On March 24, Yanic posted a contest question concerning the physics and mathematics of drumheads.
The rim of a drum head is fixed to the drum shell and tightened to modify the tuning of the drum. For physics discussions, the drum head can be approximated as a circular membrane with fixed boundaries. The mathematics of the vibrational modes of circular membranes can be explained using particular types of functions. What are these functions called?
The answer to the question is Bessel. Refer to the links below for animations
of vibrational modes and documentation on Bessel functions.