I’ve been following this thread from the start (I, like crashsite, have been thoroughly enjoying the mental exercise of thinking about sound in depth and questioning my understanding of the subject), and have been trying to resist joining this forum just to add my 2 cents, but could resist no longer.
I would like to try to give crashsite what I believe he is looking for and that is the conceptual view of sound propagation at the molecular level from the “classical” physics perspective (at least how I understand it). To do this I must start by examining intermolecular interactions, and this starts with the Lennard–Jones potential (a simple enough assumption that has been experimentally derived). Note that this is only looking at molecular energy (aka heat), a type of energy that skyhawk failed to mention in his write up on energy a few pages back (see below for a side bar about energy). If we fix a molecule in space and place a second molecule next to it at absolute zero the molecule is sitting at the bottom of the “trough” in the curve, and as energy is added to the molecule it moves back and forth along the curve to the level in which it has energy (think: a marble rolling up and down the curve). If it has energy greater than zero it is a “free” molecule (aka gas). If you add a third molecule, the molecules would arrange themselves such that they move around the corners of a triangle (assuming energy less then zero). Adding a fourth turns it into a pyramid. This 3-d vibrational system is already a fairly complex system (As more molecules are added the complexity goes up extremely quickly because even in a gas ALL molecules are constantly influencing ALL other molecules, not only those “colliding”). Now, for the system to be “liquid” it must be in an energy state such that during these movements the average molecule may pass between two others but not above an energy level of zero relative to all other molecules, otherwise that molecule would become free. From this it is easy to see were the spring mass model comes from, at least for solids. For liquids it is a little more difficult because the springs may “slip” past each other, and for a gas it is even more difficult because the intermolecular forces are very non-linear and primarily driven by repulsive forces and dependant on the repulsive forces of other molecules or some other external force, such as gravity for restoration (very different from the typical spring). This non-linearity and the shear number of molecules involved (not the assumptions made to get here) is the reason for the complexity of the math involved in solving this problem. Now if you disturb a molecule in this system with an added force (sound) the disturbance travels through the system per these intermolecular forces (read as: independent of input force, except for the molecules directly interacting with the source) and can be shown to do so with some very complicated math (which I have not done, nor do I believe I could do if I wanted to, but you can see the book referenced several pages ago if you feel the need to see this done). The complexity of this problem is one reason the linear spring mass system (aka slinky) is used for demonstrational purposes and class room calculations, another is the ease of its observation and correlation with calculations (the math involved for the simplest of true materials is over the head of the majority of even physics/math majors heads). As a side note you can also derive vapor pressure, molecular packing and other molecular concepts from this as well (Note how all of these concepts fit nicely together into a single hypothesis, as is the goal of most of physics). I do admit that because none of this can be observed directly it still is only a hypothesis, a hypothesis with hundreds of years of experimental data supporting it, but a hypothesis none the less. (In the scientific method there is no “prove hypothesis” only draw conclusion and retest)
To directly answer the original question “why does sound propagate?” simply F=ma. Here F is intermolecular forces (per Lennard–Jones potential, which is material dependant), m is the mass of the molecules and a is the resulting acceleration. From this you can easily see how the speed of sound is independent of input force.
Now my thoughts on a few of the issues brought up throughout this thread:
As far as energy is concerned skyhawk is on the right path, energy is just something we define so that we can conveniently relate how different concepts interact. Note that different types of energy have been added as our understanding of different things have developed, but the idea correlates very well to observed data, and the concept of conservation of energy is yet to be proved invalid (it probably never will, because new types of “energy” can always be added).
As to the dependence of the speed of sound on temperature but not pressure, let’s look at F=ma. Pressure is defined as force per area, from this we can see that the F is only dependant on the pressure of the gas and the “collision” cross sectional area (how head on the molecules collide, which must average to zero over enough collisions otherwise there would be a net acceleration of the air). So increasing the temperature but leaving the pressure the same leaves F the same, but decreases the number of molecules for a given distance. Therefore each molecule is accelerated at the same rate, but fewer molecules are required to be accelerated for sound to travel a given distance. Conversely, increasing the pressure but leaving the temperature the same increases the F but it also increases the number of molecules in that given distance. Therefore, each molecule is accelerating faster, but the sound must accelerate more molecules to travel a given distance, resulting in little to no change in the observed speed of sound.
Can sound travel in a medium at absolute zero temperature, NO, but only because sound is molecular energy and by definition temperature is a measure of molecular energy in the system. Therefore the simple act of producing the sound (adding energy) means that the medium is no longer at absolute zero.
The MIT steel ball on a column of air does a very good job of demonstrating the “springiness” of air, nothing more. And yes, it is a steel ball. Don’t underestimate the influence of pressure. A few psi over a few square inches gets to be a very large force very quickly.
Newton’s Cradle and the pool ball analogy are both just spring mass systems as is everything else (See: bulk modulus, young’s modulus, etc. Even setting a feather on a steel table deforms the table somewhat.) In Newton’s Cradle the kinetic energy of the initial ball goes into a compression wave that travels through the center balls at the speed of sound in steel (~6000m/s), and this compression wave throws the last ball from its initial rest. Under a high speed camera and magnification I believe you would actually be able to observe this, but I was unable to find such a video.
The pool ball is a more complex system because it is both non-linear and discontinuous (F=0 until the balls touch then it increases rapidly until the balls begin to move apart), but it is still a spring mass system. It is true that this may be the best analogy for sound moving in a gas, however it is no where near a good representation of sound moving in a solid or liquid, and even in a gas there is molecular influences on other molecules when they are not “colliding.”
Standing sound waves are common (see wind instruments, breaking a glass with sound, etc.)
Crashsite,
First, I don’t see how you can dismiss wave analysis so easily. We know that the speaker/sound source of any kind imparts energy into the medium and this energy travels at mach 1 through the medium. Anywhere along the path of this energy we can observe the increase in energy then a return to (almost) ambient. This is, I believe, by definition a “wave”, an energy wave, but a wave none the less (This is independent of molecular movement assumed, if any at all).
Second, I don’t think you will convince anyone (at least not someone who has sufficiently been taught the wave/spring-mass model of sound propagation) by the methods you are attempting. First you must fully understand classical thinking before you can argue against it and second because you are going against classical thinking, it is on you to do one of two things 1) show how classical thinking fails to meet observed results or better yet 2) plainly state your own hypothesis and show how it better matches observed results. I have yet to see either of these conditions met, but if you do you will have a much easier time convincing people. However, I believe, I can disprove your hypothesis (“The thermal energy of the air is providing the power to propagate the sound") simply by looking at water. The speed of sound in water is ~1500m/s but the speed of sound in water vapor at 134ºC is only ~500m/s (
The Nature of Sound), and I think you would agree that molecules in water vapor have much more thermal energy than those in water. If you limit your hypothesis to gasses, you are probably very close, but then your hypothesis varies from classical thinking by very little at that point as well.
Lastly, I’m having a hard time seeing how your vector biasing does not lead to molecular oscillation and on into the wave analysis. A velocity vector bias in one direction leads to bulk movement of air (and a local pressure increase, or else sound travels at infinite velocity), this movement of air forms a reduction in number of molecules (vacuum) in front of the speaker, and this vacuum “sucks” air back into this area, returning air to its original location. And as this bulk movement (local pressure increase and trailing vacuum) moves away from the source a wave is observed.
There are many issues here so I probably have missed several, but that’s enough rambling for now.
