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. > 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. 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. > 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. What about brain waves ?? >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. 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. 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. 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. 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. 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
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