On Tue, 4 Dec 2001 20:18:34 Delwin D Fandrich wrote: > > The sand >technique is a common >> method of visualizing the mode shapes of a vibrating body. This is one of >the practical >> techniques I mentioned that violin makers use. > >I can't see any advantage to this. Other than as a teaching aid to help >understand how the soundboard works. It is only going to illustrate at what >point the soundboard resonances come in and what their shapes are. Again, >this is with an unloaded board. Everything is going to change once the >strings go on and their up to pitch. > >Del > Yes it does illustrate the soundboard resonance frequencies and shapes. In the case of the violin that we have been using as an example the maker knows that to get a good sounding violin he needs to have a top something like the following (this is just an example - these are not real numbers since I'm not a violin maker. But if it's important I could in fact look this information up.): 1. A first mode at 249 hz in a symmetric diaphragm like shape. 2. A second mode at 468 hz in an unsymmetric mode with a node line centered more or less at the bridge line. 3. Etc., etc. with other modes. This is just for the top. He will have something similar for the belly. These modes are NOT the same modes the top will have in the assembled violin. But a relationship between the unassembled top and the assembled violin has been established. That is the point. Perhaps to have a good sounding violin you need an assembled first top mode that is 350 hz in an assymetrical shape centered around the soundpost (once again a fictitious example). It has been established through experiment and lab test that to arrive at that you need the top modes shown above. It has also been established through experiment and test how the top plate modes respond to changes in the top thicknessing, arching, etc. So, you make your top to your basic design (violin makers use very precise patterns for arching and thicknessing their tops) which you know from past experience will get you close to your desired result. You test your top using the sand method and you arrive at mode frequencies and shapes that don't match exactly what you're trying to achieve. Now you have some guidelines about where to thin and how much. This is a very powerful tool. It means that you can lay out and make your top and adjust it for slight variations in geometry and material properties and know that when you assemble the violin it will sound right. You would never have been able to do this if all you did was test the assembled violin. You have to relate the modal properties of the parts to the modal properties of the whole. Otherwise how do you know what to change and how much? To establish this relationship would be time consuming and tedious. As I see it the process would be something like this: 1. Find some good sounding pianos. Test their modes in the assembled condition to establish some sort of pattern for modal frequencies and shapes that good sounding pianos seem to share. 2. Build lots of soundboards with different parameters which you change one at a time: different board thickness, different grain angle, different rib dimensions, different rib spacing, etc. Measure the modal frequencies and shapes of these boards. Install these boards in a piano and build it up. Test the modal frequencies and shapes of the boards in these pianos. See how they compare to your good sounding pianos in 1. 3. Try to establish a relationship between the modal frequencies and shapes of the uninstalled boards and the modal frequencies and shapes of the assembled piano. 4. Determine what arrangement of the parameters (what board thickness, what rib spacing, etc.) gives the required modal frequencies and shapes for the uninstalled board. Use this as your basic soundboard design. 5. Test some uninstalled boards to see how varying parameters of the board changes the modal frequencies and shapes of the uninstalled board. Use this information to tweak your basic design (which is going to vary somewhat from board to board because of changes in material, slight differences in rib dimensions, etc.) to the required modal frequencies and shapes before installing the boards in your factory. Phil F. -- Phillip Ford Piano Service & Restoration 1777 Yosemite Ave - 215 San Francisco, CA 94124
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