Anders Askenfelt On Pianos

[Robin Hufford]

Richard,
     I have owned the Five Lectures on the Acoustics of the Piano for some 8 or 10
years now, and been through it many times.   When I entered into this discussion,
I was aware of Askenfelt"s views on some aspects of the subject of pianos,  at
least as indicated in the "Five Lectures", through the article he co-authored with
Jansen which is concerned principally with an analysis of the action and the
effect of the hammer on the strings.  Little, if anything, is said in this article
about soundboard
behavior.  In general, though, the tenor of the book, here and there when the
subject is taken up, is that the bridge is moved by the strings. Some may consider
this temerity on my part, but my position was taken with a ready familiarity to
the views expressed in this collection of lectures, and I maintain it still.  To
now find a statement from Professor Askenfelt supporting this view is no surprise
to me, nor, for my part,  is it conclusive.
       I am sure many of the conventional thinkers so antagonized by any other
point of view will find themselves vindicated here; they could have quoted from
the book to support their position that some motion occured at the bridge;  but
that would not have been convincing to me as to the origin, periodicity and extent
of this motion and the nature of energy transfer at the string/bridge interface.
Nor, it would seem, is this subject contained in your answer from Askenfelt.  I,
therefore, don't consider this matter at all put to rest.  I don't wish, of
course,  to get  in a kind of contest of "authorities" but would suggest, that you
take in hand some of the references from which I have quoted, upon a request from
Phil, a week or so ago.  You will find a different view expressed there.
    Hall says" we know that the bridge moves" without analyzing this motion.
Weinrich, in the opening part of his article qualifies his approach with this
sentence "To the best of my knowledge, in all musically useful string applications
the dominant mechanism of string damping is motion of the end supports, that is,
coupling of the bridge to the soundboard.   This is an evident qualification.  I
make no assertions concerning his reasons noting only the qualification of the
statement.
     I am aware that there is no consenus of opinion, among authors of books on
wave mechanics and physics,  although many support, at least theoretically, the
view I that I have upheld here and  in which I I continue to believe.   The
difference of opinion which is the present controversy,  exists, also in a much
more intensively studied subject, that of the violin.
Regards, Robin Hufford
     Richard Brekne wrote:

> List, given the doubt surrounding the nature of flexural waves / bending
> waves and whether or not they are transverse in nature or not, I asked
> Anders for a clarification which he was kind enough to provide me with.
> I shall not trouble him again as I think we have enough now to draw a
> pretty reasonable good conclusion to the present debate. I also asked
> him to put to rest the question of how sound radiates, and he included
> the correct definition (of the three alternatives I provided him with)
> along with his comments on that.
>
> Anders Aksenfelt writes :
>
> The bending waves I was talking about are identical to flexural waves.
> They
> are transversal waves, but that the propagation velocity is frequency
> dependent. This makes them a little more complex than transversal waves
> on
> an ideal string, which has a constant propagation velocity. Piano
> strings,
> on the other hand, which do have stiffness, have a frequency dependent
> propagation velocity, just like plates. The dispersion phenomenon in a
> bar
> described by Dr Russell is easily observed on piano strings.
>
> About radiation: The citation you gave below is correct. Sound is
> radiated
> when an object like a loudspeaker membrane, a violin top plate, or a
> piano
> sound board is pumping air back and forth.  The appropriate unit for the
> strength of a sound source is [m^3/s], cubic meter per second, in
> SI-units.
>
> >Others understand the word radiation as a process of putting air in motion as
> >is in line with  transverse movement from the panel.
>
>                                                  Sincerely,
>
>                                                  Anders Askenfelt
>
> The Loudspeaker analogy holds true, and interesting enough he
> equivocates this to the violin top plate as well. I found it interesting
> that longitudinal waves were given to be the cause of the back and forth
> "rocking" of the bridge there has been so much discussion about, instead
> of the strings transverse waves. And I find it intriguing to know that
> the transverse movement of the panel is such that the propagation
> velocity is frequency dependent. I didn't know that, though perhaps that
> piece of information has zipped past me once or twice before.
>
> Any ways gang, though this discussion has taxed the patience of more
> then a few, I am personally glad we stuck it out.