Sabine Absorption Coefficient Research Articles

Loudspeaker configuration in reverberation rooms for sound absorption measurement using room mode determination

For Sabine absorption coefficient measurements in reverberation rooms, it is preferable to excite as many room modes as possible. But the number of excited room modes is significantly affected by many factors, among which one dominating factor is the loudspeaker location particularly at frequencies below the Schroeder frequency. In turn, this could significantly influence the statistical absorption coefficient obtained according to ISO 354. Therefore, this study aims to investigate the impact of loudspeaker configurations on the excitation of room modes. Frequency response functions are measured using a broad band steady state noise signal using four sound sources at various locations, and the numbers of excited room modes in the one-third octave bands are quantified and compared against those by Green's function simulations. A procedure for determining favorable loudspeaker positions based on the excited room modes is proposed, which can be a useful input to the working group of the ISO 354 standard.

Flow resistivity estimation from practical absorption coefficients of fibrous absorbers

There are useful conversion methods from Sabine absorption coefficients according to ISO 354 to other acoustic properties for room boundaries, e.g., surface impedance or flow resistivity. However, most available sound absorption coefficients are practical absorption coefficients, which are simplified according to ISO 11654 from the Sabine absorption coefficients and widely used by absorber manufacturers as their absorbers’ performance indicators. In this study, practical absorption coefficients are used to inversely characterize the flow resistivity via reliable models. 15 absorber samples with varying mounting conditions are used for validating the flow resistivity estimation, having a wide flow resistivity range of 10–110 kNsm−4. As expected, the practical absorption coefficients are found to be less reliable input parameters for estimating the flow resistivity, but with more datasets, the degradation becomes insignificant compared to the Sabine absorption coefficients. The estimated flow resistivity will be a valuable parameter to predict the absorption characteristics of different thickness and mounting conditions.

Bayesian decay time estimation in a reverberation chamber for absorption measurements.

This work investigates the use of the initial decay time to obtain the Sabine absorption coefficient from measurements conducted in a reverberation chamber. Due to non-uniform distribution of sound absorption in the test chamber, measured energy decay functions exhibit multiple slopes, which cannot be evaluated unambiguously using linear regression as prescribed in the current standard (ISO 354, International Organization for Standardization, Geneva, Switzerland, 2003). As an alternative, this study proposes a Bayesian framework that allows estimating multiple decay parameters, hence capturing more accurately the energy decay features. Measurements are carried out in a reverberation chamber with and without diffusing elements to investigate the influence of diffusers on the absorption coefficient and on the decay process. Measured absorption coefficients of a porous sample are compared to theoretical values estimated with a transfer matrix model. The results show that the Sabine absorption coefficient calculated using the shortest decay time agrees well with the size-corrected theoretical absorption coefficient.

Bayesian inference of the flow resistivity of a sound absorber and the room's influence on the Sabine absorption coefficients.

A Bayesian analysis is applied to determine the flow resistivity of a porous sample and the influence of the test chamber based on measured Sabine absorption coefficient data. The Sabine absorption coefficient measured in a reverberation chamber according to ISO 354 is influenced by the test chamber significantly, whereas the flow resistivity is a rather reproducible material property, from which the absorptive characteristics can be calculated through reliable models. Using Sabine absorption coefficients measured in 13 European reverberation chambers, the maximum a posteriori and the uncertainty of the flow resistivity and the test chamber's influence are estimated. Inclusion of more than one chamber's absorption data helps the flow resistivity converge towards a reliable value with a standard deviation below 17%.

Predicting the Sabine absorption coefficients of fibrous absorbers for various air backing conditions with a frequency-dependent diffuseness correction.

Fibrous absorbers can be installed with various air backing conditions to fulfil a given low frequency acoustic requirement. Since absorber manufacturers cannot provide the absorption coefficients for all possible mounting conditions, acousticians have difficulties knowing the absorption characteristics of their own configurations. This study aims to predict the absorption coefficient for various mounting conditions from a single measurement of an arbitrary mounting condition by extracting the air flow resistivity of the test specimen and the frequency-dependent effect of the chamber on the measured absorption coefficients. With two homogeneous fibrous absorbers, the predicted absorption coefficients agree well with the measurements.

