Klarinet Archive - Posting 000117.txt from 2010/08
From: "Keith Bowen" <keith.bowen@-----.com>
Subj: Re: [kl] Location of antinodes of vibration in an air column
Date: Sat, 14 Aug 2010 19:18:55 -0400
Diego,
I also thank you for bringing up new points to me. Since you, Tony and
myself are all trained in both mathematics/science (including wave
equations) and music, to high levels but with varying emphases, between us
we may sort it out. I think we have all been guilty of patronizing remarks,
and I also apologise!
Your statement "I really cannot understand how my sentences could be used to
conclude
that "the pipe length is not only a half instead of a quarter
wavelength, but also _exactly_ a half wavelength." Perhaps you could
explain this? In any case, the correct unit is one quarter of the
wavelength, not one half." is, I believe, explained by your comment:
>>> we have an antinode at the end of the bell,... also an antinode at the
reed
which would imply a pipe length of exactly half a wavelength. Obviously this
was a slip in one of the antinodes (!). From your quote above, you clearly
did not mean this.
Michael is right that confusion has been caused by lack of clarity in
whether we are talking about displacement or pressure nodes/antinodes. Your
email below clarifies your intentions, and Tony was also careful to make the
distinction between pressure and displacement nodes/antinodes. But I can see
how other readers may have been confused.
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.
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 wave
impedance of the open room, allowing waves to be reflected back into the
clarinet and build up standing waves in the instrument.
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 much as
8 cm. This doesn't correspond with some quite detailed measurements and
calculations I made last year of bass clarinets to determine their pitch
(not being allowed to play museum specimens). But I will go back and check
these. Indeed, 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. So I
regarded measurement of overall tube length as unsatisfactory for
determining pitch. I have enough data from the Nurnberg museum publications
to run the calculation for several tone holes for some clarinets, which will
empirically determine the pressure-antinode position. I do need to do this
to verify my methodology, but it will take some time.
Best, Keith
-----Original Message-----
From: Diego Casadei [mailto:casadei.diego@-----.com]
Sent: 14 August 2010 20:47
To: The Klarinet Mailing List
Subject: Re: [kl] Location of antinodes of vibration in an air column
Hemm... I must admit to have reached the limit of my understanding and
mastering of the English language. I'm not able to fully understand
most of the quoted message :-(
Anyway, I can try to make some additional remark. First, though
implicitly, I've always being thinking about pressure variations (never
about displacements). This is because the ear reacts to them, not to
the fluid displacement. I know that strings and water, the models for
wave propagation, are better described in terms of displacements, but
sound waves in air are best described in terms of pressure variations.
[BTW, in my reply to Richard's email my language was a bit imprecise,
and at the end it seems that I speak about variations in pressure and
(variations in) velocity. The second "variations" should not be
implicitly inserted. Don't know if this was unclear but reading it
again I had this doubt...]
Second, I never used the noun "antinode" in my life, before having found
it on the paper which was at the origin of my comments. I kept it in my
email hoping to make it easier to everybody to follow it... I should
have spoken about "relative amplitude maxima" instead.
Again, I never thought in terms of "displacement antinodes" (nor nodes):
I was thinking about pressure variations instead.
I really cannot understand how my sentences could be used to conclude
that "the pipe length is not only a half instead of a quarter
wavelength, but also _exactly_ a half wavelength." Perhaps you could
explain this? In any case, the correct unit is one quarter of the
wavelength, not one half.
The last comment is about the statement that the "reed can support a
helluva pressure amplitude, even if not quite maximal unless you bite
the reed down." This statement has nothing to do with acoustics.
First, sound waves describe the propagation of pressure _variations_,
not the pressure itself. Second, the pressure here is the air pressure,
not the static mechanical pressure exerted on the reed by biting it
(which is not transmitted to the air).
Anyway, my wording was indeed somewhat imprecise, though I made my best
to avoid this problem. Please continue to feel free to criticize it.
Cheers,
Diego
Tony Pay wrote:
> On 14 Aug 2010, at 03:40, Richard Sankovich wrote, in part:
>
>> Diego, thanks for your detailed explanation of sound production by
vibrating strings and air columns. I must take issue, however, with your
conclusion that there will be a vibration antinode at the energy source, or,
in your words, a point of maximum amplitude.
>
> What Richard subsequently says fits in with what 'my guy':-) Michael
McIntyre writes to me. (I wrote to him asking whether in his opinion the
8cm is theoretically sustainable, not having yet checked your actual
experiment.)
>
> I quote:
>
>> ...havoc over elementary acoustics :-[ due largely to the usual failure
to follow (forgive me)
>> lucidity principles, even though I see you're trying to set a good
example, which of course no-one notices.
>>
>> I find the 8 cm plausible enough. I check the wavelength calculation
even though I can't check the length of a B flat clarinet just now. The end
effect adding
>>
>>> about half a centimeter outside the bell
>>
>> seems about right. But the following might repay a moment's attention,
regarding bottom written E:
>>
>>> 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.
>>
>> So, just through slight carelessness, we have a deadly combination of
inexplicitness with incongruous repetition, with the one word "antinode"
meaning two quite different things", namely
>>
>> (1) the displacement antinode near the end of the bell, and
>>
>> (2) the displacement near-node in the mouthpiece adjacent to the reed,
>>
>> which the writer calls an "antinode" perhaps because he's suddenly become
amnesic about the distinction between "some displacement" and "maximal
displacement" and about the fact that the reed can support a helluva
pressure amplitude, even if not quite maximal unless you bite the reed down.
>>
>> love M
>>
>> PS Please urge everyone concerned to take two minutes on
www.atm.damtp.cam.ac.uk/people/mem/lucidity-in-brief/
>
>
> Anyway, I am very surprised about the 8 cm. It throws off most of my
rule-of-thumb assumptions about where to modify bore dimensions in order to
change twelfth relations. Perhaps I'll do better in future:-)
>
> Thank you Diego; and apologies for reading you far too superficially at
first.
>
> It just goes to show, again, that being specific about criticism (as you
were) is worthwhile.
>
> Tony
--
Diego Casadei
__________________________________________________________
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