There's a lot of info out there, and a lot we don't yet know. It's most likely a problem that will never be 'solved' completely.
You can download a free copy of 'Acoustics for Violin and Guitar Makers' by Eric Jansson from:
http://www.speech.kth.se/music/acviguit4/
Get part1.pdf through part9.pdf; the seperate chapters of the book. He mostly concentrates on classical guitars, but the basic info applies just as well to steel strings. Some of the studies he cites are old, and we've learned a lot since then, but it's a good start.
After that, keep your eye out for books on acoustics. "Fundamentals of Musical Acoustics', by Arthur Benade, is good, and less mathematical than some. It's out in a Dover edition, so it's not too expensive. If you like partial differential equations, then try 'The Physics of Musical Instruments' by Fletcher and Rossing, from Springer-Verlag press.
Get in touch with Tim White (tpwhiteco@aol.com is the last e-mail addy I have for him) and get the reprint of the 'Journal of Guitar Acoustics'. Th
e quality of the articles is variable, but there's a lot of good info in there. Again, it's a bit dated: it came out in the '70s.
One more modern paper that has a lot to say is Howard Wright's thesis, from 1996 iirc, 'The Acoustics and Pschycoacoustics of the Guitar'. Go to the University of Wales Cardiff web site to download that.
By the time you've worked your way through those, and a few of the papers they cite, you'll be in good shape for starters. There's a ton of stuff around, but it can be hard to get hold of.
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![[xx(]](./images/smilies/smiley11.gif "Dead")
and I learned a new word today that I though fit guitar making and Alan's above quoted statement very well: