A couple of things:
As has been said, you can't get an answer that's more exact than your least accurate measurement. It's worth putting some effort into improving that first. For most of us, that's going to be thickness.
I saw a paper once that claimed there was a systematic difference in measurements of stiffness depending on the way the piece was surfaced. It makes some sense: the stress is highest on the surface, and if that's fuzzy, say, from sanding with coarse paper, you might in effect be sacrificing some thickness.
I use vibration measurements to find wood properties. It has been pointed out that the usual equations that calculate the Young's modulus (E) based on the size and mass of the piece and the resonant frequencies, are simplifications. For example, they may assume that the shear modulus is zero, or infinite, either of which would give a somewhat different result when solving for E. There are more complex models that can give answers that are closer to 'correct', but they require more measurements of other sorts of resonances and more calculation.
In the end, the 'simple' measurement and 'basic' equation are supposed to get you to within 10% or so of the 'real' value. That implies a thickness change of about 3% to maintain the same stiffness. That's about +/- .004" on a top that's .125" thick. Do any of us actually measure thickness that accurately and maintain it? Do you know how much wood you remove on final sanding?
And then there's the variation within each piece. How do you get that without actually chopping the wood up small? If you do how do you make a guitar from it?
And so it goes.
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