<html> <body> Beware Gordon! Are you  prepared to re-enter the mine field? You are about to start talking about how the energy from the string actually becomes transformed into the transversal movement of the soundboard, required to create the sound waves we hear, forcing us to ask such questions like, for instance, do the strings make the bridge move up and down, or, for that matter, from front to back?  If you choose to undertake such an adventure, you would be probably be well advised to avoid starting out with a virtual sign taped to your rear saying "KICK ME!"  By that I am referring to your portrayal of the string pulling on the bridge cap.  While I, personally have come to believe that the essence of your idea is correct, that is, all modes of string displacement being transformed into a kind of pulse energy at the termination, the string would, in no way, actually pull on the bridge cap, with the attending implication that the bridge is pulled forward and backwards, a motion you might more reasonably infer from a theoretical configuration which had the entire string terminate on the bridge,  (Of course, in such an arrangement you would be dispensing with downbearing ...but...).  If anything, it would be the pins that would be pulled, but, in that case, it would seem that the back scale would counteract any tendency to pull forward. I'm not sure what aspect of Bernhard Stopper's remarks you are reacting to.  If anything, he seems to be saying, as are seem to be, that the bridge moves back and forth.  I am doubting that such a description accurately reflects the mechanics involved, but that's only my gut speaking.  I have to go back and read 5 Lectures again, along with the last 10 years of Journals and Pianotech. David Skolnik At 07:49 PM 2/11/2004 -0800, you wrote: <blockquote type=cite class=cite cite>Excuse me, please, but is not the piano tone actually caused by the tugging of the string on the bridge cap, effectively making it a "bell crank"? Afer all, as a string vibrates, the end pulls in and out, not up and down. If it waved up and down, lifting and dropping the bridge with it, the tone we hear would be the frequency of the entire string--- from agraffe to hitch pin. But it isn't.      Thump --- Bernhard Stopper <b98tu@t-online.de> wrote: > Dear Marc & Isaac, > > Longitudinal waves of strings produce transversal > vibrations on the > soundboard caused by the bridge´s back and forth > movement. If this would not > be the case, one couldn´t measure or hear them. I > think you don´t negociate > that they exist, in the sound samples it is the > whistle you can hear. As > Isaac wrote, (he supposed it was the additional line > below the 4. > transversal but heard it an octave higher. It is > overlaid with the 13. > transveral, so that is indeed what you heard, (good > ears Isaac, i am really > impressed... ) > > Measuring and separation of transverse and > longitudinal harmonics were done > with a software spectrum analyzer (spectraplus, you > can download a test > version at <a href="http://www.telebyte.com/pioneer/" eudora="autourl">http://www.t= elebyte.com/pioneer/</a> ). A > spectrum analyzer extracts > every frequency that is in a sound wave over time, > no matter if it is caused > by a longitudinal or a transversal wave. > > To interpert the spectra, just "count" the regular > lines.. there are 39 > transversal waves, and the first longitudinal wave > (at about 712 Hz) is > overlaid with the 13. transversal (a little thicker > line) The various > additional lines (mainly around the mid of the > spectrum) are caused by the > blank ends,  the wave propagation is faster on that > part of the string what > results in splitting up several harmonics. > > to ask for a MiniMens Audio demo (the string > simulator) and more information > on the MiniMens program look here: > > <a href="http://www.piano-stopper.de/homepe.htm"= eudora="autourl">http://www.piano-stopper.de/homepe.htm</a> > > best regards, > > Bernhard Stopper > > ----- Original Message ----- > From: "Mark Kinsler" <kinsler33@hotmail.com> > To: <pianotech@ptg.org> > Sent: Wednesday, February 11, 2004 6:09 AM > Subject: longitudinal waves > > > > So there's a program that'll simulate the behavior > of a stretched string, > > non-linearities and all?  I suppose I shouldn't be > surprised, but I'm > > certainly impressed.  And the recording and > simulation sounded alike > (though > > the attack, etc. was different.) > > > > I'm sitting here wondering how you could measure > longitudinal waves on a > > string separately from the transverse waves.  It's > easy enough to detect > > motion in a plane perpendicular to the string, but > how would you isolate > > longitudinal waves? > > > > I wish those two spectra had some labels on them. > I couldn't figure them > > out. > > > > > > M Kinsler > > 512 E Mulberry St. Lancaster, Ohio USA 43130 > 740-687-6368 > > <a href="http://home.earthlink.net/~mkinsler1"= eudora="autourl">http://home.earthlink.net/~mkinsler1</a> > > > ></blockquote></body> </html>