Klarinet Archive - Posting 000186.txt from 2010/08

From: Jennifer Jones <helen.jennifer@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Mon, 16 Aug 2010 20:36:02 -0400

On Sun, Aug 15, 2010 at 3:15 AM, Jennifer Jones
<helen.jennifer@-----.com> wrote:
> On Sat, Aug 14, 2010 at 11:45 PM, Diego Casadei <casadei.diego@-----.com>=
wrote:

[snip]

>> 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 clos=
ed"
>>>> low E). =A0However, the clarinet is able to play a very wide range of =
pitches
>>>> 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 pi=
pe
>> 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. =A0Is it
> reasonable to think of this high pressure region acting as a barrier,
> creating the closed tube effect? =A0Hence, 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. =A0I 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 that the conical portion of the mouthpiece does not extend
the full length of the mouthpiece, or at least, it is more conical at
the top than at the bottom. I think that might affect the location of
the node. The other thing that I think might affect the position of
the node is the end effects. In particular, the approximation for a
simple tube (length plus two times radius [L+0.6a]) explaining the
effective increased harmonic length has been put into question for
addition of a bell, without providing a mathematical correction (4).

4) http://www.phys.unsw.edu.au/jw/musFAQ.html#end
end effects; the effective increased harmonic length

> 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 instruments" at (4)
> http://www.phys.unsw.edu.au/jw/musFAQ.html#end. =A0It states that bells
> are more complicated and links the reader to clarinet acoustic
> impedance, which does not provide a mathematical correction. =A0It appear=
s 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.

As you said:

the clarinet is able to play a very wide range of pitches
>>>> and there will be waves for which it happens that such distance is 1/4=
of
>>>> the wavelength.

And these waves are not all unique to the pitch being played...
Depending upon the pitch being played, different waves predominate.

The oscilloscope probably shows something different from, but not
unrelated to, the node-antinode patterns inside the bore of the
clarinet.

>>>
>>> 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.

And it is the combination of these regularities that produces the
node-antinode pattern in the bore.

> 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.

I am thinking of the antinode at the mouthpiece as an entity separate
from the main wave patterns in the bore itself; namely it is a high
pressure region that acts as a boundary for other waves to bounce off.

That does not preclude influence of the reed, which may modulate the
overall pressure of the region even as the region transmits vibrations
driven by the reed

Though the clarinet is an open system, I am not convinced that the
pressure throughout is uniform. This is because there is air flow.
Like atmospheric winds are driven by relative high and low pressure
regions, so to, is air flow in wind instruments driven. The small
diameter and conical shape of the mouthpiece is the highest pressure
region, the more uniform cylindrical bore is at a lower pressure and
beyond the boundary layers of the tone holes and bell will be still
lower, at atmospheric pressure. This, of course, is in an instrument
that is being played by a still person in a still room. While I
expect there is a general flow from mouthpiece to bell and a general
gradient of relative high pressure in the mouthpiece, and relative
low, probably atmospheric around the bell, there will be vortices of
varying character and degree in the vicinity of the tone holes. There
will be vortices as air leaves the bore through tone holes and there
will be vortices within closed tone holes. The vortices will occur in
low pressure regions.

>>> 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 w=
ave
>>> impedance of the open room, allowing waves to be reflected back into the
>>> clarinet and build up standing waves in the instrument.
>
> altissimo notes radiate poorly from the tone holes because of the
> impedance of the air in the tone holes and the relatively ?low
> energy? of the altissimo notes. =A0Lower notes are radiated out the open =
tone holes (this seems
> like it would be a function of wavelength to me; long wavelengths radiate=
readily short don't.... This doesn't make any sense because all the wavel=
engths we are talking about are on the order of centimeters; a scale much l=
arger than the depth of the tone holes)
>
> Impedance is a function of the inertia of the air molecules.

It is also a function of the friction between air molecules and
objects in their environment.

>> 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.

So, there is a bunch of sound coming out of the clarinet through the
bell and it creates an arc radiating out of the bell. There is a
remaining portion that goes back into the bell, because of
interference with waves that are converging at the boundary between
the bell and room. and these are complex composite wave functions.

> That makes sense. =A0Perhaps 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 =
first
>>> 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 muc=
h 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 =
me).

How does the protuberance of the register tube affect the vortices
inside the bore? There should be a relative low pressure downstream
of the register tube and a resulting vortex...

>>> (...) =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 avoi=
ds
>>> 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 publicat=
ions
>>> to run the calculation for several tone holes for some clarinets, which=
will
>>> empirically determine the pressure-antinode position. I do need to do t=
his
>>> 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
>

Bell diffuses and shortens
mouthpiece architecture w/flat taper at top half and cylindrical
portion at bottom half
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