John Delacour wrote: > 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. Aha, so it is. I assumed Weinreich's lecture in the 5 lectures was the same as his Scientific American article, so I hadn't looked at it until just now. That teaches me a lesson. Often those Scientific American articles are a little too heavy on the "American" and a little too light on the "scientific". Anyway, the problem I described before was what Weinreich calls the "massy" support, and it agrees with what Weinreich said. Richard had said that the node could be on either side of the support, and that made sense to me. But the math didn't show that solution for the massy support. That's because the string has to pull on the mass to move it. So then I tried adding a spring to see what I'd get. For frequencies less than the resonant frequency of the spring (which is the case for all frequencies when the mass is small, and that case corresponds to Weireich's "springy support"), then you get the solutions where the node is moved beyond the termination. That is, the string goes flat as the bridge is allowed to move more. I was happy about that. It's been on my mind for a while. So then I look at Weinreich and there it all is. One thing I noticed with the springy support is that if you have a finite-sized mass on there, there are some interesting things to consider. It matters what the resonant frequency of the spring is. In fact, since we're talking about a soundboard, there is more than one resonant frequency. Thus, you get a bunch of different possible solutions to the problem. I think this accounts for the phenomen where you might have the node on either side of the termination, as Richard pointed out. That seems like it could create all sorts of problems. Charles
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