Robin, JD, Phil, etc... I Have wanted to find time to write down a few thoughts on this thread for a while, but Christmas and other concerns have prevented me from doing so until now. Any ways... this rocking bridge tangent has really caused a lot of trouble relative to the original discussion. We were really talking about the mechanisms that govern the transfer of energy from the strings to the rest of the system and how that results in the generation of the sound we hear. We had two basic ideas presented about that in general. One was a rather straight forward view of the bridge being physically moved, resulting in the sound board being moved and I have to re-read these posts from Ron on the "ripples" to make sure I have understood him rightly. I believe however the idea was that the strings movement resulted in the propagation of transverse waves within the system and it was these that were primarily responsible for the generation these "ripples" which in in turn generated the compression waves we hear as sound. The other "theory" was a bit more difficult to grasp on the surface of things, though I still fail to see what about it makes it so easy for some to write off without further ado, unless it is exactly because it is difficult and perhaps also because none of this is so necessarily relevant to us above and beyond being interesting and stimulating. In any case I would like to look for a moment at the first of these two "theories". Partially because it has been described as "simple Newtonian physics" in nature, partially because I have some unanswered questions in my mind about it. One problem with this is the actual movement itself, whether up and down or forward and back at some point such movement will become significant enough to affect the tension of the strings while they are vibrating. This may seem insignificant at first glance but it can hardly be so. Either the movement of the bridge is so small that no measurable frequency change can be effected, or whatever movement there is must occur in some other fashion which results in a stable frequency for the string. In the first case one needs to ask then if the bridge movement is so small, then how can it at the same time be enough to "cause" all the system movement that results in sound ? In the second case we have a really interesting mechanism going on that somehow allows the vibral amplitudes of both bridge and string to be large enough to affect one anothers pitch, yet functions in such a way as these are stable. Neither of these eventualities has been explained or satisfactorily dealt with throughout this thread as far as I can see. Another problem is the whole idea (and premise for further reasoning) that the bridge will move up and down 440 times a second for a string tuned at that frequency. There are a number of reasons why this idea should be suspect, and these require adequate attention shall they be resolved. As previously stated, there is a certain tendency for coupled strings to counter act each others motion. Secondly a single string does not just vibrate up and down to begin with. It vibrates on many planes both up and down, sideways and all around so the effect on the bridge cannot possibly be as described to begin with. Thirdly you have the matter of partials. They originate in the string, and are determined by the strings inharmonicity. At the exact point of stress exertion on the bridge, all of these string segments are moving in their own paths and frequencies and thereby exerting force on the bridge in their own way. If we accept then without further consideration the basic premise of this "theory" and relate it to this last fact, we have to explain how a bridge can be moving both up and down at the exact same time. For that matter we have to explain how the bridge can move in all the conflicting directions the strings segments move in at the exact same time. One could be tempted to write this off by explaining that this is exactly what the string does so why shouldn't the bridge do it. But the bridge is not stretched to any particular tension and has nothing akin to the strings inharmonicity in this regard. And if it did, well we would have a problem with all the other string frequencies. In fact... the more one really starts to consider the implications of accepting the idea that it is transverse like movement of the bridge which drives the board into the movement necessary to create the sound waves we hear.... the more fantastic the whole thing becomes. In any case it removes itself completely from some concept of simple Newtonian physics. No matter what way you look at it we have some very complex mechanics to explain if we are to stand up and say "This is how the sound board works" Another point to be considered is how to define transverse wave movement in the case of the bridge to begin with. Transvers wave movement is defined as wave movement perpendicular to the vibrating medium. Does this "up and down" movement satisfy this definition relative to the bridge really ? The bridge is then "defined" as a medium which is physically and at all times in every sense perpendicular to the wave movement, by reverse implication. None of which means that this model is wrong. It's just that we haven't explained these and other issues yet, and until they are explained we remain as much in the realm of speculation as we are in the realm of theory by my understanding of the terms. Nor does any of this necessarily mean much to the actual process of building pianos. I think it was Ron N who said straight out that he (and others) do not think about the issue of how sound is actually created, transmitted, transmuted, transduced...whatever..... from the strings to the board to our ears when designing a board. Further sound boards have been produced with similar results for quite a long time indeed, despite widely differing views on this issue. Still, it remains an interesting topic for anyone who is fascinated by such things and the fact that no one has yet managed to truly explain these things beyond reasonable doubt does not change that fact. I plan on re-reading much of this thread as there are some similar things about the other so called "theory" I have questions about as well... but this is more then enough for this time around. -- Richard Brekne RPT, N.P.T.F. Bergen, Norway mailto:rbrekne@broadpark.no
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