Sound absorption by a large-size isolated acoustic resonator with a cylindrical cavity

Abstract

An acoustical structure consisting of a large-scale isolated resonator with a large-diameter cylindrical cavity may be used. This resonator differs essentially from the classical Helmholtz resonator whose cavity is only several millimeters in diameter and lined with a sound-absorbing material. Formulas are presented with which the impedance of the cavity, the impedances both inside and outside the cavity, and the impedance of the volume of the resonator are calculated. A radiation directivity pattern expressed by Bessel’s function is used to find the radiation impedance. Calculations show that the sound energy is absorbed by resonators made of sound-reflecting materials. The larger the cavity diameter is, the larger the sound absorption. Absorption is of a resonant character with the resonant frequency at 60 Hz. A resonator measuring 200×200 cm, with the cavity diameter 50 cm and the distance to the rigid surface being 30 cm, absorbs 3.5 m2 of sound energy at the resonant frequency. At very low frequencies, changes in the imaginary parts of both cavity and radiation impedances occur along with the increase in the cavity diameter and frequency.