Damping of Normal Modes by Small Absorptive Areas: Exact Solution of a Simplified Case

Abstract

The method previously developed for analyzing the diffraction of plane waves striking an absorbing strip in an infinite plane wall is applied to the corresponding problem in a finite enclosure. A particular case is selected such that component waves, which in the general case are summed to form a resultant wave, may be studied individually as isolated normal modes. A semi-cylindrical room is employed; its concave wall tends to “focus” sound upon the center of the opposite diametric wall on which the absorbing panel is centered. If the wave equation is set up in elliptic cylinder coordinates with the edges of the panel as foci, the boundary conditions are readily satisfied. The theory is strictly applicable to a semi-elliptical room only, but holds well in the semi-cylinder for strip widths up to one-third the diameter. The experimental enclosure has a 35-cm radius, a vertical “height” of 10 cm, and is constructed with highly reflective metal surfaces. The selective damping of various normal modes is investigated for strip widths varying from 5 to 25 cm, and over a wide range of normal acoustic impedances. The results substantiate the prediction that the effective absorption coefficient goes through a maximum when the ratio of strip width to wave-length is, for most modes, of the order of one-half.