Reverberation time measurements in non-diffuse acoustic field by the modal reverberation time

The increasing presence of low frequency sources and the lack of acoustic standard measurement procedures make the extension of reverberation time measurements to frequencies below 100 Hz necessary. In typical ordinary rooms with volumes between 30 m³ and 200 m³ the sound field is non-diffuse at such low frequencies, entailing inhomogeneities in space and frequency domains. Presence of standing waves is also the main cause of bad quality of listening in terms of clarity and rumble effects. Since standard measurements according to ISO 3382 fail to achieve accurate and precise values in third octave bands due to non-linear decays caused by room modes, a new approach based on reverberation time measurements of single resonant frequencies (the modal reverberation time) has been introduced. From background theory, due to the intrinsic relation between modal decays and half bandwidth of resonant frequencies, two measurement methods have been proposed together with proper measurement procedures: a direct method based on interrupted source signal method, and an indirect method based on half bandwidth measurements. With microphones placed at corners of rectangular rooms in order to detect all modes and maximize SNRs, different source signals were tested. Anti-resonant sine waves and sweep signal turned out to be the most suitable for direct and indirect measurement methods respectively. From spatial measurements in an empty rectangular test room, comparison between direct and indirect methods showed good and significant agreements. This is the first experimental validation of the relation between resonant half bandwidth and modal reverberation time. Furthermore, comparisons between means and standard deviations of modal reverberation times and standard reverberation times in third octave bands confirm the inadequacy of standard procedure to get accurate and precise values at low frequencies with respect to the modal approach. Modal reverberation time measurements applied to furnished ordinary rooms confirm previous results in the limit of modal sound field: for highly damped modes due to furniture or acoustic treatment, the indirect method is not applicable due to strong suppression of modes and the consequent deviation of the acoustic field from a non-diffuse condition to a damped modal condition, while standard reverberation times align with direct method values. In the future, further investigations will be necessary in different rooms to improve uncertainty evaluation.     

Influence of wall absorption on low-frequency dependence of reverberation time in room of irregular shape

In this paper, a modal analysis was used to describe a reverberation phenomenon in a room of complex shape. A theoretical model was limited to low sound frequencies, when eigenmodes are lightly damped, thus they may be approximated by uncoupled normal acoustic modes of a hard-walled room. A utility of this method was demonstrated in a numerical example where the enclosure in a form of two coupled rooms was considered. A reverberation time was evaluated from a time decay of spatial root mean square pressure, the overall measure of room pressure. The results of calculations, performed for three different distributions of absorbing materials on room walls, showed how various location of the material can effect a dependence of the reverberation time on a frequency of sound source.     

Computational studies of steady-state sound field and reverberant sound decay in a system of two coupled rooms

The acoustical properties of an irregularly shaped room consisting of two connected rectangular subrooms were studied. An eigenmode method supported by a numerical implementation has been used to predict acoustic characteristics of the coupled system, such as the distribution of the sound pressure in steady-state and the reverberation time. In the theoretical model a low-frequency limit was considered. In this case the eigenmodes are lightly damped, thusthey were approximated by normal acoustic modes of a hard-walled room. The eigenfunctions and eigenfrequencies were computed numerically via application of a forced oscillator method with a finite difference algorithm. The influence of coupling between subrooms on acoustic parameters of the enclosure was demonstrated in numerical simulations where different distributions of absorbing materials on the walls of the subrooms and various positions of the sound source were assumed. Calculation results have shown that for large differences in the absorption coefficient in the subrooms the effect of modal localization contributes to peaks of RMS pressure in steady-state and a large increase in the reverberation time.      

Decay rates and wall absorption at low frequencies

This paper is concerned with evaluating the error of conventional estimates of the boundary absorption of rectangular enclosures, with particular reference to reverberation room sound power measurements. The reverberation process is examined theoretically; the relative contributions to the decay rate from different modes in a rectangular room are calculated from an ensemble average over rooms with nearly the same dimensions. It is shown that the traditional method of determining the absorption of the walls of reverberation rooms systematically underestimates the absorption at low frequencies; the error is computed from the ensemble average. Finally, an unbiased estimate of the sound power radiated by a source in a reverberation room is derived. This estimate involves measurement of the initial decay rates of the room and is, unlike the usual reverberation room sound power estimate, neither based on statistical diffuse field considerations nor on the normal mode theory.     

Sound attenuation in acoustically lined curved ducts in the absence of fluid flow

A study has been made of the sound attenuation in a lined curved duct with rectangular cross-section. In this study, the derivation of the eigenvalue equation was based on the continuity of the normal component of the particle displacement and the matching of the acoustic pressure on the acoustic lining surface. The sound attenuation was calculated by using the acoustic energy expression for the waves propagating in a curved duct. For a given duct geometry and known acoustic lining impedances, a computer program was developed to solve for the eigenvalues and to obtain the sound attenuation of the propagating waves in the lined curved duct. It was found that in the case studied here the fundamental mode was least attenuated. The total sound attenuation was calculated on the assumption that the amplitudes for all propagating waves were equal at a given frequency. Effects of aspect ratio, bend angle and the acoustic impedance on the sound attenuation were investigated in the present work.     

