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 2 1 r type. The Coulomb field in electrostatics and the acoustical pressure field are important exa mples in an isotropic indefinite space. In this pap er we show that in these cases the field produced by a linear sou ce 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 belo ngs. Since the equivalence is true already at the infinitesima l level, many interesting consequences and applicat ions can be derived. Key-Words: Acoustical Field, Isotropic sources, Linear and cur ved sources, Vectorial and Central Field.