Kurtosis of room impulse responses as a diffuseness measure for reverberation chambers.

This study presents a kurtosis analysis of room impulse responses as a potential room diffuseness measure. The early part of an impulse response contains a direct sound and strong reflections. As these reflections are sparse and strong, the sound field is unlikely to be diffuse. Such deterministic reflections are extreme events, which prevent the pressure samples from being distributed Gaussianly, leading to a high kurtosis. This indicates that the kurtosis can be used as a diffuseness measure. Two rooms are analyzed. A non-uniform surface absorption distribution tends to increase the kurtosis significantly in a small room. A full scale reverberation chamber is tested with different diffuser settings, which shows that the kurtosis calculated from broadband impulse responses from 125 Hz to 4 kHz has a good correlation with the Sabine absorption coefficient according to ISO 354 (International Organization for Standardization, Geneva, Switzerland, 2003).

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.

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem.

Some comments on Sabine absorption coefficient (L)

The case of a nonzero reverberation time when all absorptive surfaces in a room have values of Sabine absorption coefficient of one, the existence of values of the coefficient that are larger than one, and the difference of the coefficient from the statistical absorption coefficient, are well known. So far, the reasons for these phenomena are still unclear. This letter provides a new perspective to the classical problem of sound absorption where physical interpretations of the Sabine absorption coefficient are given for different types of absorptive surface and conditions of the sound field in rooms.

Effects of sound radiation on Sabine absorption coefficient of modally-reactive panels

A modally-reactive panel in a room absorbs and radiates sound at the same time when it is excited acoustically by the enclosed sound field. The absorption of sound occurs when only part of the incident sound is reflected by the panel, but when the entire panel vibrates, the radiation of sound is also produced. In this paper, Statistical Energy Analysis (SEA) is used to establish a relationship between the acoustic-structural coupling of the panel with the sound field and the Sabine absorption coefficient of the panel. It is shown that the coefficient does not only consist of the sound absorption by the panel from the room but also, the sound radiation from the vibrating panel back into the room. Computational and experimental examples are presented for different acoustical properties of the panel and the sound field to illustrate the extent of influence of the sound radiation on the coefficient. The results provide a basic understanding of the conditions in both cases where the sound radiation has significant effects and negligible effects on the determination of the Sabine absorption coefficient of modally-reactive panels in rooms.

Use of statistical energy analysis for the prediction of Sabine absorption coefficient of modally reactive panels

Statistical energy analysis (SEA) is used to establish a relationship between the Sabine absorption coefficient of a modally reactive panel and the coupling of the panel with the sound field in a room. The acoustic-structural coupling is described by the coupling loss factors between the panel and the room. The application of the consistency relationship in SEA, which is based on the reciprocity principle, is shown to enable the coupling loss factors to be determined by directly exciting either the panel or the room. Each way of driving the acoustic-structural coupled system produces different values of the coupling loss factors and thus, of the absorption coefficient. The nature of discrepancy between the results of both ways of exciting the system is explained by using distributions of energy among structural modes of the panel and acoustic modes of the sound field, as well as distributions of modal coupling-loss factor among acoustic-structural coupled pairs of the modes. This paper provides an insight into the effect of the use of the consistency relationship on the prediction of the Sabine absorption coefficient of modally reactive panels by SEA.

The average absorption coefficient for enclosed spaces with non uniformly distributed absorption

This study concerns the determination of an equivalent acoustic absorption model of the flat heterogeneous walls present in industrial rooms. Numerous measurements of the reverberation time in reverberant room were carried out for several facings with different distributed spatial absorption. Experimental results were compared to classical reverberation time models. The measurements showed that the change in average acoustic absorption depends on the relative distance between the sound source and the absorbent panels, as it is this which creates heterogeneity. Therefore, taking into consideration, in the theoretical models of average acoustic absorption studied, the solid angles representing the equivalent area of the panels as viewed by the source, improved the accuracy of the calculated reverberation time compared to the measurements. This equivalent acoustic absorption model, based on Sabine's absorption coefficient and employing the solid angle ratio, was used to calculate the reverberation time of several industrial rooms. The results obtained are better than those obtained with the standard formula.

