Klarinet Archive - Posting 000603.txt from 1997/09
From: "Jon Delorey" <jondelorey@-----.com>
Subj: RE:Clarinet Material
Date: Fri, 12 Sep 1997 02:30:37 -0400
>I suggest you guys all read the somewhat technical but otherwise
>on acoustics of musical instruments by Bonade (available with Dover
>Sometime ago another excellent book on the acoustics of wind
>written Cornelius Nederveen. Unfortunately that one is out of print (it
>written in Dutch!).
Nederveen's book is (or was) also available in english. I bought a copy
about 5 or 6 years ago in a sheet music store in Van Nuys, CA (that's
Van with a captital V, probably dutch also :^) ).
There is no direct (mathematical evidence in this book for the wall
thickness of an instrument to affect the tone and I agree with the
statement that it is difficult to impossible to tell the difffernce
between horns. But I would caution that the book does make assumptions
(mathematically) to make the math tractable. Sometimes approximations
are made in math because the term that is thrown out or approximated
adds little error to the answer. This can create problems in the result
when dealing with spectra. For instance a 1 percent contribution is
equivalent to a 10 dB change in the spectrum. This kind of change can
be heard. There are also many ways of doing this analysis in addition
to those of Benade, Nederveen, and others. The type of math that is
used on the problem should be suited to the answer you are looking for.
To really tell if what affect the stiffness of the walls have, I believe
that different techniques than I have seen in most of the cited texts
needs to be used. My guess is the most likely technique to produce the
desired result (contribution to spectrum by wall thickness) may be
something like finite element analysis. This is usually used by
mechanical engineers to solve vibration and stress problems. This will
at least tell you if there is an interaction between the wall and the
air column and how great it is. Some other technique would need to be
used to determine the spectrum itself.
As for different techiniques, in one of my electrical engineering
courses we used a Smith Chart, which is a tool for doing microwave
design, to design a flute. The math is the same for both the electrical
and the acoustical problem (actually there are some assumptions here
also in that the Smith Chart is used to solve wave equation problems
that are non-dispersive, which is not the case with the acoustics).
Hope this wasn't to boring for the non-nerds of the group but I find the
subject fascinating. Most instruments seem to be built by trial and
error rather than engineered and as an engineer I just get this urge....
Thousand Oaks, CA
Get Your Private, Free Email at http://www.hotmail.com