Performance Evaluation and Effectiveness of the Reverberation Room

This research presents a thorough evaluation of the reverberation room at Acoustics Laboratory in National Institute of Standards (NIS) according to the related international standards. The evaluation aims at examining the room performance and exploring its effectiveness in the frequency range from 125 Hz to 10000 Hz according to the international standard requirements. The room, which was designed and built several years ago, is an irregular rectangular shape free from diffusers. Its volume is about 158.84 m³, which meets the requirement of the ISO 354 standard L_max < 1.9V^1/3. Cut-off frequencies of one and one-third octave are 63 Hz and 100 Hz respectively; however Schroder frequency is 400 Hz. Calculations of cut-off frequency and modal density showed adequate modes that give acceptable uniformity starting comfortably from frequency of 125 Hz. The room has a reverberation time that is suitable for its size over the frequency range of interest. The room sound absorption surface area and its sound absorption coefficient satisfy the criteria given in ISO 3741 and ISO 354. There is an accepted diffuse sound field inside the room due to the standard deviation of measured sound level, which is less than 1.5 dB over all the frequency range. The only exception was 125 Hz which may be due to a lack of diffusivity of the sound field at this frequency. The evaluation proves that the NIS reverberation room is in full agreement with the international standards, which in turns qualifies the room to host measurements inside without concerns.     

Sound decay in a rectangular room with impedance walls

The problem of sound decay in a rectangular room is considered for the case of a room with walls the acoustic properties of which are described by the impedance, which implies a dependence of the absorption coefficient on the angle of incidence of sound waves. The ray approximation is used to determine the sound decay laws for different distributions of wall absorption. It is shown that, in a room with impedance walls, the sound decay is slower than in the conventional reverberation model, in which the wall absorption coefficient is independent of the angle of incidence. The problem is also solved in the wave approximation to determine the decay law for a preset frequency band.     

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.     

Effects of damping on the low-frequency acoustics of listening rooms based on an analytical model

A study of the effects of damping on the low-frequency acoustics of listening rooms has been undertaken. The study was carried out using a new numerical implementation of an analytical solution based on a model developed by Bistafa and Morrissey. The model was designed to simulate the sound field in rectangular enclosures below the Schroeder cut-off frequency. Four hypothetical rooms were studied, a lightly damped room, a well damped room, a statistically compliant European Broadcast Union control room and a compliant European Broadcast Union control room. The most important result from the study using the proposed model was the influence of modes above the Schroeder cut-off frequency on reverberation time. This was caused by the variations in damping between mode types and variations in the modal coupling between the source and receiver. The research suggests that Schroeder's 1954 cut-off frequency for the influence of modes was more correct for highly damped rooms, in comparison with the Schroeder's 1964 relation.     

Space variances in the mean-square pressure at the boundaries of a rectangular reverberation room

It was found that it was possible to reduce the number of samples needed for power measurements by sampling at the boundaries in a reverberation room. The space variances in the mean-square pressure of oblique wave fields in a rectangular reverberation room were calculated. The sound source was assumed to be a narrow-band noise source. Space variances throughout the room sigma 2A, on the floor sigma 2B, on the edge sigma 2C, and at the corner sigma 2G were compared with each other numerically. The numerical results confirmed that the relation sigma 2G less than sigma 2C less than sigma 2B less than sigma 2A holds well. Particularly, in a rectangular reverberation room, under the condition that the receiver position is fixed at the corner of the room (corner method), the number of samples reduces to 1/2-1/3 the number of samples needed under the condition that both receiver positions and source positions are changed throughout the room. Some experimental results regarding the power measurements by the corner method are also shown. The experimental results confirmed the suitable estimation of the power for a noise source at low frequencies.     

High-frequency modes in a two-dimensional rectangular room with windows

We examine a two-dimensional model problem of architectural acoustics on sound propagation in a rectangular room with windows. It is supposed that the walls are ideally flat and hard; the windows absorb all energy that falls upon them. We search for the modes of such a room having minimal attenuation indices, which have the expressed structure of billiard trajectories. The main attenuation mechanism for such modes is diffraction at the edges of the windows. We construct estimates for the attenuation indices of the given modes based on the solution to the Weinstein problem. We formulate diffraction problems similar to the statement of the Weinstein problem that describe the attenuation of billiard modes in complex situations.     

Approaching a methodology for the development of a multilayer sound absorbing device recycling coal bottom ash

The aim of the present work has been to develop a methodology which accurately predicts the acoustic behavior of a material without having to manufacture large panels and testing them in reverberation room. Moreover, it can be predicted the sound absorbing performance at normal and random incidence of the sound wave on a material for different thicknesses and multilayer configurations, dramatically reducing the number of experimental tests. This methodology might decrease the cost of the investigation, which is particularly important when dealing with recycled materials that must compete with commercial products used in the same application.     

