If f is a scalar function of one scalar variable, we know that f (z ± ct) are solutions of the one-dimensional wave equation.

(a) Show that f (r ± ct) / r are solutions of the three-dimensional wave equation in spherical coordinates.
(b) Show that f (ρ ± ct) / √ρ are solutions of the two-dimensional wave equation in cylindrical coordinates when ρ is sufficiently large. Make a precise definition of “sufficiently large”.