Because the wave equation is linear, the sum of any number of solutions is also a solution. It is therefore possible to look for a basis for the solution set, and express any solution as a (possibly infinite) linear combination of elements of the basis. A convenient choice for the form of the basis elements is as a product of functions, each of which depends on just one of the coordinates. Choosing a cylindrical coordinate system for symmetry, we find solutions, called modes, of the form:
,
where is the th order Bessel function (of first kind), is its th root, is the radius of the drum head, and are arbitrary constants depending on n and k. In fact the general solution can be expressed as an infinite sum of such functions:
.