Klarinet Archive - Posting 000059.txt from 2010/08

From: Diego Casadei <casadei.diego@-----.com>
Subj: Re: [kl] Fundamental error on
Date: Thu, 12 Aug 2010 15:48:51 -0400

I made a measurement, just to cross check what I wrote in my first email.

My B-flat clarinet, without mouthpiece, is long 596-597 mm. The
mouthpiece itself is 71-72 mm long, but for the following it is not
necessary to know its precise length.

I played the central A (i.e. the "all closed" B) without any warmup (to
be sure that the air temperature was the same as for the rest of the
room, i.e. 26.2 C) and found it tuned at 445 Hz.

The "all closed" E, of which the B is the twelfth (2-nd harmonic) was
also in tune [don't know the frequency by my tuner was "centered" on 445
Hz and said that the E was in tune too]. Such E defines the natural
pitch of the clarinet pipe and its wavelength is 3 times the wavelength
of the "all closed" B [alternatively, its frequency is one third of the
B frequency].

Actually, the lowest pitch is a D in reality, as the "all closed" B is a
real A pitch.

At 26.2 C the sound speed in air is 346.8 m/s, so that the wavelength of
the central A is

L(A) = (346.8 m/s) / 445 Hz = 779.3 mm

hence the wavelength of the lowest pitch D is

L(D) = 3 L(A) = 2338 mm

The clarinet pipe fully contains one fourth of the wavelength of its
fundamental harmonic, hence the only node in the clarinet is at the distance

d(node) = 2338/4 = 584.5 mm

from the terminal part of the bell [indeed, we should start counting
about half a centimeter outside the bell. Test yourself], which is
12-13 mm less than the total length of the clarinet, _without_ the
mouthpiece.

Hence, as I said in my first email, the node is _not_ at the reed (which
is the sound generator) but in the top part of the barrel (about one
centimeter below the junction with the mouthpiece, i.e. about 8 cm from
the vibrating edge of the reed).

One characteristic of the clarinet is that such node is _almost_ at the
same position for all tones, which makes the closed pipe approximation
work so well. However, the fact is that the pipe is not closed at the
reed (which obviously does not make any sense). Instead, the pipe
appears closed 8 cm far away from the vibrating edge of the reed.

When I said

> (...) 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.

I indeed meant to say that the node is right shifted (by 8 cm, now I
know) with respect to the clarinet.

Again, as we have an antinode at the end of the bell, we also have an
antinode at the reed.

Cheers,
Diego

Keith Bowen wrote:
> The difference between you is that Tony is right and you are "not"!
>
> Do read the references he suggests.
> It isn't very intuitive, but it is why a clarinet behaves differently from an oboe or flute(hence is an octave lower for the same tube length).
>
>
> Keith
>
>
> Sent from my iPhone
>
> On 12 Aug 2010, at 14:46, Diego Casadei<casadei.diego@-----.com> wrote:
>
>> Dear Tony,
>>
>> I said exactly the same thing as you, apart from the "No" :-)
>>
>> The reed is the sound generator hence it cannot be a pressure node.
>>
>> Cheers,
>> Diego
>>
>>
>> Tony Pay wrote:
>>> On 12 Aug 2010, at 08:22, 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.
>>>
>>> No, the mouthpiece end of the clarinet functions like a closed tube, and so is a
>>> displacement node (or a pressure antinode).
>>>
>>> See Benade, or eg:
>>>
>>> http://www.phys.unsw.edu.au/jw/clarinetacoustics.html#pipe
>>>
>>> Tony
>>
>> --
>>
>> Diego Casadei
>> __________________________________________________________
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>> http://cern.ch/casadei/ Diego.Casadei@-----.ch
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--

Diego Casadei
__________________________________________________________
Physics Department, CERN
New York University bld. 32, S-A19
4 Washington Place 1211 Geneve 23
New York, NY 10003 Mailbox J28310
USA Switzerland
office: +1-212-998-7675 office: +41-22-767-6809
mobile: +39-347-1460488 mobile: +41-76-213-5376
http://cern.ch/casadei/ Diego.Casadei@-----.ch
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