Random Incidence Absorption Coefficient Research Articles

Random incidence sound absorption of micro-perforated panel absorbers backed with parallel-arranged cavities of different depths

This study investigates sound absorption performance of a kind of wideband micro-perforated panel (MPP) absorbers with parallel-arranged backing cavities at different depths in a diffuse field. An analytical prediction model is presented for evaluating the random incidence absorption coefficient of this type of absorbers, and it exhibits excellent agreement with finite element model and experimental measurements. Then, numerical cases were established using this model to investigate the absorption characteristics of this type of absorbers under random incidence, considering the influence of cavity depths and MPP parameters. Results show that the cavity depth and MPP perforation diameter in this absorber are primary influencing parameters controlling the overall sound absorption performance. Cavities at different depths introduce multiple resonant absorption peaks, while the perforation diameter determines matching conditions between the MPP and air impedance, which simultaneously broaden the absorption bandwidth of this MPP absorber. Although individually adjusting the panel thickness and perforation rate has a smaller impact compared to the perforation diameter, the interaction between these two parameters has significant influences across the entire absorption frequency band.

Diffusion equation-based modelling of reverberation chambers for sound absorption measurements

Recent research in reverberation chambers has revealed unacceptably large variations resulting from round-robin tests of the standardized measurements of random-incidence absorption coefficients. These variations have prompted active research activities in architectural acoustics. This study applies a diffusion equation model (DEM) in acoustics of reverberation chambers for random incidence absorption measurements by predicting both reverberant sound energies and energy flows. The DEM is of high computational efficiency when compared with other existing geometrical acoustics and wave-based methods. The DEM modeling of the sound energy flows in a reverberation room further reveals violations of the diffuse field assumption near the boundary area of absorbing sample under test. Due to its computational efficiency and higher order of the reverberant energy prediction of the statistical room-acoustic modeling, this work investigates an estimation approach to the absorption coefficients of the sample under test. The proposed approach estimates the absorption coefficients by pursuing both the DEM simulations and the chamber-based measurements. This paper investigates sound energy flux over varied absorbing degrees of absorber samples in standardized sizes, computational efficiency of the DEM for reverberant energy decays in reverberation chambers, and potential significance applied to random-incident absorption coefficient measurements.

Finite-difference diffusion-equation modeling of reverberation chambers in time-domain

Conventional chamber-based methods of random incidence absorbing coefficients overlook the non-diffused sound field in the room acoustics, which decreases accuracy and may even lead to conflicting results. This work applies the diffusion equation model to room-acoustic simulations of standardized reverberation chambers. The simulations can more efficiently capture the chamber's non-diffuse sound field and energy flows than wave-based simulation models. The diffusion equation represents the governing equation of reverberant sound energy densities within the reverberation chamber which is solved using the finite-difference time-domain method. Its computational efficiency of diffusion equation-based modeling lies in a highly sparse domain meshing condition dictated by the mean-free path length rather than wavelengths and still derives a wideband simulation result. This work also dedicates the effort to reexamine the meshing condition, particularly for standardized finite sizes of sound absorbers for measurements of random incidence absorption coefficients. By comparing the outcomes of simulations with measurement data, an a posteriori absorption coefficient is inversely estimated involving Bayesian parameter estimation.

Modeling of reverberation chambers for sound absorption measurements using a diffusion equation

The sound field in reverberation chambers used for measuring sound absorption coefficients is usually non-diffuse, leading to inaccuracies and disagreements in the results. In this paper, a diffusion equation model is applied to simulating reverberation chambers in order to obtain reverberant energy distributions and sound energy flows of the chamber under investigation in a more efficient way than wave-based simulation models. The computational efficiency of the diffusion equation lies in the fact that the meshing condition of the simulation domain is dictated by the room's mean-free path length (MFPL). Further investigation shows one-twelfth of MFPL as the meshing condition is considered practically sufficient for obtaining random incidence absorption coefficient of standardized sample sizes. With the computational efficiency given by a meshing of up to twelfth MFPL, an inversion calculation of random incident absorption coefficients of highly absorptive materials is possible with a mixed boundary condition [Jing and Xiang, JASA 123, pp. 145–153 (2008)]. Based on analysis of both chamber-based measurements and simulated data, ways to scrutinize measurement results of absorptive materials are investigated.

Go’s and no-go’s towards more correct reverberation room measurements of absorption

Measurements of random-incidence absorption coefficients have been hotly contested since the ASA was founded in 1929. Yes, you read correctly, since 1929! Theories, explanations, myths, and strange interpretations appear, disappear, and reappear over the decades. What is wrong with this method of measurement? This paper discusses some of the methodological difficulties and reasons for discrepancies when comparing results between different reverberation chambers. It also presents possibilities arising from recent developments, such as the isotropy and angle dependence of the sound field incident on the absorber, the multi-exponential model for calculating decay times, and reference absorbers.

