neglected to say
how or
why the speed of sound is related to the speed of the molecules.
That's what I'm trying to do in this thread.
Are you disputing the fact that small pressure disturbances in air behave in accord with the wave equation?
Not at all. So long as you're referring to pressure disturbances and not sound propagation.
Now the solutions to the wave equation show that what happens is that the cricket's leg moves a small amount of air locally, and this disturbance ripples out, just like ripples on a pond. The energy from the leg is spread over ever increasing area, so gets feinter.
If you're talking about the air a few millimeters from the cricket, that's probably true. Out the 300 feet, in my example and some almost 2000
tons of air removed from the cricket I'd absolutely
disagree with you.
You only collect a very small amount of this energy on your ear (in fact your ear has the external part to collect as much of the disturbance as possible to feed into the eardrum). Your ear is very sensitive and can detect very small pressure changes. You seem to be suggesting that the cricket moves all the air, I assume meaning that the pressure fluctuations at your ear would be the same as at the cricket, I can assure you that if the cricket was kicking your eardrum directly you would know how little energy you usually get.
(Emphasis mine) No, no, no, no, no! I am suggesting that the cricket moves
none of the air (beyond the air that's in the immediate proximity of the leg and thus is affected by the ripple effect). Any of the air that's involved in propagating the sound of the cricket is only displacing the position of the molecules (as you so correctly pointed out earlier) and,
that is being done by the thermal energy contained in the air. The cricket is completely passive when it comes to propagating that chirp.
The fact that the molecules are still almost exclusively in random motion and changing positions (and direction) every few picoseconds precludes them from bunching up and making "pressure cells" or "pressure waves" (or whatever you might want to call them). But, that positional bias does get carried from molecular collision to molecular collision and, because the molecules are traveling at an average speed (taking every effect into account) of Mach 1, that positional bias also gets propagated at that speed.
Whether you show that graphically with three molecules or statistically with 10^20 molecules, the process is the same.
To your central contention that seems to be that there is some conspiracy that 'hides' the fact that the speed of air molecules is the 'same' as the speed of sound.
I don't think it's a conspiracy any more than I think it was a conspiracy that people used to think the world was flat. After all, it sure looks flat and, by golly, those ripples sure do look like they might well be a solution to any sort of propagation, huh?
Just something else to ponder, from the kinetic theory and the wave equation it is easy to show that the speed of sound is equal to 68% of the rms speed for diatomic molecules and to 75% of the rms speed if the molecules are monatomic. So for two containers, one full of say Argon, the other full of nitrogen, at the same temperature they will have identical molecular speed distributions, however the speed of sound will be 9% faster in the Argon!
I can't comment on that because I have no knowledge or experience with it. But, thanks for the info...I'll tuck it away in my memory banks.
* * * * * * * * * * * * * * * * * * * * * * * * *
The first part of this is how the sound gets encoded onto the molecules by molecular displacements. The second part is how it propagates by those displacements. The third part is how those displacements are decoded (turned into the pressure that vibrates the ear drum or whatever). If we can get through this part, I'll explain that third part. But, unless or until you accept the molecular displacement model, the third part will make no sense to you either.