John Delacour wrote: > At 9:31 PM +0100 1/17/02, Richard Brekne wrote: > > >Why do I insist on the wave front being the direct source of > >vibration in the panel. Well, for a couple reasons. The speed of > >transverse bending waves is dispersive.... that is to say that the > >wave velocity is frequency dependent. > > Richard, I've not heard the epithet "transverse" used to describe > bending waves (flexural waves). Is that something you have added to > what you've read? It seems that these 'bending waves' are indeed > very significant, but let's get a clear picture of how they behave > and not adorn them with properties they don't have. Nope... Fletcher and Rossing use the term "Bending Waves" in several places to describe transverse waves in solids. I am not 100 % sure this is the same as "flexural waves" as the latter may include bending in more then one direction at one time but I will see if I can find this out. Bending waves are transverse and are dispersive of nature, i.e. speed of the wave is frequency dependent. > > > Yet we operate with a constant when we use the formula for the > >speed of sound through wood. > > Far from it! Any wood, but especially fir or spruce, is anisotropic > and will behave differently in different planes. If sound waves will > pass through spruce at nearly 5500 metres per second along the deal, > its speed across the grain of a quartered deal might be only 1500 > metres per second and if it's not cut on the quarter, then there will > be other complications My mistake. I didn't make myself clear at all. I was trying to draw the difference between dispersive waves and non dispersive waves. I think I have mentioned this about the difference in stiffness depending on the orientation in a few other posts. > . You were extremely vague yesterday when I > asked the question about Sitka spruce, and now you are talking about > formulas and constants. Ron Overs answered the question briefly but > did not extend his answer to say that for the good reasons he gave, > sound propagates faster along the grain in soundboard wood than in > any other wood. In Douglas Fir it might travel at only 4900 metres > per second. > I was very vague because, as I stated in the outset of that paragraph, this particular subject matter is something I know waaaaaayyy to little about. I am still trying to find that post you wrote about the different variants of spruce used in Steinways through the years, as my first reading of that was interesting. But then there are some 100 contributions to this thread alone to keep track off... :) > > That says to me that that formula is referring to a compression > >wave or perhaps some form of quasi longitudinal wave, as in Rayleigh > >surface waves for example. > > Are you saying that Rayleigh waves are at play here? Please explain. Rayleigh waves are certainly common in solids, if I am to believe what's written on the subject mater. They would account for the surface waves (ripples) and at the same time remain within the realm of sound waves I would think. But this is speculation on my part.... but hey... you guys asked me to think for myself about this stuff I have been reading... so this is where it has taken me so far...:) I like Rons Ripples... and I like Delecours Compressions.. both seem sensible > > >Also I cant escape the fact that the panel has three dimensions, and > >any force acting upon that simply has to propagate though all three. > >I don't see this is in conflict with the 2 dimensionalilty of the > >panel as a vibrating plate. > > That's all very confused. It's no good just blurting out all these > great new things; you need to get some sort of understanding of them > first. Panels and plates are not two-dimensional. In physics they are analyzed as 2 dimensional vibrating systems. A string is in this sense 1 dimensional. Hey... I didn't write the rules... :) But I agree, as I pointed out... I cant escape the fact that there are 3 physical dimensions. But so far I have not seen anything relative to a thickness mode in plates relative to this discussion. > The reason I was so loth to talk of the vibrations of the soundboard > from the outset of these discussions, and still am, is that I do not > have a clear picture of its very complicated behaviour. If anything has become clear in this discussion, it is that none of us have a clear enough picture of the nature of vibration to speak with any real authority. That's part of what makes this so fascinating, as we are pushed to find understanding of things that are at present over our heads. And we each bring our own perspectives and preconceptions and notions about what we think we understand into the game. As long as we just help each other along the road... we cant loose ! > Very slowly > I am getting a better grasp of the elements involved and the picture > is becoming extremely rich if nothing else. The more I discover, the > more interesting and significant it all becomes and I have no doubt > that for me at least it will have most important design implications, > contrary to your doubts on the matter. I do not doubt them... no no no... I just was asking for specifics as to what they are.. I was opening for another angle in the discussion. > There are certainly different types of vibration at issue, and owing > to the non-rigid nature of the system, there is certainly 'movement' > involved at least as regards the natural frequencies of the board. I > don't think any piano man on this list is anywhere near capable of > the mathematics required to describe accurately all the phenomena of > the string and the soundboard -- some of the texts I have read are > quite frightening, involving huge equations including imaginary > numbers and lots of calculus -- but out of it all it is still > possible to gain a proper picture in the end and everyone interested > in this topic will be wiser as a result and, I believe, in a better > position to make informed design decisions. I agree... as long as we don't really speak the math... we are to some degree guessing at the true meaning of descriptions which in English are subject to being understandably interpreted in several ways. > > Here is an interesting exchange between me and a very well-informed > acoustician who expresses himself clearly and simply and from whom I > hope to get more: > > > > c) Given that the system will manifest flexural vibrations at its natural > >> frequencies (many questions here alone) can it be said also to have flexural > >> vibrations at the manifold frequencies fed to it from the strings? > > > >You don't have to vibrate a structure at exactly its natural frequency > >for it to resonate. If you are slightly to one side of the natural > >frequency then resonance can still take place. The further you move away > >from the natural frequency, the less resonance you will get. If the > >structure is highly damped then you do not have to be so close to the > >true natural frequency to get resonance. If the soundboard is big enough > >and flexible enough and the damping is sufficient then the modes > >(resonances) overlap and almost any frequency will resonate. Yep... as I understand it, can cause us quite a few problems. When string frequencies are close to panel resonance's, then you have all kinds of affects coming into play. I have a few things marked about that in these books, and we get into, among other things, this business about para inharmonicity real quick by moving in this direction. > By a strange coincidence I had already demonstrated this the day > before in the following way: > > I struck the soundboard of a strung piano and noted the frequency of > the fundamental mode very roughly. I then played the note > staccastissimo on the piano that corresponded to this frequency and > heard a sort of distant resonance which I would previously have > ignored. Playing notes a semitone or a tone each side of this, I > noticed I got a similar resonance and was prepared for disappointment > until I then played notes four or five tones distant from the > resonant note and discovered that the resonance was practically > absent. It is interesting that while this resonance is quite clearly > perceptible when you are listening for it, it does not give undue > loudness to the notes affected, though I presume that it might in a > less well designed piano. Very interesting. > > JD Interesting indeed ! This was a pleasure to read JD ! -- Richard Brekne RPT, N.P.T.F. Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html
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