Arching guitar backs and their function

[Jacob Porter]

Okay, I'm currently on my third build and had a question posed to me to which I had no answer. (And am not having much luck finding an answer in the library, but I know must be there.) So, maybe some greater minds would like to chime in?

Here's the question: What, if any, is the acoustic function of arching the back of a guitar, and how is this different from a totally flat back? (Aside from aesthetic reasons.) Does this change with the severity of the arch? (Say between a Smallman style build and a more typical Spanish style build?)

Cheers, Jacob

[Mario Proulx]

The back's radius/arching stiffens it, and yes, varying the amount does change how the back responds.

[Michael Lewis]

Resonant frequency rises as the stiffness increases. To make a flat plate stiffer you need to use thicker material, like bigger braces and or thicker back. By arching the back plate you get the stiffness but with less weight than the flat counter part.

[Jacob Porter]

Thank you Mario and Michael. That's what I was thinking, just wanted to be sure I had it right. Is there a particular resonant frequency that I should be shooting for with the back stiffness? I ask that, but realize that it's probably dependent upon other variables in the guitar, style of build, and builder's philosophy...

Again, thank you for the insight.

Jacob

[Jeff Highland]

Some brace their back stiffly enough that it does not couple with the top.
Others look to make it a certain number of semitones above the top frequency 1 for Caruth, 4 for Gore.
I am looking for 4 myself, and tuning to that by shaving down the lower bout brace after the box is finished complete with bridge and strings.

[Jacob Porter]

Thank you Jeff. When I get my current build strung up I'll see what I'm close to. Right now I'm putting finish on it and the bridge is not yet in place. That being said, tapping on both sides gives me close to 1/2 step difference right now (which I think is one semitone across the pond.) I'll tap again when I complete it.