A plane-wave mode feeds an axisymmetric horn radiating from an infinite baffle towards an open half space. The radius of the feeding waveguide is assumed to be fixed, as well as the depth of the horn and the size of the hole where the horn is attached to the baffle. By varying the curvature of the initially conical surface of the horn, its directivity and impedance can be changed.
This model shows how to apply boundary shape optimization to an axisymmetric horn. For the sake of simplicity, the far-field sound pressure level is maximized for a single frequency and in a single direction. The focus is on the optimization procedure, which involves parametrization of the geometry, choice of objective function and optimization solver settings.
The results from this analysis shows that by changing the shape of the horn within the limits of the selected parametrization, the on-axis sound pressure level can be raised by about 1 dB compared to the simple cone. The optimal shape with respect to on-axis SPL however leads to deep undesirable minima in other directions.