Effective densities and resistivities for acoustic propagation in narrow tubes

A finite element method is used to determine the velocity profiles and boundary shear forces for sound propagation in narrow tubes of various sections. The slit, circle, triangle, square, rectangle and hexagon sections are considered and the results are shown to depend upon a dimensionless frequency parameter √ {ϱω}/{η overliner}. From the profiles, the effective density and resistivity based on the mean velocity are given. These can be used to obtain data on attenuation and absorption.