Klarinet Archive - Posting 000135.txt from 2010/08
From: Diego Casadei <casadei.diego@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Sun, 15 Aug 2010 12:43:54 -0400
Always, I have been speaking about pressure variation dP. Hence,
"node", "amplitude", "maximum" etc all refer to the pressure waves,
which describe the perturbations dP = dP(vector{r},t) of the constant
pressure field P. And "node" means "here the amplitude is identically
zero" (not just twice per oscillation, as in any other point). The reed
cannot be a pressure node: it is the source of the pressure
perturbations hence it cannot be constantly at zero dP.
Again, "amplitude" has nothing to do with "displacement", though we can
also define the amplitude of the fluid displacement. "Amplitude" is
relative to the wave which is under study, and is by definition the
maximum positive value which the wave can reach. Pressure perturbations
have an amplitude which is measured in pascal or atmospheres or bar
etc.: their amplitude is a pressure. The amplitude of the fluid
displacement is measured in meters or inches etc. and is a length.
There is no way in which we can mix them: they are like apples and oranges.
I cannot explain the 8 cm, I simply measured it. My measurement does
not claim to be as precise as 1 mm but it should be at least within 1 cm
from the true position. It would be good if the real experts with the
needed equipment could make this measurement, repeated over different
tones. Unless I made big mistakes, I have experimentally shown that the
node is far from the vibrating edge of the reed.
I find it strange to think that the pressure is identically zero at the
exit from the bell, which is the source of the sound for the "all
closed" positions. However, I did not study the math of this process
well enough. I hope to learn about it in the future, but this will take
a lot of time.
Cheers,
Diego
Tony Pay wrote:
> 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
--
Diego Casadei
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