Phillip, I don't say that there is no applied force from the string. I tried in earlier posts to indicate the nature of forces applied to the bridge/soundboard, especially in regard to the nature of loading. Calculating the static loading of the board by the strings and the point of equilibrium of the board/string system, and this is a simplification, is obviously the effect of forces. However, the loading of the bridge itself is better approached by the mechanisms of dynamic loading where, in my opinion, there are very substantial implications for the design and behavior of soundboards. With regard to the nature of motion at the string/bridge interface I have expressed, to the point of tedium, that the transfer of energy from string to bridge is essentially through stress propagation. Call this sound, if you will. 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. Were there perfect rigidity, the wave organizing function of the terminations would be at their greatest efficiency. However the effect of this ridigity on the soundboard would be a significant and deleterious matter, as the effect of the bridge on the soundboard/rib system should in some way facilitate or at least minimize any counterproductive effects on stress concentration and acoustic radiation. 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. The surface expression in the soundboard of the waves in it is a matter of substantial complexity which is another subject distinct from the questions arising at the string/bridge interface. As to the subject of force with regard to which I have made comments to which, apparently some have taken offense where absolutely none was intended, I say that stress is not a force, and when used as such, a certain inadequacy of conceptual efficiency is inherent in such use. With all due respect to its advocates, I believe this inadequacy resides also in the prevalent view of soundboard behavior that is the deflection model, and by this a view predicated on force, mass and acceleration solely and relating it to the basic equation for mechanical waves, that is, the square root of the ratio of elastic properties to intertial properties. 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. 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. 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; 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. 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. A very useful and inexpensive device can be had in auto parts stores which can be used to explore firsthand some of the distribution of sound or stress/strain relationships in a piano. This is a mechanic's stethoscope - a device which itself uses longitudinal waves to transmit energy to the ear. The cost is usually under ten dollars. The stethoscope is like that of a doctor but has a long, thin rod on the end which is placed in contact with the object in which one wishes to listen to sound. By using this device and placing it on various parts of the bridge, soundboard, strings and other parts of the piano, substantial facts can be brought immediately to light. That is, one can trace the stress trajectory, or sound through the system. At the bridge/string interface this is, essentially, and at first at least, in the areas in contact of string and bridge. One may place the tip of the rod on the vibrating part of the string next to the bridge, an immediate extinction of sound is heard accompanied by a short rattle. Placing the tip of the rod on the top of string past the bridge pin and point of contact of the string at the notch, one will hear a clear sound, similar to that heard by placing the tip onto the birdge itself. Sliding the tip across the top of the string as it lies on the bridge, one can hear a slight diminution of the sound as the rod is brought away from the speaking length. Crossing the second bridge pin and placing the tip next to the pin, a major reduction of sound is heard, a fact of substantial importance in its implications. Listening to the sound of the rear duplex section one may note a still present, yet much reduced sound by contrasting it with the essential lack of sound of a string of a neighboring unison while the first examined string still vibrates. One may make similar observations at the front duplex. The attentuation of sound of a continuous string may be followed as it rounds the hitch pin. One may contrast areas of the bridge and soundboard and will be able to trace out the soundfield and soundpaths rather easily. One may contrast the acoustic transfer of the board with that of the plate, rim, legs, etc. etc. Numerous implications arise from these observations; they generally impeach the bridge rocking motion in my opinion. Although, I have said, I believe further consideration should be given to the string/bridge interaction and agree with John Delacour in that that question should essentially be kept separate from the function of the soundboard itself. What one hears with the stethoscope are stress/strain relationships in the form of sound, along with their distribution. It is important that note be taken, at least in my opinion, of the heterogeneous and particular distribution of the soundfield. 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. 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. Numerous areas in pianos may be noted where similar observations apply. Where I could not hear sound I don't say absolutely no sound exists, although that may in fact be the case, I simply am not able to detect it using my hearing. At some point the coherent nature of energy distribution, which may have the result of the motion and energy of translation of an object, the motion and energy of rotation, or a combination of the two, or the motion and energy of wave propagation or a combination of any of these, will eventually become incoherent and in the case of mechanical wave propagation be manifested as that which incoherent motion is, namely, heat. Regards, Robin Hufford > On Fri, 11 Jan 2002 00:42:28 > John Delacour wrote: > > >PF: > >>I interpret this to mean that the bridge and top are moving in direct response > >>to the input from the string. > > > >That's a pretty ambiguous statement. The bridge and top are > >obviously moving because the string has caused them to move, but they > >are _moving_ at a frequency that is not related to the frequency of > >the sound generated by the string. It is not this movement that is > >responsible for the acoustic radiation that reaches our ears. How > >many times do I have to draw this distinction?! > > > >JD > > > I can't speak for others John, but in my case you're going to have to keep > repeating it or rephrasing it until I understand what you are trying to say, > and I can repeat back to you what I believe you said and have you say > Yes, that's what I said and what I meant. I haven't been able to do that > so far. What I thought you had been saying was that the bridge and soundboard > do not move as a result of applied force from the string. (Aside-If I understand > Robin correctly he says there is no applied force from the vibrating string). > The bridge and soundboard only move because some sort of input at the bridge > causes some sort of wave or pressure which then causes something else > to happen which then causes the soundboard to move. It has nothing to do > with string movement. > > Now, what I believe you are saying is that the bridge and soundboard do > move as a direct result of force applied by the string but that movement is > unrelated to the frequency of the string and has nothing to do with sound > radiation from the soundboard. Is this what you said and meant? > > Phil F
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