Klarinet Archive - Posting 000283.txt from 2010/08

From: "Keith Bowen" <keith.bowen@-----.com>
Subj: Re: [kl] Fundamental error
Date: Sat, 21 Aug 2010 18:35:22 -0400

Diego

You're right of course that pressure variations are a more direct phenomenon
in wind instruments but - as misled you initially - the use of displacement
is embedded in the literature. Hence the problem will be with us for ever.
The best advice is to clarify to which parameter one is referring (as Tony
did in his first reply to you).

Indeed it was stimulating!

Best, Keith

-----Original Message-----
From: Diego Casadei [mailto:casadei.diego@-----.com]
Sent: 21 August 2010 21:58
To: The Klarinet Mailing List
Subject: Re: [kl] Fundamental error on
http://www.woodwindcourse.co.uk/user/image/clarinet_bore_design.doc

Just to close this thread: I was wrong in the interpretation of the
diagram on the linked paper. It has to be interpreted in terms of
displacement and not of pressure variation (as I assumed). The pressure
is max at the vibrating reed but at the same time that is a node for the
air displacement.

[I would invite everybody to think and speak in terms of pressure
variations, which are the physically relevant quantity in musical pipes
(displacements are better suited for vibrating strings or membranes).
Unfortunately, the figure lacks a caption with all explanations.]

Many thanks for all messages which followed mine, because they have been
very stimulating. Apologies for the long list of emails to the people
who were not interested into.

Best regards,
Diego

Diego Casadei wrote:
> Dear all,
>
> there is one big mistake on
> http://www.woodwindcourse.co.uk/user/image/clarinet_bore_design.doc
> which is worthwhile explaining here (few other details have been already
> commented by other people).
>
> In every wind instrument (*) the sound generator is just at the edge of
> the pipe which is controlled by the mouth. In particular, for the reed
> instruments the sound generator is the vibrating reed (or reeds for
> double-reed winds). This means that the clarinet reed exerts the
> pressure with the maximum amplitude on the column of air which is
> resonating inside the pipe.
>
> In diagrams like the drawing on page 4 of the document mentioned above,
> a "node" is a position along the tube in which the amplitude is minimum
> (ideally, it is null). The paper calls "antinode" a position which
> senses the maximum amplitude (**). Hence, the diagram on page 4 is
> clearly wrong: a node is not allowed at the reed position, because that
> is by definition the only certain place in which the amplitude is maximum.
>
> The clarinet has one antinode at the reed and one just at the exit from
> the bell. They are always there for all pitches. If I remember
> correctly, there is also a node in a fix position quite near the
> mouthpiece, in the barrel (perhaps at the end of the mouthpiece?) which
> is a characteristic of the clarinet, hence the diagram on page 4 of the
> mentioned document should be translated a bit to the right and an
> antinode should be added to its left, in correspondence with the reed.
>
> For people who master a bit of math, the suggested reading is "The
> Physics of Musical Instruments" by N.H.Fletcher and T.D.Rossing
> (Springer). An interesting web site (which I had no time to read through
> carefully enough) is http://userpages.umbc.edu/~emrich/clarinet21.html
>
> Cheers,
> Diego
>
>
> (*) Apart from the organ pipes and the flutes, which have the sound
> generator where the "cut" is (not exactly at one edge of the pipe).
>
> (**) Whereas the nodes have a fixed position, the position of one
> antinode depends on the harmonic under consideration.
>
>

--

Diego Casadei
__________________________________________________________
Physics Department, CERN
New York University bld. 32, S-A19
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office: +1-212-998-7675 office: +41-22-767-6809
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http://cern.ch/casadei/ Diego.Casadei@-----.ch
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