Modelling of sound fields in enclosed spaces with absorbent room surfaces Part II. Absorptive panels

This is the second part of a report on the modelling of sound fields in enclosed spaces with absorbent room surfaces. Both Sabine and Millington absorption coefficients are used to further investigate which approach produces the most accurate predictions. Classical formulae and geometric acoustic models, previously detailed, were used to predict the reverberation time in a test room with highly absorbent room surfaces. In addition the test room was configured with a partially absorptive surface. This configuration has previously only been predicted inaccurately. It was shown that the Millington formula predicted more accurately than either the Sabine or the Eyring formulae in the configurations of the room investigated. Verification of the previous results were confirmed when two of the computer models gave consistently more accurate predictions using Millington absorption coefficients than Sabine absorption coefficients.

On the units of Sabine absorption and the Sabine absorption coefficient

A century ago, W. C. Sabine demonstrated that sound absorption is fundamental to room acoustics, and introduced the idea for a measure of absorption that has become known as Sabine absorption. Because Sabine absorption and area have the same dimension, e.g., square-meters, many acousticians presume that Sabine absorption has the units of area. For a number of years Robert W. Young has been trying to convince us otherwise, arguing that a dimensionless logarithmic unit distinguishes Sabine absorption from area. [By dimensionless logarithmic unit is meant a scale factor that defines unity on a log scale. The neper (Np) and the decibel are two such quantities.] The metric sabin (Sa) is a unit of Sabine absorption. Defining the metric sabin to be one-half neper square-meter (1 Sa=0.5 Np m2) introduces a logarithmic unit while preserving the numerical scaling of current measurement practice. It follows that the unit of the Sabine absorption coefficient is the half-neper, and a difference between the Sabine absorption coefficient and coefficients from other methods becomes explicit. Among other things, a partial explanation for the experimental observation that Sabine absorption coefficients can exceed unity is provided.

Acoustic absorptivity of direct acoustic rate feedback control

The fixed‐gain feedback methods often provide the only means of limiting transient noise and excessive sound pressures due to unmeasurable, incoherent disturbances. The use of direct acoustic rate feedback (DARFB) to control an enclosure’s reverberant energy has the benefit over other feedback methods of larger stability margins and improved stability robustness. It also provides a means for achieving acceptable sound pressure levels in locations and environments which are not suited to surface treatments of sound absorbing materials. The effect of DARFB on the growth and decay of sound in enclosures is investigated and the change in the reverberation time of a sound field is discussed for active absorption using single and multiple controllers. Various models for the dynamics of sound growth are used and are shown to provide equivalent or similar results. Effective Sabine absorption coefficients are shown for active absorption and are compared with sound absorbing materials. The effectiveness of transducer placement is also discussed with respect to active absorption and the closed‐loop reverberation time. Numerical examples of acoustic absorption are given for a rectangular enclosure.

Sabine reverberation equation revisited.

About 1900 W. C. Sabine reported the ‘‘sound absorbing power’’ of materials in a reverberant room as proportional to a logarithm of the ratio of an initial to a final ‘‘residual sound,’’ after the source is stopped. In present-day terms, sound pressure level (a logarithm) decays at the rate d decibels per second, after the source is stopped. At least as far back as 1965, ASTM C423, ‘‘Sound Absorption⋅⋅⋅Reverberation Room Method,’’ obtained the Sabine absorption A in metric sabins by A=0.9210 Vd/c; 0.4 ln 10=0.9210 is a pure number. The volume of the reverberation room is V, cubic meters; the speed of sound of air therein is c, meters per second. On substituting reverberation time T=60 dB/d, Sabine sound absorption A=55.3(dB)V/cT; this dimensionally complete equation shows the decibel explicitly. The Sabine absorption of a surface of area S in square meters, and Sabine absorption coefficient a, isA=Sa. The unit of the Sabine coefficient a is thus the decibel; it is dimensionless in the sense of length, mass, or time; the unit is usually omitted. Being derived from a decay rate, the Sabine sound absorption coefficient is not ‘‘Ideally the fraction of the randomly incident sound power absorbed... .’’

