-----Ursprüngliche Nachricht----- Von: owner-pianotech@ptg.org [mailto:owner-pianotech@ptg.org]Im Auftrag von Ron Nossaman Gesendet: Montag, 7. Januar 2002 23:51 An: pianotech@ptg.org Betreff: Re: Sound waves(The behavior of soundboards) Robin, Salmon aside, there are still the two fundamental problems I have with this explanation that I've had from the beginning. The first is string supplied compression waves going through the bridge without displacing it in space (physically moving it), and the second is these waves somehow turning the corner and becoming longitudinal waves in the soundboard which, upon reflection from the rim, meet themselves coming and transform into transverse waves, which then move the bridge. There are, of course, compression waves happening in the bridges and soundboard assembly, but I have a little more straightforward concept of what does what. Give this an honest read and see what you think. The problem with the idea of a compression wave not moving the bridge is that the driving frequency cycle must be high enough that at least one complete cycle is completed while the wave started at the beginning of the cycle is still in the bridge. In it's simplest form, assume a string vibrating at it's fundamental at 440 CPS, and a bridge 1.5" tall. Call a string cycle 360° starting (for visualization) at 3:00 on a clock face and progressing to 90° at 6:00, 180° at 9:00, 270° at 12:00, etc. So 0+-180- would be putting positive pressure on the bridge, and 180+ - 360- would be applying negative pressure. The speed of sound cross grain in hard maple is about 35,000"/second. One cycle at 440cps takes 0.0022727+ seconds. The compression wave travels from bridge top to bottom in 0.000042857+ seconds. Arbitrarily, benchmark from +0° with the string moving downward. At +0°, positive pressure change is being applied to the bridge. Surface molecules are compressed closer together and compression wave starts in bridge, moving down. Actually moving everywhere but up, so the net direction is down. At 6.79° into the string cycle, the compression wave reaches bottom of bridge. Meanwhile, pressure at the top of the bridge has steadily increased, so there is no rarification pulse behind the pressure wave to allow the bridge molecules to return to their original positions. At this point, at the precise moment that the leading edge of the compression wave passes from the bridge into the soundboard material, the bridge molecules >from the string to the soundboard have *all* been moved down. Not half up and half down in compression and rarification where they will average no net bridge displacement, but *all* down at once. That means the bridge has moved before the soundboard has, and the string was what moved it, not the soundboard. This also means that the bridge has not only moved, but it is now *moving*, and is *accelerating* because there is still pressure on top, and unrelieved compression in the bridge. In fact, the *acceleration rate* is *increasing* because the pressure on the bridge top is still mounting faster than it is being relieved on the bottom. This is still at under 7° of the 180° "compression " phase of the 360° string cycle. The bridge will continue to move downward until at some point between 180°+ and 360°- in the string cycle, the negative pressure will overcome the momentum by the reverse of the process that built it up on the pressure side of the cycle, and the bridge will follow along faithfully behind the string movements. Note that, as that quote I posted from the "Vibration Theory and Applications" book, the bridge movement will lag behind the string movement, and will be of lower amplitude than the string movement because the string will have to overcome the system inertia and drive the system at a frequency higher than it's resonant frequency. Once the bridge is put in motion by the string, the soundboard, by virtue of being attached to the bridge, goes with it very much like the string does when it is struck and moved by the hammer, except that the board is pushed by a gradually applied load rather than struck by the bridge. A local transverse deformation of the assembly results because the forced movement can't overcome the inertia of the system all at once. The local deformation then propagates outward as a progressive transverse wave as the transverse deformation and stiffness of the material overcomes the inertia in the section of the assembly in it's path. The propagation rate is dependant on the stiffness and mass of the material, so it won't progress at the same rate in all directions. These progressive transverse waves, or traveling waves, will then reflect from the rim, back on themselves, and form the interference patterns of standing waves displacing air at cyclic frequencies similar to the driving frequency of the string, and forming the compression waves we hear as sound. That's essentially it. The strings move the bridge, the bridge moves the soundboard, the soundboard moves the bridge, the bridge moves all the strings, and it cycles until all the energy absorbing parts, whether they contribute to the sound or not, disperse the energy. Beyond the action of physically displacing the bridge by carrying the surface displacement from the top to the bottom of the bridge and back, and carrying the results from the assembly to our ears in the air, I don't think longitudinal or compression waves have much to do with soundboard action. Ron N
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