I worried about that too, On my simplified model, I calculated between 109 and 139 Hz depending on the percent of the rose that was open. The actual resonance I found was a little above 116 hz, about A#. Not too bad. especially since I expected my rose to fall between the the upper and lower figures. It seems that the division of the total open area into all of the fiddley bits of the rose is not enough to make a big difference in the outcome.
The Helmholtz resonance is just one factor in how the instrument works. Helmholtz resonance is just the acoustic property of a closed cavity volume and an aperture. It does not consider the vibrational modes of the soundboard, the torque applied by the bridge to the soundboard, energy transfer to the other strings and the various ways that happens ...ad infinitum. After all of that, what I really learned is that in spite of the cavity resonance near A#, the loudness and responsiveness of this particular lute seems quite even over its entire range, no big hot spots or dead spots. bill ----- Original Message ----- From: "Timothy Motz" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, December 14, 2003 2:10 PM Subject: Re: calling Dr. Helmholtz... > Okay, I'll admit that I'm too lazy to try the experiment myself. I'll > take everyone's word for it. But what, then, is the effect of the > lattice-like rose on the sound of a lute? Is it simply a combination > of the areas of all of the openings, or is more happening? Does > something different happen when you have a very complex rose pattern > from a simple one with bigger openings? > > I would think that all of the free edges of the rose pattern must > vibrate to add their own layer to the sound. Sort of like the F-holes > on a violin. And the wood of the rose pattern is thinner than the rest > of the soundboard, so it's resonant frequency must be different. But > then, I'm just barely following the explanation of the Helmholtz > effect. I was a Humanities major, so I'm hoping that Dr. Science can > explain it in terms I can understand :-) > > > Tim Motz > > > On Sunday, December 14, 2003, at 10:57 AM, Leonard Williams wrote: > > > Dear Dr. Helmholtz: > > I tried the experiment with an empty 12 oz. bottle. Using my > > Korg tuner I found that I was able to > > alter the pitch from an f# down to an e, even an eb. The higher pitch > > came with the completely open bottle > > neck; to get the lower pitch I placed my finger across the far side > > of the opening from where I was > > blowing. The pitch change was certainly noticeable without using the > > meter for a more precise analysis. > > Howard--the room did not move much, but I got the distinct > > impression that the lights were dimming! > > > > Leonard Williams > > [] > > (_) > > ~ > > > > ----- Original Message ----- > > > > Subject: Re: calling Dr. Helmholtz... > > > > > >> BobClair wrote: > >> > >>> Try this at home and report back. Take a wine or beer bottle. Fill > >>> it 2/3 full > >>> with water. (The change in pitch for a given change in area is > >>> bigger when the > >>> volume is smaller - patially filling it with water makes the effect > >>> easier to > >>> see (hear) but if you think this makes the results suspect leave the > >>> bottle > >>> empty). Blow across the bottle, note the pitch. Now cover half the > >>> opening > >>> with a > >>> finger. Try it again (it may take a bit of practice to get the > >>> note). Did the > >>> pitch go up or down? > >> > > > > > >
