<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> John Delacour wrote: <blockquote TYPE=CITE><style type="text/css"></style> At 5:22 PM +0100 1/9/02, Richard Brekne wrote:  <blockquote type="cite" cite>Well, see the reason I ask is that your "radiate" seems to correspond pretty good with Olsons description of sound board radiation in which case I see almost the exact same description when it come to Benades description about the longitudinal nature of transverse like surface waves. In all this you could sort of look at these as a huge collection of tiny  ... Olson uses the word "pumps" pushing away at the air in his description of sound board radiation.... btw.. I read your stress waves reply to Phil and this also points in this same direction. You said then <blockquote>"Acoustic radiation is caused by minute pressure differences at the surface of a body."</blockquote> </blockquote>  Interesting that Olson should have used such a very similar analogy.  You've mentioned him before but given no details.  Who exactly are Olson and Benades or what are the books in question? RB:   Arthur H. Benade "Fundementals of Musical Acoustics" ISBN  0-486-26484-X, Dover press New York Harry F. Olson "Music, Physics, and Engineering" ISBN 0-486-21769-8, Dover press New York Neville H. Fletcher & Thomas D Rossing "The Physics of Musical Instruments" ISBN 0-387-98374-0, Springer W.V. McFerrin "The Piano, Its Acoustics" All available at Amazon.com McFerrins book is interesting enough, tho contains the least information of these four and is the oldest of them. Benades book should be a must for anyone who is really interested in these aspects of pianos, and is the easiest to comprehend for the layman. Olson is a bit heavier, a bit more math intensive.... more for the engineer with a few years of college level math and engineering behind him. Fletcher and Rossings book like Oslo requires that you can relate a good deal of math. I havent read a whole lot in that book yet so I will reserve further comment. JD:The analogy of his tiny pumps or my little pulsating fountains is, of course, an extreme simplification.  The final picture will be vastly more complicated.  What I hope we can eventually arrive at is a good basic understanding of the principles involved and the nature of the wave forms generated.  As I've recently said, I think it would be helpful in the early stages to consider the system as composed of one homogeneous isotropic solid body (which would, I guess, actually work after a fashion) and to avoid discussion of the behaviour of fluid bodies.  RB: I agree that a good understanding of these principles, and adherence to a common terminology based on that understanding would be really helpfull. My insistance on the fluid bodies examples is as much to build my own understanding of wave mechanics in general as it is anything else. Actually Benade puts the soundboard in the catagory of a 2D plate where longitudinal waves and transverse waves both occur. And it looks to me like he is saying that one cannot exist without the other and that where one exists the other must occur. Personally I find the whole discussion fascinating and there are lots of little peices of information that pop up out of nowhere.... For example...some months ago there was a discussion about something refered to as para-inharmonicity and there has been quite a bit of speculation as to what it is and isnt, or indeed if it does exist. Benade describes some aspects of how soundboard and string modes (as in partials) effect each other when each have modes whose frequencies nearly coincide. The description could explain to a "T" the whole concept of para-inharmonicity.     JD:We have a lot of studying to do. Yup...but its fun really. JD </blockquote>     -- Richard Brekne RPT, N.P.T.F. Bergen, Norway <A HREF="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</A>  </html>