Anders Buen

Just found alink to a open access book chapter from Springer on wood and moisture, for the "nerds" among you: https://link.springer.com/chapter/10.1007/978-3-030-81315-4_7

I wonder if the "ring modes" are able to build up around a violin with the sharp corners where the plates meet the ribs. I am sure there is energy going there, but in a tube this is supposed to be a travelling compression wave, the ring frequency is the first "ring mode" stretching the tube and compressing it successively. Above the ring frequency a pipe and a tube behve more like a flat plate with less or no stretching, mostly bending. We see clear effects of the ring frequency for tubular ventilation pipes. The sound insulation of a pipe, or circular tube, is way better than for square, or rectangular, ventilation tubes below the ring frequency. The rectangular ones leak more low frequency noise and tend to rumble more, equal to the sound we hear by tapping them. The stiffer circular tubes sound more mid and high frequency.

I rather think this preference is related to their greater stability to humidity cycles than the higher arched instruments, rather than the sound. Maybe it is a combination. Other makers made shallow arches too, like Bergonzi and Guadagnini, I believe. I haven't studied this in detail, though. The guitar is kind of a strange instrument, with the low bridge and sideways excitation. Seen against the light there are some tension arch there. And lots of bars under the plates.

I do not think the stress is the main cause of increased sound level here. It is just a better contact between the tuning fork and the wood. The resonance of the plate increases, so maybe a modal overlap fitting happens there between the fork and the bent wooden plate. Tension is not the cause of the sound level increse per se. The thickness, surface mass and plate size influences sound levels. Normally curvature of plate supresses the viobration energy into stretching of the plates and thus giving the opposite effect, a reduction of sound producing vibrations as some of the vibrating energy goes into non sound producing stretching energy.

I think the idea with the inflection lines are sound.

Like! :-)

I feel no need to. If you go to the textbooks in acoustics can you find support for your ideas? Will you find anything on "Shape and stress condition are responsible for the acoustic outcome"?

No, not alone!

A blink of an eye then? :-)

I think Colins point was to be able to track the free plate modes (violin body with very weak ribs) gradually into the assembled violin range and somwhat beyond (2-3 times normal stiffness, or so). I think his mode tracing curves are rather smooth. I guess he must have done quite a few runs of that model. Not 10^6, likely more than 10 and less than a 100. The rib model is parametric I think. Just one number to change and then re-run. Chat with his wife for a while, save the run data and redo.

You will have to figure out yourself. I had an insturment where i reduced the opening of the f-holes. It has a substancial effect. If I told you the percent, you would have problems figuring out how much that would be in area. Cut and see. :-)

I already know the content.

I have seen a version of this before. So I won't this time!

If you like to have a higher A0 frequency, you can increase the f-hole area and/or reduce the plate thicknesses near the edges of the f-holes. Rounding the edges may also have a slight effect in that direction.

The arch is likely to come from empirical means. Some stringed musical instruments are made of natural cavities from seed containers, or the like. Some are simply hollowed out. By the answers here I can see that you are likely to have the "answers to all this" yourself, and do not pay attention to what I have written. Moderately curved plates work better because they can be made thinner and the design, if it is of the right type, will resist and survive humidity cycling better than the less good designs, like too high arch and too fast changes of the curves. Arch suppress the low frequency response and does little to the highs. Maybe a balance there is achieved in better instruments. It is perfectly possible to make a useless instrument with "right arch", but other important factors incorrect. Arching itself does not make the sound. Violin sound and instrument stability is a balancing act of lots of factors.