Klarinet Archive - Posting 000183.txt from 2010/08
From: "Keith Bowen" <keith.bowen@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Mon, 16 Aug 2010 20:16:03 -0400
I've done quite a lot more reading, and as often happens in science, one
does not need to do any more measurements because they have been done in
great detail already :-).
The best reference is 'Acoustical aspects of woodwind instruments' by C.J.
Nederveen, original publication 1969 revised 1998, Northern Illinois
University Press. I've had it on my bookshelf for years, but this discussion
has stimulated me to go back and plough through the wave equations and
physics it contains, at least on a first pass. Not for the faint hearted or
the mathematically unqualified, but Tony and Diego will do just fine.
This work (Nederveen's PhD thesis) set out to calculate completely the
pitches produced by woodwind instruments, including all the factors we have
been agonizing about and some we haven't: bore, flare (though not much on
that), mouthpiece shape and lay, reed shape, size, stiffness, tone hole
positions, diameters, wall thicknesses etc etc.
He also made detailed acoustic measurements where they did not exist
already; in fact, Backus and Benade had made many of them already, and he
compares the theory to measurement of pitches across the instrument and gets
about as close as it is reasonable to expect, given variations between
players etc.
On the matters we have been discussing:
1. There is indeed a velocity node near the top end. A velocity node is,
identically, a pressure antinode (position of maximal value), from the
equation of motion of the particles in vibration.
2. The node position is deduced from the wave equations, which are far too
complex to reproduce here. But a simple argument is that at high blowing
pressures a softish reed does completely block the aperture and close the
pipe. There is no or little discontinuity in the pitch before or after such
events; therefore the closed-pipe-at-the-top (=velocity node, pressure
antinode) at the top is pretty close to the truth.
3. How close? When we say AT the top, do we mean the very tip of the reed?
The bottom of the vibrating bit where it hits the lay? Or something else?
4. Nederveen gives very detailed examples of two clarinets which he
calculates and measures. The corrections for all the factors involved in the
mouthpiece/reed combination work out at between 16 and 24 mm for the
examples calculated. The truncated shape of the mouthpiece shortens the
effective length of the tube, and the reed effects lengthen it, but only by
about half as much.
5. Thus the velocity node (pressure antinode) in the clarinet is located
between about 16 and 24 mm below the tip of the mouthpiece. The error is
primarily in the estimation of the effects of the reed.
6. It seems to me that Diego's calculation of tube length disagreed mainly
by not taking account of the flare/bell effects.
7. I haven't found anything to indicate gross errors in the simplified
discussion in the Newark document that started this trail.
Having got this far - and incidentally having concluded that the methodology
I used for bass clarinets was sound, phew! - I think I can't contribute much
more on this topic, at least not until I have done a great deal more study -
months rather than days. I do thank the contributors and questioners, since
I have certainly gained a deeper understanding in the process.
Keith
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