On the parametric model of point directional source. (Q2718118)

The author establishes the expression for the potential of the sound pressure due to a point directional source NEWLINE\[NEWLINE \psi \left( r,\theta ,\varphi \right) =\sum_{n=0}^\infty \sum_{m=-n}^nC_{nm}h_n^{(1)}\left( kr\right) P_n^{\left| m\right| }\left( \cos \theta \right) \exp \left( im\varphi \right) , NEWLINE\]NEWLINE (where \(h_n^{(1)}\) are spherical Bessel functions of the third kind and \(P_n^{\left| m\right| }\) are the associated Legendre functions) and proves that under suitable conditions the real sources with arbitrary spatial extend may be replaced by an equivalent point directional source