Numerical Investigations of a Helmholtz Equation with Unique Solution for all Wavenumbers applied to Acoustic Radiation Antoine LAVIE a and Alexandre LEBLANC b a Univ Lille Nord de France, UArtois, LGCgE, Technoparc Fuura, 62400 Béthune, FRANCE, e-mail: antoine.lavie@univ-artois.fr b Institut Langevin, ESPCI Paris Tech, CNRS UMR 7587, Laboratoire Ondes et Acoustique, 10 rue Vauquelin, 75231 Paris Cedex 05, FRANCE ABSTRACT The acoustic exterior Neumann problem is solved using a new numerical process based upon the boundary element method and able to eliminate effects of irregular frequencies (natural frequencies of the associated interior Dirichlet problem). This technique is performed as follows: (i) two computations are done around the characteristic frequency, decreased and increased by a small imaginary part; (ii) average between pressures at these two frequencies ensures unique solution for all wave numbers. Depending on the time dependence, one of these frequencies matches with an amplified oscillation and the other with a damped oscillation. This method is numerically tested for an axisymmetric cylinder in the case of the point-source check at some irregular frequencies. Then, the study is extended to the sphere. For these geometries, an estimation of the magnitude of the imaginary part is given. Finally, an application to a three dimensional cat's eye radiation test is carried out in an extensive frequency range. This work highlights the ease and efficiency of the technique under consideration as computations have shown the ability of the average process to remove the irregular frequencies effects of the Helmholtz integral equation.