The sound absorption properties of a cross-shaped isolated acoustic resonator

The paper examines a new acoustic construction which differs from the classical Helmholtz resonator. The proposed acoustic resonator consists of massive plates with a rectangular-shaped slit of varied width. Sound-absorbing materials are not used in such a resonator, and the effect of absorption is achieved due to the resonance qualities of such a construction.
In a theoretical model of such construction, both the main resonance and the overtones, i.e. the odd harmonics, the impedance of the slit itself, the impedances of added air masses outside and inside the slit, the impedance of the resonator air volume, and the radiation impedance are taken into account.
On the basis of the formulas obtained, the change in the sound absorption depending on the slit width and the distance between the slit and the rigid surface is computed. It has been established that the absorption has a resonant nature and it is enhanced with the increase in the slit width. When the slit width is 65 cm, the absorption area reaches almost 4 m$^2$ at 60 Hz. The volume of the resonator is significant. When the resonator's height is increased to 150 cm and the slit width is 30 cm, the area of absorption is as large as 3.5 m$^2$ at 35 Hz.
The dependence of the real and imaginary parts of the slit impedance and the radiation impedance on the slit width is computed, as well as the dependence of the real and imaginary parts of the resonator volume impedance on the slit width under constant distance to the rigid surface of the ceiling.