The influence of an isolated acoustic resonator with a cross-shaped slit on sound absorption/Vienetinio kryžiaus formos akustinio rezonatoriaus tūrio kitimo įtaka garso absorbcijai
Abstract
The paper deals with the dependence of the sound absorption of an isolated acoustic resonator with a cross-shaped slit between the planes. A theoretical sound absorption calculation method employing the radiation impedance and the directivity diagram. Formulas were derived that enable to calculate both real and imaginary parts of the radiation impedance of the resonator, the radiation directivity diagram, the volume impedance and the impedance of the slit, in which the added air masses both inside and outside the slit have been assessed.
In the calculation of the resonator parameters, the elasticity of the entire air volume and the fluctuating air mass were set apart. The elasticity of air is determined by the air volume and height, while the fluctuating air mass is determined by the air in the hole and the added air mass characterised by the radiation impedance. When the slit is wide, the added air mass is little dependent on frequency. When the air elasticity is equal to the fluctuating air mass, a resonance takes place. The influence of this volume on the resonator's sound absorption and the impedances has been evaluated by calculations.
When the volume increases along with the increase in the height of the resonator, the real parts of the impedance decrease uniformly up to 160 Hz. From this frequency, resonances start, while their repetition becomes more and more dense. When the volume increases along with the increase in the width of the resonator, the real parts of the impedance decrease uniformly as the frequency becomes higher. However, in this case the resonance frequency becomes lower with the increase in volume, while their amplitudes grow.
The imaginary part of the impedance characterises the reradiation energy, which is equal to zero at the time of the resonance.
When the volume of the resonator increases with the increase of its height, the imaginary parts of the impedance are sharply reduced to 160 Hz. Afterwards repetitive resonances take place, with their frequencies becoming denser. When the volume increases with the increase in area, the resonant frequencies start from lower frequency. In both cases the increase in volume has little influence on the character of change of the impedance imaginary part.
Two possible cases of change in volume were chosen in the calculations: (a) the volume increase along with the increase in height. The height was equal to 60, 180 and 240 cm, while the volume to 2.6, 7.77 and 10.3 m^{3}respectively. The area of the resonator was constant and equal to 2.4×1.8 = 4.32 m^{2}; (b) the volume increase along with the increase in area, with the constant height of 60 cm. The area was changed from 4.2×3 m = 12.6 m to 4.8×3.6 = 17.28 m^{2}, while their volumes were equal to 7.77 m^{3} and 10.3 m^{3} respectively. In all cases the width of the slit was taken as 30 cm.
When the height of the resonator is increased and its area is constant, there are no marked changes in the sound absorption. When the height of the resonator is 60 cm, the maximum absorption of 2 m^{2} is reached at 35 Hz. As the height increases, the absorption maximum is 2 m^{2} and is observed at very low frequencies. Resonances become apparent in the frequency range from 70 Hz to 300 Hz, at which there is a reduction in the sound absorption.
When the volume grows with the increase in the resonator area, the sound absorption is much larger than in the first case. When the area is 7.77 m^{2} and 10.3 m^{2} respectively, the absorption maximum is at 17–20 Hz and equals 2.9 nr and 3.4 m^{2} respectively, when in the first case this area was 2 m^{2} only. As the frequency increases, the absorption gradually diminishes and no resonant phenomena are observed.
Two types of resonators were chosen for the investigations in natural conditions: with one cross-shaped slit and with two cross-shaped slits. This was done in order to determine the effect of increase in the slit number and slit area on absorption when both area and volume of the resonators are constant. In both cases, the resonator height H was taken as 60 cm and 180 cm. The resonators were made of wood shaving slabs 18 mm thick.
When the small volume of the resonator is small (2.6 m^{3}), the reverberation time depends on the number of slits only at the medium and high frequencies, whereas the increase of the volume to 7.8 m^{3} causes a prolongation of the reverberation time by as much as 0.2–0.7 s. Thus, the reverberation time reaches 1 s at 800 Hz. When the resonator has two cross-shaped slits, its reverberation time is reduced, particularly in the frequency range of 125–1000 Hz. When the volume is increased from 2.6 to 7.8 m^{3}, the reverberation time is prolonged more in the case when the resonator has one slit.
The sound absorption coefficients and the sound absorption were calculated on the basis of the measured reverberation time. At the small volume of the resonator and two slits, the absorption coefficient is reduced and the frequency of its maximum value shifts from 315 Hz to 200 Hz. The situation changes when volume becomes larger: the values of the absorption coefficient increase from 0.25 to 0.4 as the number of slits is increased. This phenomenon may be explained by the fact that different sound energy is radiated to the environment by a resonator with a different number of slits.
First Published Online: 26 Jul 2012
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