Sound waves(The behavior of soundboards)

[Charles Neuman]

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