On Fri, 11 Jan 2002 00:20:30 Robin Hufford wrote: > I >continue to say that any physical motion induced by the so-called cyclic loading of >the system is very, very small, would be detrimental, and that soundboards are in >fact intentionally or otherwise designed to miminize, control or eliminate this. > Local yielding, or local deformation of the bridge in the area of contact with >the string is inherent in the notion of strain propagation. This however, is not >physical, substantial, bodily movement of the bridge itself, that is, motion which >is claimed to be capable of moving the soundboard. It may well happen that >subsequent to the loading of the soundboard by stress propagation and cyclic strain >that the board may indeed cause flexural waves or other behaviors at the bridge but >this is not a motion that is a consequence of the transfer relations between string >and bridge but rather the result of stress concentration in the sounboard/bridge >itself, a different subject altogether. >Rendering the system analygous to a simple one degree of freedom system such as one >finds demonstrated with the dashpot and spring analyis of harmonic motion so >frequencly encountered in the beginning of texts on harmonic motion is but one >example. Well, we seem to still be where we started. There are those that feel that the soundboard acts in a similar fashion to the one degree of freedom system you mention here. Subject to a dynamic load, the mass of this system will have movement, and if the forcing frequency is near the resonant frequency, substantial movement. You, however, are stating that the soundboard does not move as a result of the input from the strings, or that it would be better if it didn't move. This seems to put us at an impass. A lot of discussion hasn't really budged proponents of either view. > Although the factors generated by these introductions are absolutely basic >and necessary of course, their utility to the analysis of soundboards is of a much >greater complexity and a different perspective is required especially regarding >transfer relations of energy from one part of the system to another. As I have said >before, this is not by any means an original view of mine but rather, can be found >in any reasonably comprehensive book on the various aspects of mechanics and >acoustics. Several references have been provided by the proponents of bridge and board movement. I take it that none of these has altered your view. You say this view can be found in any reasonably comprehensive book on acoustics. Perhaps you could provide some specific references. If a reference is in a book would you also be so kind as to give chapter or page references? > Viewing the string as a force component, that is, a vector which in >conjunction with a vector provided by the stiffness and mass in the soundboard, is >capable of moving the bridge distant to the agraffe or capo vertically is >progressively laden with problems as the frequency of loading increases, that is as >the rate of loading increases. Of particular importance is the general inability of >the system to follow, due to its intertia, this so-called cyclic loading or forcing; You would see this same inability in the one degree of freedom system you mention above. At forcing frequencies close to the resonant frequency of the system there is a lot of movement. At forcing frequencies far from the resonant frequency of the system there is not much movement because of the system's 'inability to follow'. This doesn't mean there is no movement. Depending on where you are in the frequency spectrum relative to the resonant frequency of the system the phase between forcing and following will be shifting, a further indication of the system's inability to follow. Once again this does not mean that there is no movement. This seems to me to be what selectively tailoring the flexibility of the soundboard is all about. You are trying to match the vibrating frequency of the string to the flexibility of the board in that area so that the board has more ability to follow. >the mutual implicit complications of the effect of this on all of the other strings, >the changes in the effects due to vibrating of the string or not, the fact that I >have reported of pianos built where substantial parts of the bridge, even though >having the strings pass normally across the top of the bridge, and having large >areas not even contacting the board under the unisons: where yet one, >in these areas, cannot tell where the difference lies through the sound, and many >other complications suggest, in my mind, the utility of other approaches. I don't see why gaps in the bridge are indicative of no bridge or soundboard movement. If the board is moving as a direct result of applied force then the force is being applied where the bridge is attached to the board rather than directly under the string. This is the same in the violin. At least one of the papers that I've referenced shows substantial movement of the top of the violin from string input. It even seems to imply that the top movement is greater because the bridge is not attached at every point. > Of >course, statically the downbearing load imposed upon the soundboard system is a >system of forces but to apply vector methods to the vibratory, rapid, dynamic >loading imposed upon it by the string is incorrect. Yes, you've said this before and I still don't see why. > For example, athough I think it likely the bridge motion proponents will >contest this, and I await the next ingenious denial, their ideas would suggest that >the agraffe itself must be moving similarly to the bridge, although on an obviously >reduced scale- that is rocking fore and aft, flexing side to side and moving the >plate underneath it. I rather doubt it. No I don't contest or deny it. This is consistent with the idea of force being applied by the string to its supports as it vibrates. If a force is applied, unless the agraffe and plate are infinitely stiff then they must move. This seems consistent with what the designers try to do - make the agraffe and plate system very stiff here so that they move as little as possible so that string energy is dissipated as little as possible at this point. This would certainly be easy enough to prove or disprove. Simply put an accelerometer on an agraffe and strike the string. If you are correct then the accelerometer would register zero. In my opinion, if this were to happen, it would be in your words 'fantastic'. > Similarly, the rear duplex, where sound >can be heard by examining the string with the stethoscope, should cause the hitch >pin to be subject to a similar effect. Yet, when one listens with the stethoscope >to the neighboring string very little sound is heard. This occurs as the stresses >in the wire rounding the pin becomes so great relative to the stresses that are >the propagating sound in the wire that they are unable to propagate coherently >through the more intense stress concentration rounding the pin. >Regards, Robin Hufford > That's your explanation. Mine would be that the speaking length is vibrating, which moves the bridge, which causes the backscale to vibrate. Most of this vibration is reflected at the duplex bar so very little makes it through to the short length of string between duplex and hitch. Since this portion of the string is not vibrating there is no oscillating or vibratory force applied to the hitch pin. What the hitch pin essentially sees is the static load from the string. So it doesn't surprise me that there isn't much vibration in the area of the hitch pin. Phil F
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