Klarinet Archive - Posting 000200.txt from 2010/08

From: "Keith Bowen" <keith.bowen@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Tue, 17 Aug 2010 06:12:18 -0400

Indeed, Benade's notes and work are fascinating. I have the privilege of
knowing Virginia Benade, Arthur's widow, who was 85 yesterday, and playing
one or two of his modified instruments. The maker Stephen Fox has put many
of Benade's theories into practice, and I own a Fox 'Benade' Eb clarinet,
which actually plays in tune!

Well you were half wrong (or half right :-)). The main effect at somewhere
near the bell (or the first open tone hole) is the pressure node, (velocity
antinode), which causes a reflection of the waves back up the clarinet,
leading to the standing wave pattern inside the clarinet. This is of
dominant importance in playing notes at all, let alone in tune. The node is
caused by the discontinuity in acoustic impedance between the tube and the
air. It's formally analogous to the reflection of vibrations in a violin
string at the bridge, which allows standing waves to build up in the string,
or the interface between two regions of different refractive index in
optics. Thus Fresnel's laws apply, and you would expect (except in certain
pathological cases which are not relevant here) to find partial reflection
and partial transmission.

The transmitted part is what we hear in the room, the bell, or the lowest
open tone hole, acting as a source of roughly spherical waves.

The reflected part interferes with the travelling wave coming down the
instrument, to make a standing wave inside it. There's a phase change, so
the compressive wave coming down becomes a rarefaction going back up. The
sum of two waves of the same frequency travelling in opposite directions is,
as you will know, a standing wave (Jennifer, these are the dominant effects
of interference inside the clarinet). The particular standing wave pattern
in a clarinet, and its change as tone and register holes are opened,
contains virtually everything connected with tuning of notes, twelfths etc
and the playability of notes.

An interesting demo is given by Benade. Take a piece of tubing about 150 cm
long and 20 - 25 mm diameter, close your mouth round it and sing a
glissando. You find that certain pitches are unsustainable. Short pieces of
tubing do not have this effect; in these cases the vocal chords/larynx
dominate the generated waves, but when the tube is long the standing wave
pattern dominates. This effect is also related to the semitone jump obtained
by hand stopping a French horn.

Keith

-----Original Message-----
From: Diego Casadei [mailto:casadei.diego@-----.com]
Sent: 17 August 2010 10:12
To: The Klarinet Mailing List
Subject: Re: [kl] About clarinet acoustics

Please check page 2 of Benade's
https://ccrma.stanford.edu/marl/CASL/Files/benade/Benade-ClarinetData-1970.p
df

It seems that I was wrong about the bell, at the end of which there
should be a node in the pressure variations, and right about the reed,
which is a maximum.

I'm fascinated by the logbook of a physicist of the old school (pre-PC) :-)

The web site https://ccrma.stanford.edu/marl/Benade/ is a great resource.

Cheers,
Diego

--

Diego Casadei
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