Absorption cross section of absorber cylinders

Abstract

The paper covers derivation and calculation of absorption and scattering cross sections of three types of cylinders made out of porous absorber material. These types are, respectively, (a) completely bulk reacting (homogeneous and isotropic), (b) axially locally reacting but bulk reacting about the circumference (rigid partitions inserted normal to the cylinder's axis), and (c) locally reacting in all directions. The sound field may be either plane waves with oblique incidence or diffuse sound fields. The characteristic data used for the absorber materials, propagation constant and wave impedance, are in the form of simple approximations taken from a model theory of fibrous absorbers for low frequencies, with experimental data being used at medium and high frequencies. A formulation of the scattered sound field in series of Bessel function is used. The numerical results show the influence of the frequency, the diameter, the materials' flow resistance and the angle of incidence. Maps are plotted of lines of constant absorption cross-sections for the different types of cylinders and sound fields, revealing the dependence upon these parameters. Acoustical phenomena of the sound absorption by absorber cylinders are discussed, such as resonance scattering, surface waves, frequency ranges with small angular dependence and parameter combinations with only small frequency dependence of the absorption. Such cylinders would be appropriate as calibration objects in round robin tests of sound absorption measurement in reverberant rooms.