Radiation of a pulsating portion of a sphere: application to horn radiation
Résumé
This paper introduces the modelling of the radiation of a sphere, part of which, S0, is pulsating with an uniform velocity while the other remains motionless. Velocity and pressure can be expressed analytically in the space outside the sphere using spherical harmonic decomposition. The radiation impedance can then be deduced, providing a model approximating the radiation of horns, accounting for the curvature of the wavefront. The angular dependence of the radiation impedance is eliminated by averaging on S0 to remain compatible with most of simplified models of horns whose equations depend on a unique space variable. This averaging provides an analytical expression representing the optimal approximation, minimizing the mean square error. Three simple parametric models, which are inexpensive to simulate and approximate this model of impedance with various precisions, are proposed. They are well adapted to real-time applications, such as the simulation of wind instruments. Their parameters are given according to the geometrical characteristics of S0 and the stability is checked. The error introduced by these models is negligible compared to the original due to averaging on S0.