Length correction of 2D discontinuities or perforations at large wavelengths and for linear acoustics

This work focuses on the length correction due to radiation effect of a duct discontinuity or at the surface of a perforated plate in the linear acoustic domain and at large wavelengths. Two results are obtained from the comparison of models used in the literature for different geometries of duct discontinuities or perforations. First, the mode-coupling at the discontinuity between two ducts or a perforated plate and air is negligible for low frequencies. Second, all consistent models of the length correction proposed so far, for any geometries except slit-like, are similar when plotted as a function of the square root of the perforation rate (the ratio of the duct cross-section areas for ducts). These two results imply the effect of the thickness of the ducts or the perforated plate can be accounted for in the length correction expression independently from other geometric variables. A single approximate formulation for all geometries of perforations or duct discontinuities, except slit-like geometries, is proposed for practical uses.