Acoustic Propagation in Flaring, Axisymmetric Horns: I. A New Family of Unidimensional Solutions

A curvilinear-unidimensional-horn-with-flare equation (CH) is derived based upon the assumption that there exists a family of time-invariant equipotential surfaces normal to the profile and the axis of an axisymmetric horn. The formulation is independent of the choice of equipotential surfaces geometry, and takes into account the local changes in horn flare. Two particular choices are presented: spherical surfaces (leading to the spherical-wave horn equation, SH) and oblate ellipsoidal ones (leading to the OH equation). The particularization of SH and OH is presented for an exponential, a catenoidal and a Bessel horn. The application of this new approximated horn equation to a particular case and its comparison with the exact solution is dealt with in a parallel article.