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## 12.6. Radiation from a spherical cap in a sphere

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 [2] 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 $MathML$ such that the velocity distribution is described by

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