On Radiation from Elliptic-Cylinder Geometries

Acoustic radiation from cylinders with elliptical cross-section can be solved analytically by employing Mathieu functions. The analytic expressions obtained for such a simple convex boundary with different surface curvatures show a spatially varying specific acoustic impedances. This paper provides a physical interpretation of this fact, which applies to radiation from general convex boundaries as well. Its implication on the solution of radiation and scattering problems using a multipole expansion in elliptic-cylinder coordinates are discussed. Moreover, simple analytical expressions for the radiated sound power and the local modal acoustic impedance are derived. The necessary formulas for Mathieu functions are presented together with a detailed description of their efficient numerical generation.