Equivalence between Linear and Curved Sources in Newtonian Fields: Acoustics Applications

An infinitesimal scalar source of a vectorial field produces a central field. If the density of energy must be conserved, the dependence from the distance must be of 1/r(2) type. The Coulomb field in electrostatics and the acoustical pressure field are important examples in an isotropic indefinite space. In this paper we show that in these cases the field produced by a linear source and the one produced by a circumference arc are equal in the center of the circumference, if this one is tangent to the line to which the linear source belongs. Since the equivalence is true already at the infinitesimal level, many interesting consequences and applications can be derived.