Contribution of wood to a bass's sound
 

Fellow KSB folks,

I've read on this site and others that the choice of wood is important to the sound of a bass. Two questions:
1. If you were to pull out the pups from your bass and hold it over the strings so that the pups are not anchored to the body in any way, would there be a difference in sound? I've tried this with a cheapo bass and didn't notice a huge difference, at least subjectively. Perhaps I wasn't fully in tune with the subtleties of the sound.

2. How do the vibrations of the string get transmitted to the body and then to the pups? Of course, the strings are anchored at the nut and saddles, and if the impedance mismatch is not too great it can be transmitted to the wood. But then how do those vibrations affect the output from the pups? Do they vibrate the pups?

Note that I am not a luthier and am not questioning the influence of the wood on the sound. I just want to understand how it happens.