At 8:32 AM +0000 1/24/02, Phillip L Ford wrote: >Agreed, except I would say that how much it is free to move is not dependent >on string energy but on soundboard and bridge properties. How much >it actually >does move depends on string energy. Of course. >Agreed, except that I would not say that the termination of the string is >exerting a force at the bridge but that the string itself is exerting a force >at the bridge. Now that really is playing with semantics :-) > > If I press on the unloaded soundboard (no strings) it is > > clear that every molecule of this column will move downwards at > > exactly the same speed... > >This doesn't seem consistent with your stack of magnets analogy to >me. Even in an unloaded board, the bridge has stiffness and the >board has stiffness, so you're offering some resistance to the >bottom magnet.... No, I said press on the _soundboard_, not press on the top of the bridge. >The top of the bridge starts to move before the bottom of the bridge. The >bottom of the bridge moves 7 or 8 microseconds behind it but is then >moving too. I would call this bodily movement of the bridge. If this is >the reason for saying that the bridge does not move bodily and does >not move the soundboard bodily then there would seem to be little >disagreement about what's going on except over definition of terms. In that case there is little disagreement according to you. When I set off this thread or its predecessors so many weeks ago, I approached the discussion with far less understanding of things than I have now and I don't mind admitting that with my present level of competence in integral and differential calculus, there's a limit to where my understanding will ever get. My initial picture was of the pulses introduced at the string termination by the disturbance of the top particles of the bridge, travelled to the soundboard, were somehow distributed at the speed of sound throughout the structure and that the soundboard then vibrated as a whole, causing the bridge as a whole to vibrate. At that time I pictured transversal vibrations of the board something like the modal or resonant vibrations and I saw these as independent from the vibrations in the board that cuased the sound of the strings to be radiated from the board. There is actually a certain amount of sense in this as a first shot at understanding the phenomena, but I now see it as flawed. What perplexed me then was how the sound waves introduced at the string termination caused the soundboard to pulsate at the same frequencies as the strings. It seemed quite impossible for a three dimensional shape to vibrate at the frequencies required by the strings. I next envisaged the water pressure analogy in a reply to you and At 5:22 PM +0100 1/9/02, Richard Brekne wrote: >your "radiate" seems to correspond pretty good with Olsons >description of sound board radiation in which case I see almost the >exact same description when it come to Benades description about the >longitudinal nature of transverse like surface waves. In all this >you could sort of look at these as a huge collection of tiny ... >Olson uses the word "pumps" pushing away at the air in his >description of sound board radiation.... btw.. I read your stress >waves reply to Phil and this also points in this same direction. You >said then > >"Acoustic radiation is caused by minute pressure differences at the >surface of a body." More recently, the Bending Wave has been given as the main source of acoustic radiation, and seen in one dimension this is simple enough to accept and to visualize. For the moment I am inclined to depreciate my previous notion of compression waves acting orthogonally to the board as the source of the radiation and to see the board as the "pond in a rainshower" puckered with tiny craters due to the travelling bending waves criss-crossing it from all directions. Another notion I have had to take on board is the notion of the plate (soundboard) as essentially a two-dimensional object for mathematical purposes at a basic level. With this notion on board, it is easier to conceive of the mechanics of acoustic radiation. >You say that some molecules of the bridge will be pressed together and some >will be moving apart? Why is that? On the first downward cycle of the string >it seems that all the molecules will be pressing together. On the >upward cycle >of the string the molecules would be pulling apart? At the frequencies we are concerned with, what you say is true most of the time. As the direction of the pressure at the top changes, there will be an upward pull at the top while there is still a downward push at the bottom. Besides, the degree of displacement of the top will be different from that of the bottom -- and we are talking here only of a one-dimensinal cut down through the bridge; what is happening to the bridge a few cm. along? Something quite different, I'd suggest. This is why I do not accept the notion of bodily movement and the consequences claimed. >So, as I see it, what you're saying is, on the initial downward >cycle of the string, the string exerts a downward force on the top >of the bridge, which causes the top of the bridge to start moving, >the bottom of the bridge moves shortly thereafter, and the >soundboard follows as the load or pressure wave propogates to the >rim. This sounds like the string moving the bridge which moves the >soundboard. On a macro scale we would see that as a result of the >string moving down the top of the bridge moves down but lagging >somewhat the downward movement of the string. The words that some >people would use for this are that the string is moving the bridge >and soundboard. This would also seem to be the behavior described >by vibration theory for a one degree system with a mass and spring. >I thought there was some disagreement about whether such a model was >correct for this situation. >And what does the output from the accelerometers mean? Does it indicate >that those points are physically moving? I thought this idea was scoffed at >before? Not at all. When a particle or a tiny part of the medium is first set in movement (oscillation) it will be moving with reference the remainder of the medium which remains undisturbed until other particles are affected in the passage of time. The particles of the medium in equilibrium (neglecting their constant vibration due to heat, which is not a factor) are in a fixed relation to each other. If a force is applied to the medium in one direction and meets no opposition, this relation will not change. If pressure is applied at the top and an irresistible force opposes it at the bottom, there will be a change in this relation and compression. If a periodic force is applied at the top opposed to a firm resistive (but not irresistible) force at the bottom, there will be vibration and localized differential movement of particles within and at the surfaces of the medium, which I distinguish from bodily movement. JD
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