Klarinet Archive - Posting 000124.txt from 2010/08

From: Jennifer Jones <helen.jennifer@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Sun, 15 Aug 2010 06:15:17 -0400

On Sat, Aug 14, 2010 at 11:45 PM, Diego Casadei <casadei.diego@-----.com> w=
rote:

[snip]

> Below I try to answer Jennifer and Keith. =A0I must admit that the
> discussion is moving toward a quite advanced state and I need to tell
> you that I'm a particle physicist who never worked on theoretical nor
> experimental acoustics. =A0I don't claim to have any particular authority
> on the latter fields (nor in the first, to be honest).

That is ok. You have a leg up on me. You are actually working with
physics. I am a botanist and biochemist. Last time I had physics was
in high school.

> Jennifer Jones wrote:
>> Dear Diego,
>>
>>> indeed the distance from the vibrating reed to the node is less than a
>>> quarter of the fundamental wavelength of the instrument (the "all close=
d"
>>> low E). =A0However, the clarinet is able to play a very wide range of p=
itches
>>> and there will be waves for which it happens that such distance is 1/4 =
of
>>> the wavelength.
>>
>> but if the clarinet is playing the low E, that note corresponds to a
>> certain wavelength. =A0If the distance between the first antinode and
>> node is so much smaller than the distance between the node and the
>> second antinode, it appears that there are two wavelengths involved.
>> Unless we have one wavelength with asymmetrically distributed nodes
>> and antinodes, namely, a shortened interval between the reed antinode
>> and the barrel node, which seems strange.
>
> Strictly speaking, we don't have an asymmetric wavelength in the sense
> you mean. =A0The problem is that we must be aware of the approximations,
> when we make use of them.
>
> Now it is true that a stationary wave has a regular pattern of nodes and
> maxima. =A0The closest case to the clarinet is the closed cylindrical pipe
> of infinite length, in which we assume that the source is infinitely
> distant from the closed end.
>
> I hope this sounds a clear ideal case... For the clarinet, the length is
> not infinite and the source is located near the supposedly closed end!
>
> The node at ~8 cm from the vibrating reed is a feature of the source,
> not of the stationary wave. =A0As a matter of fact, there is a reflected
> wave which comes back from the clarinet bell, which implies that the
> source cannot freely vibrate, but it is forced to do so in such a way
> that we finally get a stationary wave, from the node to the bell.
>
> Between the vibrating reed and the node there is no stationary wave, in
> the sense of the approximation made above. =A0It is the interplay of the
> source and reflected wave which determines the details in this region,
> which (I guess) is highly non-linear and needs a tricky treatment.

So, it looks like there is a high pressure region in the conical
portion of the mmouthpiece that gradually decreases towards the
barrel, resulting in the node ~8 cm down from the mouthpiece. Is it
reasonable to think of this high pressure region acting as a barrier,
creating the closed tube effect? Hence, the node is effectively the
end of the closed tube of the main body of the clarinet.

I am not quite satisfied with that solution. I just stuck my pinky up
my mouthpiece and it does not seem to taper significantly, to the
extent that I am able to get my finger up there (second knuckle;
almost, but not quite to the bottom of the baffle). It appears there
are some end effects that make the (L+2a) approximation not quite
correct in the presence of a bell, as indicated by the section "End
corrections are more complicated in real instrumetns" at (4)
http://www.phys.unsw.edu.au/jw/musFAQ.html#end. It states that bells
are more complicated and links the reader to clarinet acoustic
impedance It appears the end correction is non-linear in the
presence of a bell.

>> All the diagrams I've been looking at put in mind a series of high and
>> low air pressure points in the clarinet that are regularly positioned,
>> like the sine wave we learn about in school.
>>
>> Is the high and low air pressure point distribution more like the wave
>> seen using an oscilloscope? =A0If that is the case, then I figure there
>> would be more nodes and antinodes of varying extremes of pressure.
>>
>> Sincerely,
>>
>> Jennifer
>
> Likely, most diagrams show the approximate case of an infinite pipe with
> one close end (see above). =A0Inside the clarinet, there is some
> regularity between the vibrating reed and the node, tied to the source
> details and to the lower part, and some (different) regularity between
> the node and the bell, tied to the tube and tone hole details and to the
> source in a different way.

