Luthier is a name originally for lute makers, but now refers to people who make guitars, mandolins, etc. Before luthiers assemble their instruments, they test the quality of the individual pieces (specifically the soundboard and the backboard) by a method known as "tap tuning". Essentially, they hold the piece without dampening it, tap it, and check the pitch with a tuner.
There's not really one right answer for what note each piece should produce. Soundboards and backboards that produce lower notes will give the instrument better bass response, and ones that tap higher notes will produce a brighter-sounding instrument. Although, luthiers may have certain target notes for each of the pieces, so that their instruments produce a consistent tone. Also, a piece that produces a more sustained and clearer note is an indication that it's been properly carved.
The wood's thickness affects the pitch, although not all woods will produce the same note when carved to the same thickness. Harder woods will tune higher than softer woods.
Tap tuning can even be used to tune drums for maximum loudness. This is done by removing the heads and tapping the shell to find the resonant pitch. Then the heads are tuned to that note.
