Klarinet Archive - Posting 001105.txt from 1998/12

From: Martin Pergler <pergler@-----.edu>
Subj: [kl] Sharpness after inhaling
Date: Tue, 29 Dec 1998 12:34:47 -0500

Friends,

we had considerable discussion on this phenomenon (playing sharp
right after taking a breath) about a month ago. At one point,
I promised to estimate the magnitude of the effect theoretically.
I finally got around to it, and as best as I can tell, the
theoretical answer is "somewhat less than 20 cents".
Those interested can see the 3-page calculation on my
web page---undergrad-level calculus, physics, chemistry, and
phisiology alert.

The Url is
http://www.math.uchicago.edu/~pergler/breatpit.dvi for those
who can read DVI files (from the scientific typesetting package
TeX); or
http://www.math.uchicago.edu/~pergler/breatpit/ for an
approximate HTMLized version, with some formulas slightly
mangled, since displaying math on the web is a known bugbear.

Comments appreciated. It turns out not only density of
exhaled air, but also its compressibility, are significant.
The imprecision in my answer "somewhat less than..." is due to
things I don't know about air exchange inside the clarinet. If
all air in the vibrating column was immediately 100% exhaled air,
my answer would just be "22 cents".

Martin

--
Martin Pergler pergler@-----.edu
Grad student, Mathematics http://www.math.uchicago.edu/~pergler
Univ. of Chicago

-------------------------------------------------------------------------