Infinitesimal equivalence between linear and curved sources in Newtonian fields: applications to acoustics

The equivalence between the vectorial field produced by a scalar linear source and the one produced by a scalar curved source is proved in the centre of the circumference which contains the curved source, if this circumference is tangent to the line of the linear source. Since this equivalence is true already at the infinitesimal level, many consequences come out. Applications of this result can be highlighted in electrostatics and in acoustics, since these fields fulfil the above requirement. In particular, in acoustics, the problem of isolated receiversalong a high velocity rail line can be approached by means of studying the equivalent curved source.