An experimental study on acoustical performance of cross rib diffuser

The preset paper proposes a novel acoustic diffuser which we call cross rib diffuser (CRD) and investigates its acoustical performance in rooms experimentally. CRD consists of overlapping two one-dimensional periodic rib diffuser (OPRD) with different structural configurations. CRD can achieve high scattering coefficient with wider frequency band than OPRD. Moreover, unlike other diffusers with high scattering property such as metadiffuser and two-dimensional quadratic diffuser, CRD keeps simple and familiar design of OPRD suitable for use in various architectural spaces. In the paper, we firstly evaluated random-incidence scattering coefficient of CRD using 1/5 scaled reverberation room. Then, random-incidence absorption coefficient was measured in 1/1 reverberation room. Finally, an implementation experiment was conducted to examine applicability of CRD in improving acoustics in small meeting room with small absorption treatments. The results indicated that CRD reduced EDT and reverberation time, and increased D50 more than JND values. Additionally, CRD improved reverberation and speech intelligibility more significantly than OPRD with same installation area.

Calculation of statistical absorption coefficient using ensemble averaged surface normal impedance of material

To predict and control the indoor sound field, it is important to comprehend sound absorption characteristics of building materials. In the previous studies, the authors have proposed an in-situ sound absorption measurement method of materials using ensemble averaging technique, namely EA method. The method yields a simple and efficient in-situ measurement of surface normal impedance of materials at random-incidence. In this paper, the authors calculate the statistical absorption coefficient using the surface normal impedance of material by the EA method to obtain random incidence absorption coefficient. At first, the procedure of calculating the statistical absorption coefficient from the normal impedance by EA method is described. Next, the sound absorption characteristics for five kinds of materials are measured by the EA method and the reverberation room method. Finally, the statistical absorption coefficients are calculated from results obtained by the EA method and are compared with absorption coefficients by the reverberation room method.

Design of a new test chamber to measure the absorption, diffusion, and scattering coefficients

This presentation will describe the design for a new 384 m3 test chamber that will allow the measurement of the random incidence absorption coefficient, according to ISO 354, the scattering coefficient, according to ISO 17497-1, the diffusion coefficient, according to ISO 17497-2 and the normal incidence low frequency absorption coefficient, according to ISO 10534-2. The rev room design incorporates optimal modal dimensional ratios in accordance with (T. Cox, P. D’Antonio & Avis, J. Audio Eng. Soc. Vol. 52, No. 6 (June 2004)), both boundary and hanging panel diffusers to allow satisfactory diffusivity, in collaboration with the research at DTU. Diffusivity will be verified using a reference absorber, consisting of 100 mm porous absorber with a 100 mm cavity. A sufficiently large reflection free volume is provided in the chamber for diffusion coefficient scale model measurements. The diffusion goniometer and 12 m2 absorber samples are rotated in accordance with test. Scattering coefficient measurements are made according the ISO 17497-2 and the correlation method, using correlated polar responses. A steel and concrete lined low frequency impedance tube measuring 600 mm x 600 mm x 5.8 m long and 7 tons will be used to measure absorption from 25 to 250 Hz.

Importance of correlation between reverberation times for calculating the uncertainty of measurements according to ISO 354 and ISO 17497-1

The calculation of measurement uncertainties follows the law of error propagation as described in the Guide to the Expression of Uncertainty in Measurements (GUM). The result can be expressed as a contribution of the variances of the individual input quantities and an additional term related to the correlation between the input quantities. In practical applications, the correlations are usually neglected. This has, e.g., led to the expression included in Annex A of ISO 17497-1 to calculate the precision of the measurement of random-incidence scattering coefficients. To determine whether it is actually justified to neglect the input correlations, this contribution investigates the correlations between the reverberation times used to determine the random-incidence absorption coefficient (ISO 354) and scattering coefficient (ISO 17497-1) in a reverberation chamber. The data used here are taken from measurements in a real-scale and a small-scale reverberation chamber. It is found that for ISO 354 correlations can be neglected. However, for ISO 17497-1, it is important to take correlations into account to obtain the correct measurement uncertainty using error propagation.

An experimental study on the acoustic absorption of sand panels

Potentially sand panels could be used as novel sound absorbing materials that are fire resistant, environmentally friendly, mechanically strong and have good durability. However, the performance of sand panels as sound absorbers has not yet been studied. Results of measurements in a reverberation chamber of the random-incidence absorption coefficients of 13 different sand panel compositions and configurations with air gaps are reported. Also the flow resistivities and bulk densities have been measured. The results prove that sand panels could offer effective and wide-band acoustic absorption. As is the case with conventional sound absorbing materials, adding an air space is found to be the most effective way to widen the absorption bands and improve the overall absorption. Comparisons of the measured sand panel absorption data with predictions of the Delany and Bazley and Voronina models reveal that, while neither model is very accurate, the former gives more accurate predictions especially for sand panels with lower flow resistivity and smaller thickness.

