Klarinet Archive - Posting 000324.txt from 2001/06

From: George Kidder <gkidder@-----.org>
Subj: Re: [kl] Re: Tuning rings
Date: Fri, 8 Jun 2001 08:39:59 -0400

>From the viewpoint of another physiologist:

While Diane is right that the change in resistance to flow can be a very
strong
function of the radius, I will assert that the amount of this change, and even
its direction, is suspect when applied to the clarinet situation because 1)
the
equation used applies to linear (non turbulent) flows only, which is certainly
not the case for the clarinet, 2) the equation assumes that the density of the
medium is independent of flow rate, which is certainly is not since air is
compressible, and 3) there are standing waves of density along the length of
the instrument, the positions of which vary with different notes being
produced. Thus Poiseuille's law (which Diane used for her calculation) would
be a very poor fit - worse even then when applied to blood flow in
capillaries,
for which it is most often used.

HOWEVER, having said this, these considerations do shed some light on the
observation that certain notes are stuffy, but not all of them, since the
density (and flow) patterns vary down the tube depending on the note being
produced, and for some notes a constriction may be more serious than for
others. This is probably also the cause of the inverse effect, where a joint
is pulled without a tuning ring, leaving a gap which can interact in the
opposite sense. And finally, some authors (sorry, I forget who) have stated
that "steps" are desirable at certain places in the instrument - at the bell
joint, for instance, and (if I remember rightly) at the mouthpiece-barrel
juncture. This does not seem to be universally accepted, which points
again to
the complex nature of the process, defying simple calculation.

At 04:21 PM 06/07/2001 -0500, you wrote:
>>>> DGross1226@-----.com wrote (greatly truncated)
>Indeed, but on a 1950 low Eb Selmer Paris bass clarinet...
>To lower the pitch, I found fibre washers at my local plumbing supply store
>that were perfect as far as the outside diameter goes.... He replied, "Did
you notice that the inside diameter of your tuning rings is at least 1/16"
smaller than the bore of your mouthpiece. You've had some really stuffy
notes,
haven't you?" Removing the washers eliminated all the stuffiness. Never
underestimate the need for smooth air flow.
>********
>Warning: Science spoken below!
>I'll add another caveat: never underestimate the effect of a decrease in
radius...
>Since the equation for resistance is:
>R = (8 {viscosity}{length of the tube})/({radius to the fourth}{pi})
>a small change in the radius has a LARGE effect on the resistance to flow.
>
>The stuffiness is then due to both changes :
>
>1) the turbulence produced by the edge of the tuning ring i
>
>2) The 1/16" decrease in the bore (radius or diameter?) will have a
significant effect on the resistance to airflow without the turbulence. Using
the numbers for the I.D. of a Buffet R-13 (couldn't find numbers for the bass
clarinet), I did the math on what that tuning ring would do to the resistance
when it decreases the radius of the bore of the clarinet.
> If the diameter of the bore was decreased by the 1/16th inch (i.e.
1/32" of
the ring sticking into the bore all the way around), the blowing resistance of
the clarinet itself increases 59%
> If the radius of the bore was decreased by 1/16" (i.e. 1/16" of the ring
sticking into the bore all the way around), the resistance increases by
260%!
>
>Adding turbulence into the mess only makes it worse, but I avoided that
because the equation becomes non-linear and the math is way beyond a foolish
physiologist such as myself :-)!
>
> Since you have a series of resistances down the length of the tube you
add
all the resistances together to get the total resistance. The greatest
resistance is still at the mouthpiece tip with the reed, so that dominates,
but
you've added a substantial amount of resistance to the clarinet just by
decreasing the bore by that little amount in that one place.
>
>
>Diane R. Karius, Ph.D.
>Department of Physiology
>University of Health Sciences
>1750 Independence Ave.
>Kansas City, MO 64106
>(816)-283-2219
>dkarius@-----.edu
>www.uhsweb.edu/physio
>
>
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-----------------------
George Kidder
MDIBL
gkidder@-----.org

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