Consider the wave equation
where v is the speed of the wave. In cylindrical coordinates Eric Weisstein's World of Math with angular and azimuthal symmetry, the Laplacian Eric Weisstein's World of Math simplifies and the wave equation
The solutions are Bessel functions. For large r, however, they can be approximated as
Note that, unlike the plane and spherical waves, cylindrical waves cannot assume an arbitrary functional form.
Plane Wave, Spherical Wave, Wave