Applicability of locally reacting boundary conditions to porous material layer backed by rigid wall: Wave-based numerical study in non-diffuse sound field with unevenly distributed sound absorbing surfaces

To clarify the applicability of locally reacting boundary conditions in wave-based numerical analyses of sound fields in rooms, we numerically analyzed a non-diffuse sound field in a room with unevenly distributed sound absorbing surfaces and investigated the differences between the extended and local reactions. Each absorbing surface was a porous material layer backed by a rigid wall. Simulations were performed by the fast multipole boundary element method, a highly efficient boundary element method using the fast multipole method. At low frequencies, the extended and local reactions yielded similar reverberation decay curves because of the influence of the room. However, when the random incidence absorption coefficients were small at low frequencies or frequencies were high, the difference was greater than expected from the corresponding Eyring decay lines. We conclude at high frequencies, the locally reacting boundary conditions lead to a longer reverberation time than that expected from the absorption coefficient differences between the extended and local reactions. These differences were similar in sound-pressure-level and sound-intensity-level distributions, and in the oblique incidence absorption coefficient of the absorbing surfaces, but were increased at low frequencies.

Experimental study for improving sound absorption of a composite helical-shaped porous structure using carbon fiber

A composite sound absorption structure constructed with fibrous layer and carbon fibers was proposed and its acoustic performance was experimentally studied. Proposed structure’s sound absorption properties depended on the gap of the air cavity between fibrous layers. To increase the absorption efficiency, carbon fiber was applied between the gaps. The normal incidence sound absorption coefficients and specific acoustic impedance were measured with the two-microphone impedance tube method to determine the effects of the carbon fibers on the acoustic properties. Random incidence absorption coefficients were determined from the measured specific acoustic impedances of the proposed structures. The measured results were compared for various fractions of carbon fibers. Modified wave propagation equations with empirical density equations were suggested to predict the acoustic behavior of the proposed absorbers. After application of the carbon fibers, the composite helical-shaped sound absorber showed better sound absorption efficiency under both normal and random incidence conditions. This suggested that the carbon fibers introduced additional sound dissipation when properly distributed along the gap of the sound absorber.

Improvement of the measurement of the sound absorption using the reverberation chamber method

The random incidence absorption coefficient is measured in a reverberation room according to ISO 354 or ASTM C423-09a. It is known that the inter laboratory accuracy under Reproducibility conditions of these results is still not very well. It is generally assumed that the limited diffusion properties of reverberation rooms, especially with a strongly sound absorbing sample, are the main reason for the bad reproducibility values for the sound absorption between laboratories. Reverberation rooms should be made much more diffuse to reduce the interlaboratory differences. However there are practical limitations in quantifying and improving the diffuse field conditions. The measured sound absorption still seems to be the most sensitive descriptor of the diffuse field conditions. A way to further reduce the inter-laboratory differences is the use of a reference absorber to qualify a room and to calibrate the results of a sound absorption measurement. In the presentation an overview will be given of the research performed and some suggestions for the new version of ISO 354 will be given.

The equivalent incidence angle for porous absorbers backed by a hard surface.

An equivalent incidence angle is defined as the incidence angle at which the oblique incidence absorption coefficient best approximates the random incidence absorption coefficient. Once the equivalent angle is known, the random incidence absorption coefficient can be estimated by a single experiment using a free-field absorption measurement technique with a source at the equivalent angle. This study investigates the equivalent angle for locally and extendedly reacting porous media mainly by a numerical approach: Numerical minimizations of a cost function that is the difference between the oblique incidence absorption coefficient at a specific incidence angle and the random incidence absorption coefficient. The equivalent angle is found to be around 55° under local reaction conditions, and 45° for extendedly reacting porous absorbers. As practical guidelines for measuring absorption coefficients by free-field techniques, a broad incidence angle range can be suggested: 20° ≤ θi ≤ 65° for extended reaction and θi ≤ 65° for locally reacting porous absorbers, if an average difference of 0.05 is allowed.

