Comparing the end correction of a spherically baffled piston to infinitely baffled and unbaffled circular radiators (L)

Models of acoustical systems commonly employ end corrections to represent the radiation impedance of a vibrating element. Although several analytic solutions appear in the literature, the end corrections of an infinitely baffled circular piston and an unbaffled semi-infinite circular pipe remain popular in modeling applications. This Letter compares the end correction of these two configurations to that of a radially vibrating cap on a sphere. The results show that the spherically baffled end correction, when expressed as a function of spherical-cap radius, falls between these two extremal boundary conditions.