Robin Hufford wrote: > 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. Well, of course Professor Askenfelt's views taken by themselves are not conclusive. But when taken with Dr. Russells views, and with that of Rossing and Fletcher, and that of four (now) other men of their calibre in this field I have to allow myself to be swayed. I cant see that your arguments are supported by any data or hard science. And I cant see that you have provided more then speculative argumentation in the end, tho I will be the first to admit that it has all been very interesting and I am glad for the chance to have heard these views presented and argued. But I think to be honest, that if you are going to show that literally all the major acousticians who have written on this subject are wrong, then you have quite a task ahead of you. No doubt you will be able to find varying opinions also in that field. And I will be the first to acknowledge that what is "known" today has this nasty habit of turning out flawed tommorrow, also in the world of physics. That being said, I find Askenfelts answers to my direct questions, along with the other information I have assembled and attempted to digest quite convincing. > > 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. I have, and I dont see where a different view specific to these exact questions are presented. Tho I will look at them again just to see. Dr. Askenfelt answered my question very directly. I presented him with the two basic views argued, along with my own speculations about quasi-longitudinal waves, and he ruled out the those and the compression view. > > 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. I beg to differ. Physics books dealing with wave mechanics and the physics of musical instruments seem to all agree on this issue in the end. At least in the 4 books I have all are in aggreement. There are statements in each that easily can be interpreted to mean other things, and the most difficult of these is the one sentence in McFerrins book (which is by far the weakest treatise on the acoustics per se of the instrument) I quoted earlier. Still, the overwhelming bulk of my readings and experience point in one direction. I think we gotta yeild on this one Robin. In anycase until someone can present some decisive evidence as to why we should not. And heck.... we picked up on a few interesting and new (at least for some of us) facts. For the moment, its time to call it a day. Again.. this is not about being right or wrong... its about learning. > > 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. -- Richard Brekne RPT, N.P.T.F. Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html
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