Converting Sabine absorption coefficients to random incidence absorption coefficients

Absorption coefficients measured by the chamber method are referred to as Sabine absorption coefficients, which sometimes exceed unity due to the finite size of a sample and non-uniform intensity in the reverberation chambers under test. In this study, conversion methods from Sabine absorption coefficients to random incidence absorption coefficients are proposed. The overestimations of the Sabine absorption coefficient are investigated theoretically based on Miki's model for porous absorbers backed by a rigid wall or an air cavity, resulting in conversion factors. Additionally, three optimizations are suggested: An optimization method for the surface impedances for locally reacting absorbers, the flow resistivity for extendedly reacting absorbers, and the flow resistance for fabrics. With four porous type absorbers, the conversion methods are validated. For absorbers backed by a rigid wall, the surface impedance optimization produces the best results, while the flow resistivity optimization also yields reasonable results. The flow resistivity and flow resistance optimization for extendedly reacting absorbers are also found to be successful. However, the theoretical conversion factors based on Miki's model do not guarantee reliable estimations, particularly at frequencies below 250 Hz and beyond 2500 Hz.

Absorption and impedance boundary conditions for phased geometrical-acoustics methods

Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.

The use of multi-microphone measurements of directional and random incidence acoustical coefficients

This paper will review the use of multiple microphones in the measurement of the normal incidence absorption coefficient, ISO 10534-2, the random incidence absorption coefficient, ISO 354, the scattering coefficient, ISO 17497-1 and the diffusion coefficient, ISO 17497-2. Multiple microphones are used to quadruple the plane wave frequency range providing a bandwidth from 63 Hz to 4000 Hz in a single 150 mm square impedance tube. Random incidence measurements are accelerated by simultaneously measuring 12 impulse responses from two speakers and 6 distributed microphones. Scattering coefficient measurements can be very time consuming, due to the fact that at least 72 MLS averages are required per rotating table revolution. By using the dual source and simultaneous 6 microphone measurement technique, measurement times are reduced from 43 minutes to roughly 4 minutes for a 3 sec MLS stimulus. Diffusion coefficient measurements are greatly accelerated by simultaneously measuring 32 scattered impulse responses ...

Diffusivity of diffusers in the reverberation room

The random incidence absorption coefficient is measured in a reverberation room according to the ISO354 or ASTM C423-09. According to these standards, the diffusivity of a reverberation room is usually obtained with panel diffusers. Besides the fundamental problem that a reverberation room with a highly absorptive specimen is not diffuse, these panel diffusers introduce a number of uncertainties like the acoustical effective volume and the total boundary surface of the reverberation room. This might be one of the causes that some laboratories are structurally able to measure absorption coefficients larger than 1, even if the volume of the specimen, edge absorption, and the absorption of the surface covered by the specimen are taken into account. To reduce the difference in measurement results between different laboratories, the possible use of volume diffusers instead of panel diffusers is investigated. The following criteria are investigated to substantiate the hypothesis that volume diffusers lead to better results: (1) Deviation between microphone-source positions. (2) Comparison to maximum relative standard deviation (ASTM). (3) Comparison to theoretical variance. (4) Influence of place of specimen. The investigations have been performed in a 1:10 scale model. The results are presented in this paper.

On the reproducibility of measuring random incidence sound absorption

For over 50 years, the American Society for Testing and Materials (ASTM International) has promulgated a method for the laboratory testing of random-incidence sound absorption coefficients (Test Method C423). This test method falls under the purview of ASTM Committee E33 (Environmental Acoustics). In 1999, the protocols in this test method became significantly more stringent with the goal of improving inter-laboratory “reproducibility” (i.e., quantitative differences among laboratories when testing the same specimen). ASTM calls such an inter-laboratory test a “round robin”; its outcome is an array of computed precision (i.e., uncertainty) values. This paper presents results from several “round robin” evaluations and discusses some possible causes for the range of values. If time permits, the fine points of the test protocols in C423 will be described and compared to those in ISO 354.

New developments in the measurement and calibration of absorption, scattering, and diffusion coefficients

Round robin experiments have confirmed that current methods to measure the random incidence absorption coefficient are inaccurate and not reproducible from lab to lab. As a result, various improvements to ISO 354 are being considered. Among them include measures to prevent the coefficient from exceeding unity and achieve reproducibility, using calibration. Since all measurement equipment is calibrated, it seems prudent to calibrate the rev room as well. We will describe approaches used at RPG to replace suspended clouds with boundary diffusors, the use of Eyring instead of Sabine and calibration, using a non-diaphragmatic reflective sample, with the same area, thickness and perimeter as the absorber, as a “zero” or low absorption reference. The new rotating table ISO 17497-1 scattering coefficient apparatus, using dual source/simultaneous impulse response measurements will be described. Since the technique utilizes subtraction of the reflective table as a reference, some of the problems associated with the rev room method are mitigated and reproducibility is achieved. Finally, the new diffusion coefficient goniometer, utilizing 32 simultaneous impulse response measurements, will be described. As with the scattering coefficient, the normalized diffusion coefficient benefits from the use of a reflective calibration reference, thus removing edge diffraction and other effects.