Then there is the effect of the tone holes on effective bore size.
Steven Fox's description of the Benade NX clarinet mentions the way
the two throat eb / clarion b'b tone holes increase the effective bore
size.

> Keith Bowen wrote:
>> (...)
>>
>> I think we all agree that
>> 1. A clarinet has a pressure antinode somewhere near the reed end. This
>> corresponds to a displacement node, i.e. a tube closed at the top.
>
> I'm not completely sure about it, but it sounds likely, given that we
> are very near the source. =A0What I've found is that there is a phase
> shift between pressure variations and displacements, but found no
> precise statement about the size of the shift. =A0One would need a phase
> change of 90 degrees to get the picture described above. =A0This can well
> be, but I have nothing to prove or disprove it.
>
>
>> 2. It has a pressure node somewhere near the bell, corresponding to the
>> discontinuity between the wave impedance of the tube and the very low wa=
ve
>> impedance of the open room, allowing waves to be reflected back into the
>> clarinet and build up standing waves in the instrument.

altissimo notes are not radiated out the tone holes because of the
impedance of the air in the tone hooles and their relatively ?low
energy? Lower notes are radiated out the open tone holes (this seems
like it would be a function of wavelength to me)

Impedance is a function of the inertia of the air molecules.

> This sounds very strange or at least counter-intuitive to me. =A0The bell
> is not only a point in which the reflected wave is bouncing back toward
> the mouthpiece, it is also the source of the spherical waves which we
> hear. =A0I would need to check the mathematics, but I'm pretty sure that
> the situation is that we have refraction at the discontinuity between
> the pipe and the external world. =A0This would imply that we have a
> pressure maximum at the exit of the bell.

That makes sense. Perhaps partial refraction and reflection?

> Now, above 1/6 of the wavelength pressure variations and displacements
> should be already quite in phase and at the bell we are at least at 1/4
> of the wavelength for the lowest possible pitch (for all higher tones,
> we are beyond this limit). =A0Hence I would deduce that:
> =A01) we have a relative maximum in the pressure variations at the bell
> =A02) we also have a relative maximum for the displacements at the bell,
> for most of the range
> =A03) all diagrams I've seen so far are completely wrong
>
>
>> I think the points of debate are the distance from the reed tip to the f=
irst
>> pressure antinode (fundamental vibration), and for my part I also am
>> concerned about the effects of the mouthpiece and the bell. I, too, am
>> surprised that the distance from the reed tip to the antinode is as much=
as
>> 8 cm.
>
> I was not very surprised. =A0Indeed, the register key is at a fixed
> position with respect to this node and it is quite near to it. =A0I would
> have been surprised to find the node more distant from the register key,
> because this would have implied that a lot of harmonics would have been
> impossible to play. =A0So, before making the measurement, I was expecting
> to find the node a bit above or below the register hole, and I was even
> more relaxed when I found it to be above (this makes very much sense to m=
e).
>
>
>> (...) =A0Indeed, the method I used was measurement of tone holes, bore
>> diameter, wall thickness to calculate the pitch of notes other than the
>> bottom note, using Benade's tone hole lattice end-correction. This avoids
>> the problem of the bell, for which there isn't a simple calculation; and
>> anyway the effective length of the bell is frequency dependent.

I see why the references I looked at did not indicate how to deal with
the bell mathematically

>> So I
>> regarded measurement of overall tube length as unsatisfactory for
>> determining pitch. I have enough data from the Nurnberg museum publicati=
ons
>> to run the calculation for several tone holes for some clarinets, which =
will
>> empirically determine the pressure-antinode position. I do need to do th=
is
>> to verify my methodology, but it will take some time.
>
> I know nothing about this approach and will be delighted to know about
> it. =A0I hope you'll have time to make this check and let me (us) know.

Yes. Definitely.

Good night,

Jennifer
_______________________________________________
Klarinet mailing list
Klarinet@-----.com
To do darn near anything to your subscription, go to:
http://klarinet-list.serve-music.com