Hello Richard,
I reproduce due to a lack of time part of a recent private email concerning the
subject of soundboards, the reliance placed upon the five lectures, which, I think it
is well known that I disagree to some extent with, and the new study which you
provided me last year by Giordano. I think it important for those who wish to make an
effort at this complicated subject to be aware of the new study.
In the long arguments on soundboard behavior last year and the
>occasional few since I made those points then, which was based upon a
>certain, mathematically-based, physical point of view I have been taken
>to task by some for offering a kind of non-conventional,
>"non-established" model and set of conclusions which I, however, think
>are very much obvious on reflection.
> Now, thanks to Richard Brekne, I have received, some months ago,
>something which I have only been able to give due attention to lately,
>and that is a new study which tends to support some aspects of this
>view, at least partially, and according to my reading, although, of
>course, the author should speak for himself and other may well
>disagree. The author, Giordano of Purdue, takes the view that only
>two other studies of any significance have even approached the subject,-
>those of Wogram and Suzuki in the five lectures, something I agree
>with. He notes that these two disagree in their results as regards
>changes in acoustic impedance at various points in the scale and that
>his study tends to agree with the conclusions of Suzuki along these
>lines.
> He makes, at least initially, the same assumptions of string driven
>behavior represented in the other two studies, that is, in accordance
>with the views of the flexurists emphasizing the importance of a
>perpendicular force supplied by the string, and attempts to simulate
>this with the use of the shaker (a bridge/soundboard driver) applied to
>the bridge perpendicularly to the plane of the soundboard. A
>measurement is then taken of the ratio of pressure to particle velocity
>with appropriate instrumentation which is the acoustic impedance at the
>point of measurement. Various comments are made as to the changes in
>the value of the impedance in various areas, its dependence on
>frequency, its origin in inteference effects and, interestingly,
>relatively much lessened dependence on the mechanical impedance of the
>board, etc. etc.
> The particularly interesting part to me is what he acknowledges to
>be unstudied before: that is the in-plane motion of the bridge which he
>finds in the study to be "suprisingly large" . He does not make the
>claim that it is caused by anything other than longitudinal vibration of
>the string. On this point, of course, I disagree as I think the stress
>transduction model I proposed last year will account for the motion of
>the bridge in this direction through wave behavior itself, in what amounts to the
"quasi-longitudinal >state of forcing" to repeat a term I included in a post to Sarah
Fox.
Along these lines the recent article on this subject in the Journal seemed, as
far as I could tell, to present little new along these lines, except for the claim,
which seems questionable to me, that dispersion is the source of inharmonicity, and,
consistent with a criticism I have expressed against others on this same subject,
merely once again taken recourse to assertion about this fundamental mechanism of
energy transfer. Perhaps, subsequent articles will be more original. Also, I am
somewhat disinclined, on the limited, cursory glance afforded in my quick read of the
article, which is all that I have had time for, that the equation of motion he uses
in this situation is, in fact, the correct one, although it may be so.
Also, I really believe the readership of this list and, particularly piano
technicians who go on about this subject with the security of certainty, should make
an effort to understand at least a little of the mathematical physics behind a
differential equation such as this. It is not a simple algebraic expression in which
one "plugs in values" and calculates results. Rather, it is more a conceptual
statement which indicates relations between what can be thought as the rate of change
of one variable with respect to another, or several or the function itself or of the
rate of change of the rate of change itself, and so forth. . The solutions found to
these equations, of which there are several kinds, are, ultimately, arrived through a
kind of guesswork which aims to reduce the equation to an identity. Parts of these
solutions are, then, the algebraic expressions which we are familiar with and use in
the "plug in value" method which is bandied about here as if it were the last word in
analysis.
Also, the references to the mosquito and the aircraft carrier still demonstrate
what seems to me, at least in the present context, a disregard of the central critical
point of a proper analysis of the energy transfer in such situations and that is the
individual behavior of a set of particles which, in the aggregate represent the
transfer relations which normal continuum mechanics affects to comprehend. This,
again, comes to how it is that energy can be transferred from one object to another in
such situations, how coherent or incoherent is the subsequent particle behavior in
such situations, and that this can only be, in the string/bridge/soundboard context,
due to the relative size of the forces involved, through mutually induced strain which
partakes of the nature of wave motion and not flexure, although flexure is then
subsequently present in the board. This is the subject of impact and dynamics and
soundboard behavior should be studied as such, in my opinion.
As I have said before the spring theory, of which we have had a very lucid
exposition of on this list recently, cannot, in my opinion, be defended
mathematically, as, if for no other reason, and there are numerous other points of
attack, two adjacent springs would necessarily have differing periods of oscillation
that were dependent upon whether one or both springs were vibrating, that is, the
frequency of the first when vibrating alone, would be changed by the interplay of
forces produced by the addition of a second vibrating spring, much less 86 more. In
terms of pianos this means that when A440 is ringing playing any other note, but,
particularly, those close to it, would alter the frequency of A-440. Nor could its
periodic character, displayed when ringing singly, be maintained.
Regards, Robin Hufford
Richard Brekne wrote:
> Ron Nossaman wrote:
>
> > >WHAT ??? ahhhh.... and here I was expected a triple barrelled broadside :) ...
> > >or maybe this is some new kind of satiric reverse rhetorical commentary....
> > >you SAY I'm right... but you dont really MEAN it. Hmmm...
> >
> > No, I mean it. You're right. You'll have to find something else to argue
> > about or just argue amongst yourself.
>
> Amoungst myself ??... plural in the singular ?? what an interesting concept.
>
> > >Well... In anycase.. As the point is trivial really anyways... I'll withdraw
> > >for the moment and get back to my project.
> >
> > Yes, I think you've nailed it. Trivial is the definitive term.
> >
> > Ron N
> >
>
> Seemed in keeping with the general spirit around these past few days. Besides.....
> we've had this precise discussion up at least 4 times that I can remember... been
> there and done it. I'm still waiting for all these concepts to result in the
> significantly more wonderful type piano that will convince the world of pianists
> that S&S is a saga past by. Seriously. Should be tough tho... this last years
> experiences have taught me that pianists absolutely detest historical
> temperaments... until unknowingly they play a piano tuned thus. I mean with
> awareness like that you got a major type obstacle to overcome.
>
> Now... if you dont mind.. :)
>
> --
> Richard Brekne
> RPT, N.P.T.F.
> UiB, Bergen, Norway
> mailto:rbrekne@broadpark.no
> http://home.broadpark.no/~rbrekne/ricmain.html
> http://www.hf.uib.no/grieg/personer/cv_RB.html
>
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