Influence of Periodically Varying Slit Widths on Sound Absorption by a Slit Pore Medium

A simple pore microstructure of parallel, identical, and inclined smooth-walled slits in a rigid solid, for which prediction of its geometrical and acoustic properties is straightforward, can yield useful sound absorption. This microstructure should be relatively amenable to 3D printing. Discrepancies between measurements and predictions of normal incidence sound absorption spectra of 3D printed vertical and slanted slit pore samples have been attributed to the rough surfaces of the slit walls and uneven slit cross-sections perpendicular to the printing direction. Theories of the influence of (a) sinusoidal walls and (b) periodically varying uniform slit widths on the normal incidence absorption spectra of a slit pore medium are outlined. Although the slit wall surface and geometrical imperfections due to 3D printing differ from these idealizations, predictions assuming the ideal forms of roughness confirm that pore-wall roughness could account for differences between predictions and data. Pore-wall roughness is predicted to increase both flow resistivity and tortuosity, thereby increasing the low-frequency sound absorption of thin hard-backed layers. The extent to which sinusoidal slit walls or periodically varying uniform slit widths could improve the sound absorption of a low flow resistivity hard-backed layer containing identical vertical slits is explored.