In reality, loudspeakers do not have vanishingly small diaphragms, and at high frequencies the size and shape of the radiator strongly influences the resulting sound field.
The spherical cap 
represents a curved finite diaphragm which follows the contour of the sphere. This makes it easier to analyze than a flat piston, which we shall consider in Section 12.8
. The spherical cap shown in Fig. 12.16
is set in a rigid sphere of radius R
and moves with an axial velocity
such that the velocity distribution is described by