This paper presents a new method for calculating the velocity potential in the nearfield of a circular concave piston source in an infinite plane baffle for both the case where the vibration is normal to the piston surface and where it is parallel to the axis. The solution is given in the form of an infinite series of spherical surface harmonics in the spherical coordinate system, taking the origin at the center of curvature. The theoretical framework has the advantage that it includes neither approximations nor numerical integrations.
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Hasegawa et al. (1986) studied this question.