Multimodal radiation impedance of a waveguide with arbitrary cross-sectional shape terminated in an infinite baffle

Simulations of waveguide acoustics require a description of the boundary condition at the open end. For problems involving higher order transverse modes, it is often described by a multimodal radiation impedance matrix. Expressions for the computation of this matrix for an infinite flange condition are available only for circular and rectangular cross-sectional shapes. Thus, a general expression valid for arbitrary cross-sectional shapes is of interest. Such an expression is proposed, validated against known cases, and applied to an arbitrary cross-section shape. The solution is shown to be computationally efficient.