How to drive a magnet with a coil from an amplifier (to test acoustic guitar resonant frequencies)?
What you propose is unlikely to yield good results.

First, the wood used to make a guitar doesn't have resonance by itself.  A final piece of wood of the right thickness, moisture content, finish, and other factors, has the relevant acoustic properties.  Every time you work the wood, these will change.  Measuring a hunk of wood before working it will tell you very little.

Even the finished piece of wood alone will have very different properties than the same piece after it is part of the guitar.  Being glued to something else along its edge is going to significantly change the acoustic properties.

Second, adding a magnet to the wood is adding mass.  That will change the resonant properties.

You can still do take some measurements that might be relevant to building a guitar.  One way would be to measure the impulse response at different places.  This is basically giving it as short of a "tap" as possible, then recording the resulting sound.  The Fourier transform of that is a spectrum that should tell you something relevant.

You should probably sample at around 100 kHz.  If you care about frequencies up to 20 kHz, then the absolute minimum sample rate is 40 kHz.  However, if the wood can produce sounds higher than what you care about, then those frequencies would cause aliasing.  To avoid that, sample high enough so that you can use a analog filter that doesn't attenuate the frequency you care about, but does attenuate a reasonable amount at half the sample rate.

For example, let's say you care about frequencies up to 20 kHz.  If you sample at 100 kHz, then your analog filter has room between 20 kHz and 50 kHz (half the sample rate) to kick in.

There is a lot more to this method than can be reasonably described here.