I don't know if postings from a non- (or not-yet) technician are permitted here, but I believe I can contribute a bit of engineering insight here that could clear things up. Mechanical impedance is the result of the springiness and inertia of a mechanical part. Your sounding board has some inertia due to its mass. It also has some springiness. Wood (and most other materials in a piano) will push back in direct proportion to the amount of deflection applied to them. (Exceptions: felt and buckskin, by design.) The sounding board's springiness derives from the behavior of wood in compression and bending. From an engineering standpoint, a crowned sounding board that's glued at its rim to a rigid piano frame is an arch. When you push down on the crown of an arch, the ends of the arch try to spread. (This force is due to the downbearing of the strings on the bridge.) Since the arch 'ends' (in this case, the glued rim of the sounding board) cannot move, the material of the arch is compressed. Wood in compression behaves like a spring. The situation is really a bit more complex than this because of the stiffening ribs. These experience bending stress, but also behave like a spring. It doesn't matter very much from a purely physical point of view, but since the wood in a crowned sounding board is under compression, we get a somewhat stronger structure since wood is a bit stronger in compression than in tension, especially across the grain. I don't think I've told anyone here anything new thus far. But there's a bit more. If the impedance of two coupled mechanical parts--say the string and the sounding board--are different, any energy applied from part #1 will not be completely transferred to part #2. What happens to the energy that's not transferred? It isn't lost: it is _reflected_ back into part #1. In a piano, the impedance of the string is different from that of the sounding board. Thus part of the energy imparted by the hammer to the string is reflected back into the string. We want this to happen: it's what makes the string keep vibrating. If all of the energy from the string went into the sounding board, we'd hear only a dull thump instead of that splendid ringing sound. The piano is a highly efficient system. (System=chain of parts.) The energy that's reflected back into the spring is not lost, but stored in the vibrating string. It is transferred to the sounding board gradually, on each vibration. Could the sounding board have a negative crown (like a dish), and the downbearing be "upbearing?" From a physical standpoint, yes. There would be no difference in the behavior of the system, though the bridge would peel off the sounding board pretty quickly and the design of the bridge pins would be interesting. Or, in another possible configuration, could the sounding board have a negative crown and the downbearing still exert force downward? Again yes. (The bridge would have to be rather high.) The sounding board's wood would be in tension and the rim of the sounding board would tend to be pulled away from the frame, but again from a purely physical standpoint the system would work about like a normal piano. Structurally, of course, this configuration would be a disaster, but the sounding board and strings would behave pretty much normally if the whole works didn't peel apart. The relationship of the sounding board to the outside air is a bit more complex than the relationship of string to sounding board. Ideally, we want the impedance of the sounding board to match that of the outside air. This makes the piano loud enough to hear. And the sounding board does just that: it's an 'impedance matching' device that tries to match the impedance of the strings to that of the air. (Side note: the bell of a brass instrument is also an impedance matching device.) >From an efficiency standpoint, we do not want energy from the air to be reflected back into the sounding board. From an artist/craftsman standpoint, we _do_ want this to happen, because that's part of what gives the piano its tone. It's also worth examining the resonant frequency of the strings vs. that of the sounding board. The resonant frequency of each string is obvious to anyone. The resonant frequency of the mounted sounding board is known to the technician, who can determine it when the piano is unstrung: only one note sung into the unstrung piano will resonate loudly, and that's the resonant frequency of the sounding board. (This is the simplest case: a real sounding board will resonate at several different frequencies. The resonant frequency of the sounding board will also change somewhat under the force and mass of the strings.) We really don't want the resonant frequency of the sounding board to be a large factor in the behavior of a piano. Ideally, the sounding board should be forced to vibrate at the frequency of the struck strings. In practice, however, this is not the case. I don't know if the terms are equivalent from one sort of instrument to another, but in the bowed string instruments, we get what's called a 'wolf' tone when the string's resonant frequency approaches that of the sounding board. On the 'cello, this occurs at the F played on the C string. I have read about 'wolf' scales on the piano, and perhaps this is the same phenomenon. So as it happens, the resonant frequency of the piano sounding board is a factor in its behavior, but it's not necessarily a bad thing: it contributes to the overall tone of the instrument, as do all the other 'imperfections.' I have read the other posts in this thread, and it's clear that everyone has a good understanding of these concepts. However, descriptions, terms, and experiences vary, thus making the various contributions appear inconsistent. What I've given here are the terms used in engineering and physics. I gladly defer to the experience of the craftsmen who read this list. A far better treatment of the matter is given in an old Scientific American article called 'The Physics of the Piano.' I believe that the complete reference is given in Art Reblitz' textbook. Mark Kinsler 512 E Mulberry St. Lancaster, Ohio USA 43130 740-687-6368 http://home.earthlink.net/~mkinsler1 _________________________________________________________________ Learn how to choose, serve, and enjoy wine at Wine @ MSN. http://wine.msn.com/
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