Klarinet Archive - Posting 000134.txt from 2010/08

From: Tony Pay <tony.p@-----.org>
Subj: Re: [kl] About clarinet acoustics
Date: Sun, 15 Aug 2010 12:10:01 -0400

On 15 Aug 2010, at 12:35, Diego Casadei wrote:

> The reed is the generator of the sound, which is the source from which
> all the power of the wave comes from. For this reason, it must
> correspond to the absolute maximum of the amplitude. Again, we are
> speaking about the amplitude of the small variations dP superimposed
> with the constant pressure field P, which is the same everywhere (the
> clarinet is open).

It seems to me, as it did to Richard Sankovich, that this is certainly wrong, though it doesn't explain the 8cm, which is what worries me most.

If the absolute maximum of the amplitude occurred at the reed -- so therefore the reed is at a pressure node (remember that pressure node = displacement antinode) -- and, equally, the bell is (more or less, because of end effects) at a pressure node (there, the pressure is always atmospheric) -- then we would have symmetry of the waveform, and the displacement node would be half-way down the instrument.

That would mean that the clarinet would behave like a flute, which we know is wrong:-)

(That's what Mike McIntyre meant when he wrote:

> [Diego wrote:]
>

>> we have an antinode at the end of the bell,... also an antinode at the reed
>
> which is plainly wrong whether "antinode" means "pressure antinode" or "displacement antinode", as well as in failing to replace "at" by "near". That creates the double absurdity that the pipe length is not only a half instead of a quarter wavelength, but also EXACTLY a half wavelength.

)

Mike also just wrote to me, about my 8cm worry:

> [You wrote:]
>
>> ...about reed-biting.. you can't change the pitch of a clarinet
>> on a low E by very much by reducing the aperture, certainly.
>
> That's what I was presuming. The implication is that the reed
> presents _almost_ a closed-end boundary condition to the pipe
> and probably that the 8cm is too much.
>
> So Diego's nonzero displacement and velocity at the reed
> -- while certainly nonzero -- must be very small in comparison
> to displacement and velocity at a displacement antinode. This
> in turn implies that the pressure antinode nearest the reed must
> be correspondingly close to the reed: of course it would move
> right up to the reed if you bit it completely closed.
>
> The only way out I can see is that the textbook "cylindrical bore"
> is at best an approximation -- especially near the mouthpiece?
> If the bore cross-section varies along its length, then that
> shifts the node-antinode pattern, of course, as with the extreme
> case of oboes and saxophones. If you tell me how the
> cross-section varies I could think about this a bit more.
>
> in haste, M

Tony
--

Tony Pay
79 Southmoor Rd
Oxford OX2 6RE
tel/fax +44 1865 553339
mobile +44 7790 532980
tony.p@-----.org

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