The effect of fluid–structural coupling on acoustical decays in a reverberation room in the high‐frequency range

The effect of the fluid–structural coupling between the modes of a sound field and the modes of test panels placed in the sound field upon their decay behavior is investigated in the high‐frequency range. Quasitransient solutions of the average energies in the room and the panels are used to estimate the reverberation times in the room and to calculate the decay curves of a test panel. Experiments are conducted that verify these solutions. The estimated and measured results are in good agreement, which indicates that the average decay behavior of the room and panels can be analyzed in terms of the average modal parameters. The average modal parameters of the test panels and the reverberation room can be related to the Sabine absorption coefficient αSab of the panels. This result suggests an interpretation for the Sabine absorption coefficient of a modally reactive surface and provides a way to estimate this quantity using the statistical energy analysis (SEA) method. The dependence of the αSab upon the room properties, in which the panel is measured, is demonstrated both experimentally and analytically.

Effect of fluidal‐structural coupling on the acoustical decays in a reverberation room in high‐frequency range

The effect of the coupling between a sound field and test panels upon their decay behavior is investigated in high‐frequency range. Quasitransient solutions of the average energies in the room and the panels are used to estimate the reverberation times in the room and to calculate the decay curves of a test panel. Experiments are conducted to verify these solutions. The estimated and measured results are in good agreement in high‐frequency range, which indicates that the average decay behavior of the room and panels can be analyzed in terms of the average modal parameters. The amalgamation of the average modal parameters (of the test panels and the reverberation room) can be related to the Sabine absorption coefficient αSab of the panels. This result provides a possible interpretation for the αSab of a modally reactive surface and suggests a way to estimate this quantity by statistical energy analysis (SEA) method. The dependence of the αSab upon the room properties, in which the panel is measured, is demonstrated both experimentally and analytically.

Sabine Absorption Coefficients of Aluminized Rubber

Since 1930, the work of Eyring and others has indicated that the effective Sabine absorption coefficient of highly absorbing materials is not given by αi, the randomly incident energy absorption coefficient, but is instead given by −ln(1 − αi). This indicates that for αi>0.63, the Sabine coefficient should be greater than 1.0. A search of the literature provides many measured values of 0.99 for the Sabine coefficient but rather surprisingly only one or two measured values in excess of 1.0. This paper reports on reverberation measurements made at frequencies from 10 to 100 kc/sec in water contained in a small tank completely lined with either flat or cone structured aluminized butyl rubber. The maximum value measured for the Sabine coefficient was 2.56 which corresponds to αi = 0.923. In carrying out these experiments, decay rates in excess of 25 000 dB/sec were measured through use of a Memoscope. Information as to the advantages of using a Memoscope in making reverberation measurements will be presented.

Example of the Dependence of Sound Absorption on the Area of Sample

The sound absorption in a solid concrete room was measured by the reverberation method, first with the room entirely bare, then with a “border” of 114-in. Acousti-Celotex (46 ft2 in area) around the ceiling, then with a “border” added around the top of the walls (total acoustical tile 112 ft2), and finally with the entire ceiling and one-third of the side walls covered (265 ft2 of acoustical tile). The test sound, generated by mechanical impact, was filtered on reception into third-octave and half-octave bands. The volume of the rectangular room was 1350 ft3 and its area 793 ft2. With the border of 46 ft2 the coefficients determined in the customary fashion by the Sabine reverberation equation were near those published for 114 in. Acousti-Celotex. At 125 and 8000 cps the coefficients changed little with the area of sample. At 1000 cps, however, the measured coefficient dropped from 0.93 to 0.44, to 0.25 as the sample area was increased. This is possible evidence for a change in effective mean free path and for the need of an appropriate adjustment in the reverberation formula. The name Sabine absorption coefficient is suggested for the usual coefficient computed by the reverberation technique, to distinguish it from the energy absorption coefficient that does not exceed unity.