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