At 1:01 PM -0500 1/23/02, Charles Neuman wrote: >Again, the model I described above is not intended to model a piano string >exactly. But it does demonstrate that a string can have vibrational modes >where one termination point can move. >[....] >P.S. I guess it's time I "came out" as having a significant physics >background. However, that doesn't mean I'm an expert in acoustics, so I >haven't had much to say before. Charles, Thanks for a very clear and informative message. Yes, everything you have written makes sense, and a lot of it is covered in the Weinreich lecture with illustrations of three types of termination considered. It's good to have someone with a physics background entering the discussion, because you may well be able to point out fallacies in my arguments. If you've been following the thread, you will have seen that I have chosen to consider the whole question at a molecular level since it has seemed to me that it all has to do with forces if one kind or another, whether intermolecular forces or forces at interfaces. The reason I have chosen to do this is that this is the only way I can begin to picture to myself, let alone anyone else, how things work. In adopting this approach, it is possible I am committing a fallacy and that a mathematical model approach using calculus would reaveal the fallacy. I'd be interested to hear what you think about this approach. In particular, since I posted a message this morning giving a decription of the way a vibration passed down the bridge, do you see any sense in this? You talk in your message both of the movement of the termination of the string (which so far as I am concerned has never been in doubt) but then you refer also to the movement of the bridge in response to the movement of the termination. I am seeing this as a progression of displacements of the particles of the bridge or a pressure wave, as I have described in my one-dimensional example. This is just part of what happens, put at its very simplest, of course, since by the same analogy I would see similar pressure waves moving in other directions, being reflected etc. not to speak of bending waves as well. I ask this because someone, nothing to do with the list or pianos, but extremely well qualified to talk of the vibration of plates and an acoustics PhD has today responded to a message I sent asking about precisely this. He writes: >1) a finite structure such as the bridge, can only really be considered >to carry waves if the wavelength is small compared to length of the >bridge. I haven't done the calculation but I suspect the frequency where >waves can be considered to occur in the bridge is very high. > >2) a bending wave passing down the bridge (if it can occur) will still >have a rotation at the very end which will provide a moment excitation >to the sound board. I have not yet pondered very long on this and would welcome your comments. If my view of the "movement" of the bridge is fallacious, how would you describe the "movement" of the bridge, say when a single string is sounding and vibrating in the vertical plane? Hope you can throw some light on this. In spite of the "interminable length" of this discussion, I have actually learned a great deal from it and I can hardly imagine that others have not had to modify their view considerably as a result of the thread. When it began, there was no evidence that anyone had even heard of Acoustic Radiation or Bending Waves and at this stage in the proceedings we have discovered, it seems, that the latter is almost solely responsible for the former. In a little while we may discover that this is a gross over-simplification of the case -- who knows? At any rate I am glad to have been forced to learn so much, and will be equally glad to unlearn anything that I've got wrong. I've learned more by mistakes in my life than by any other method. Look forward to hearing more from you. JD
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