That gets REALLY complicated! You'll just have to experiment!
The shape and materials for a (acoustic) guitar or violin were developed empirically over a long period of time. As far as I know, with modern science and computers, we have not come up with any new-better designs.
From the approximate wavelength, I'd say your box is going to resonate around 500Hz or 1kHz... I don't know if a "closed box" resonates at 1/2 wavelength or a full-wavelength.
(1.5ish cm thick)
cm or mm? Again, most wood instruments are quite thin (with the exception of woodwinds & pianos where the resonance of the wood itself isn't that important).