Klarinet Archive - Posting 000112.txt from 1997/03

From: "Diane Karius, Ph.D." <dikarius@-----.EDU>
Subj: Re: A Clarinet bores (was: barrels)
Date: Mon, 3 Mar 1997 21:24:13 -0500

Beware: Science being spoken below!:
> At 01:50 AM 3/3/97 EST, you wrote:
> >This is correct. Have you ever noticed that your A clarinet is more
> >resistant than your Bb? This is, no doubt, a result of the smaller bore.
>
> I've often wondered about this. I have always theorized, with no
> scientific evidence to cite at all, that the reason an A Clarinet is
> normally made with a smaller bore was to avoid having to lengthen the
> instrument body (and therefore the tone hole/finger spacings) any more than
> necessary. The reason for this would presumably be a less drastic change
> for the player's fingers when switching instruments. If an A clarinet were
> made longer with a correspondingly larger bore diameter so that the pitch
> of the instrument were still correct, would the resulting instrument play
> more freely than most modern A clarinets do? Or would the additional
> resistance over what we get from a normal Bb clarinet still be there, now
> because of greater air volume that needs to be moved?
> I guess the ultimate direction of this question is to ask whether for the
> price of a little more hand stretch (or maybe some additional mechanical
> linkages to reach where my fingers wouldn't) I could in theory end up with
> an A clarinet that doesn't fight back as hard as most do? Have there been
> experiments in this direction?
>
The equation relating the length of the tube (in this case, the
clarinet), and the radius of said tube to the resistance to
airflow (R) is: R = [8 x (viscosity of air (in this case)) x (length
of tube)] / [(radius to the fourth power) x pi].
To cut to the chase: What this means is that if I decrease the radius
of the tube (clarinet) by 1/2, the resistance to airflow increases by a factor
of
16 (2 to the fourth @-----. Increasing the length of the
tube doesn't have nearly that great of an effect - doubling the length
of the tube will only double the resistance to airflow - well within the
range of the human respiratory musculature assuming a normal person
(witness the existence of the bass clarinet - even if that's not a
complete doubling of the length!).
I knew that PhD in respiratory neurophysiology and mechanics would
come in handy!
Diane R. Karius, Ph.D.
Department of Physiology
University of Health Sciences
2105 Independence Ave.
Kansas City, MO 64124
email: dikarius@-----.EDU