JD: One of the problems I see with your tube of magnets analogy is the internal flexibility compared to a solid. The molecules of a bridge are indeed in constant motion (if the bridge is somewhat warmer than absolute zero, that is!), but that's not the issue here. If the top of the bridge is moved, the whole bridge moves. In spite of molecular motion, it IS a solid. That cute Java enabled illustration intimated that the middle of the object was in motion, but the outside was not. While that shows the molecular motion of all things above absolute zero it has nothing to do with the transmitting of vibration through a bridge. dave *********** REPLY SEPARATOR *********** On 1/18/2002 at 10:28 PM John Delacour wrote: >At 7:34 PM +0000 1/17/02, Phillip L Ford wrote: > >>John, >>I don't have a problem with any of this. Please proceed. > >OK, to continue -- though I've gathered quite a bit on new and very >interesting stuff in the meantime. > >At 7:44 PM +0000 1/15/02, John Delacour wrote: >>.....If we move the top magnet a certain distance and maintain the >>pressure, the magnets will (very fast but _not_instantaneously_) >>take up different positions in respect to each other. Each magnet, >>or particle will have been displaced a different amount and the ray >>will be in a state of compression. > >I don't know how other people's minds work, but I'm one who needs to >visualize models and more than that actually make things and >experiment during designing things. I very rarely begin with the >drawing board and an idea; the drawing board comes second and the >maths comes in when its needed. Anyway, with this soundboard thing, >I found that the only way to get a proper mental picture of things >was to see the whole system as particles subject to forces; that way >I can magnify the picture in my mind or on paper and see whats >happening. Things like the animated gifs at > ><http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html> > >which Stephen mentioned a few weeks ago are most useful to me because >they cut through all the calculus and present a very simple picture >of what's going on in certain types of wave. It's a pity he doesn't >go a bit further. > >So...I have so far given an analogy of a ray of magnets/particles >held in equilibrium in a perspex or glass tube by a repulsive >magnetic force. We press on the top magnet and one by one down the >tube the other magnets are displaced downwards, except for the bottom >one which comes up against a rigid obstacle at the moment. Before we >leave this analogy, let's immerse the tube in a tank of syrup and >press down the same amount and the same distance on the top particle. >The magnets will rearrange themselves exactly as before but this time >very much more slowly. It will now be possible to observe the wave >of pressure reaching each particle in turn as it travels downwards. > >PARTICLES IN AN ISOTROPIC MEDIUM > >o o o o o o o o o o o o o o o o o o o o o o o o o o o > o o o o o o o o o o o o o o o o o o o o o o o o o o o >o o o o o o o o o o o o o o o o o o o o o o o o o o o > o o o o o o o o o o o o o o o o o o o o o o o o o o o > >In order to get a more useful picture of an isotropic elastic medium >and to allow us to consider it in two and three dimensions, let's now >get a tank of transparent liquid silicone rubber and suspend lots of >ball bearings equally spaced in the fluid until it sets. I'll now >refer to the balls as particles. The silicone rubber is, of course, >the forces that keep them in equilibrium, equally spaced one from >another. The distance separating the particles will be infinitessimal >in comparison with the ascii picture drawn above. > >The density of the material and Young's Modulus of elasticity for the >material will determine how it behaves and how fast waves will move >through it. A disturbance of any kind to one particle will upset the >equilibrium existing between it and its neighbours, and this >disturbance will be passed on through the medium as a wave. at the >instance of any stress, the particles will tend to restore themselves >to a position of equilibrium, so if you imagin the picture above is a >12 mm thick sheet of our stuff and you curl it round a hammer-head as >you would hammer felt, then the particles at the bottom will be >forced closer together and those at the top pulled further apart. >When the force is removed, the internal forces between the particles >will resore the sheet to its flat state. > >If you whack the left end of the sheet, the particles at the end will >push the neighbouring "column" of particles to the right and bounce >back and this wave of column-pushing will proceed along the sheet at >a definite speed. See the Dan Russell animation of this. > >Soundboard wood behaves very differently along the grain and across >the grain and would be considered roughly 'orthotropic' as opposed to >isotropic (same in all directions) and anisotropic (different in all >directions). As a result there are varying values of Young's Modulus >for spruce and the speed of longitudinal sound waves in the material >will be far greater along the grain than across it. This is why I >find it useful to think rather of a homogeneous, isotropic system >first and introduce the complications of the real wood later, since >the priciples are the same. > >However, the speed of sound (longitudinal wave speed) along the grain >of a plate of spruce (as oppused to a bar or rod) is maybe 5,000 >metres per second and is related to its elasticity and density as >follows > >CL = sqrt( E / (rho * (1 - mu^2)) > >CL = Wave speed >E = Young's modulus for the material (effectively, it's stiffness) >rho = material density (0.33 for Sitka spruce) >mu = Poisson's ratio (depends on the material but say 0.3) > >The speed of a Bending Wave (or Flexural Wave) is directly related to >the longitudinal wave speed, and consequently to stiffness; but also >to its frequency. I will come to bending waves later on, when I've >got a better picture not so much of how they look as how they are set >up. > >I will repeat that I find it useful to see all waves as what they >are, namely phenomena that happen to particles of a medium in reponse >to forces. > >Let me know if all that makes sense. In the meantime here are a >couple of URLs of limited interest, but which deal with some of the >quantities I've mentioned. > ><http://www.fpl.fs.fed.us/documnts/pdf1998/ross98d.pdf> ><http://www.fpl.fs.fed.us/DOCUMNTS/pdf1998/liu98a.pdf> ><http://www.fpl.fs.fed.us/documnts/pdf2000/liu00c.pdf> ><http://www.ndt.net/article/apcndt01/papers/988/988.htm> > >JD _____________________________ David M. Porritt dporritt@mail.smu.edu Meadows School of the Arts Southern Methodist University Dallas, TX 75275 _____________________________
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