More precisely, the walls of a lute are elastic (i.e., deformable), especially the top. The fact that the walls can flex in response to the vibration is not taken into account in the simpler analyses of resonance (and I suspect it becomes a nasty non-linear problem).
----- Original Message ----- From: "Herbert Ward" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, January 19, 2004 9:55 AM Subject: Lute resonance. > > Here's a simple, but physically accurate, discussion of lute resonance. > > An organ pipe has a simple geometry. Let's start with it. > > An organ pipe of steel would have a sharp frequency response. > An organ pipe of soft wood would have a broad frequency response. > > The mathematics is too involved for discussion here. If you're > interested, look up "Q factor width resonance cavity" in, say, the > McGraw-Hill technical encyclopedia. > > Now think of a rectangular box instead of an organ pipe. You'll see that > it has three resonant frequencies, because, in comparison to the organ > pipe, it has three "lengths". > > The geometry of the lute is even more complicated than our box. You have > many complications: > walls of varying softness and connectivity > complex geometry > the sound hole > internal obstacles such as braces > The resonance response is, of course, not calculable with pen and paper. > I would not even trust a computer simulation from MIT. However, I would > guess that it spans many octaves. > > Then too, the cavity resonance is complete different the soundboard > vibration, which basically makes the sound. > > Bottom line: be glad there are lute makers who, through talent and > tradition, do it right, even if we cannot describe their result with > mathematical precision. > > > >
