The objective of the paper is to present a formulation for the evaluation of the power spectral density of the acoustic pressure at any given point in the field in terms of the power spectral density of the transpiration velocity: this is a quantity defined in terms of the vorticity and is closely related to the equivalent source concept introduced by Lighthill 5. Specifically, the formulation used allows one to obtain, in the frequency domain (Fourier transform) a matrix relationship between the transpiration velocity and the pressure at a given point in the irrotational region. The approach used here is based upon formulation introduced for aerodynamics in Ref. 9, and refined in
Refs. 12 and 11. The commonality between aerodynamics and aeroacoustics is addressed in Ref. 10 (which provides a synthesis of all the preceding work), and is exploited here. Although applications to aeroacoustics implicitly imply compressibility, for the sake of clarity in the main body of the paper the formulation is presented for an incompressible fluid. Numerical results are also included, simply to illustrate how the formulation may be usefully employed to evaluate the pressure in the field.