Well this isn't exactly a banjo. Actually it's a banjo-uke that I picked up at a garage sale many years ago and did some work to. Several of the hooks were missing so I made some to match the originals. Also the thing came with those useless tapered pegs so I filled them in and put four tuners that I took off the Hofner Verithin. I still have the other two in case I ever want to restore the Verithin to original, nonfunctional condition.
Here is our friend the tympanic membrane coupled to some strings. Notice the position of the bridge, which is not in the center. Chladni you think, here he goes again about Chladni. You are right.
The point here is that the position of the excitation matters a lot. What difference does that make in a microphone? Doesn't the whole surface get excited at once? The answer is not in the case of the off axis sound: an off axis wavefront reaches the nearest portion of the membrane first. A sound wave is long until you get to the higher frequencies where the waves can be less than an inch (2.54 cm), which means that the crest of the wave can hit one part of the membrane while the trough reaches the other. This isn't very good because it can get one portion of the membrane to move away from the backplate while the other portion moves toward it, cancelling the sound, and creating a notch function. A couple of posts ago there is a link to Olsen's depiction of exactly that. Here it is again.
Here is a link to a frequency to wavelength converter.
I like the banjo sound up to a point. It certainly has a honky character. That honky character may be in part due to the standing waves on the head. If course guitars, violins etc. all have standing waves too, so why don't they sound like banjos?