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.     

Prediction of reverberation time and speech transmission index in long enclosures

It is known that the sound field in a long space is not diffuse, and that the classic theory of room acoustics is not applicable. A theoretical model is developed for the prediction of reverberation time and speech transmission index in rectangular long enclosures, such as corridors and train stations, where the acoustic quality is important for speech. The model is based on an image-source method, and both acoustically hard and impedance boundaries are investigated. An approximate analytical solution is used to predict the frequency response of the sound field. The reverberation time is determined from the decay curve which is computed by a reverse-time integration of the squared impulse response. The angle-dependence of reflection coefficients of the boundaries and the change of phase upon reflection are incorporated in this model. Due to the relatively long distance of sound propagation, the effect of atmospheric absorption is also considered. Measurements of reverberation time and speech transmission index taken from a real tunnel, a corridor, and a model tunnel are presented. The theoretical predictions are found to agree well with the experimental data. An application of the proposed model has been suggested.     

Reverberation time and maximum background-noise level for classrooms from a comparative study of speech intelligibility metrics

Speech intelligibility metrics that take into account sound reflections in the room and the background noise have been compared, assuming diffuse sound field. Under this assumption, sound decays exponentially with a decay constant inversely proportional to reverberation time. Analytical formulas were obtained for each speech intelligibility metric providing a common basis for comparison. These formulas were applied to three sizes of rectangular classrooms. The sound source was the human voice without amplification, and background noise was taken into account by a noise-to-signal ratio. Correlations between the metrics and speech intelligibility are presented and applied to the classrooms under study. Relationships between some speech intelligibility metrics were also established. For each noise-to-signal ratio, the value of each speech intelligibility metric is maximized for a specific reverberation time. For quiet classrooms, the reverberation time that maximizes these speech intelligibility metrics is between 0.1 and 0.3 s. Speech intelligibility of 100% is possible with reverberation times up to 0.4-0.5 s and this is the recommended range. The study suggests "ideal" and "acceptable" maximum background-noise level for classrooms of 25 and 20 dB, respectively, below the voice level at 1 m in front of the talker.     

Field measurement of airborne sound insulation between rooms with non-diffuse sound fields at low frequencies

Procedures for the field measurement of airborne sound insulation between rooms with diffuse fields are described in International Standard ISO 140-4. However, many dwellings contain rooms with volumes less than 50 m³, where low frequency measurements are less reliable; hence there is a need for a measurement procedure to improve the reliability of field measurements in rooms with non-diffuse fields. Procedures are proposed for sound pressure level and reverberation time measurements for the 50, 63 and 80 Hz third octave bands. The sound pressure level measurement combines corner microphone positions with positions in the central region of each room. This provides a good estimate of the room average sound pressure level with significantly improved repeatability.     

Acoustically induced vibration of,and sound radiation from,beams inside an enclosure

The velocity response of a single cylindrical beam to pure tone sound in a rectangular reverberation chamber is analysed. The variation of the response with position within the chamber and the effect of proximity of other similar, parallel beams is considered. A reciprocity relation is established between the response of a beam to sound in the chamber and the sound radiation by such motion when otherwise generated; this relation is found to be valid even for non-diffuse fields, below the Schroeder “large room” frequency (i.e., above this frequency, the average frequency spacing between modes is less than one-third of the bandwidth of a typical mode [1]). The mean square velocity response, averaged over all possible beam positions within the chamber, is found to be directly proportional to the radiation loss factor of that vibrational mode, and inversely proportional to (frequency)³. The maximum normalized response occurs when the beam is excited in its fundamental vibrational mode. One application is to the estimation of fatigue life of heat exchanger tubes in gas-cooled nuclear reactors; the large number of tubes necessitates an estimate of the variation of the tube response with position within the exchanger casing. Another important application is in a reverberation chamber; in many cases a suitable direct excitation experiment is very difficult, or even impossible to perform, while the corresponding reciprocal experiment is relatively easy.     

非线性内波存在下的浅海远程混响模型

研究了浅海非线性内波对远程混响场的影响。通过分析非线性内波活动引起声源到海底散射元以及散射元到接收点之间的声传播变化,给出了非线性内波引起远程混响强度变化的表示,建立了非线性内波存在下的浅海远程混响模型,数值计算了非线性内波运动引起远程混响强度的变化。理论和数值计算表明,非线性内波的活动能够引起远程混响强度的变化,在某些情况下会导致远程混响强度增强。通过讨论非线性内波引声简正波的耦合效应,给出了其引起远程混响强度增强的原因。      

Measuring sound scattering coefficients of uneven surfaces in a reverberant workplace – Principle and validation of the method

In workplaces, wall facings are often based on periodic or aperiodic sound scattering surfaces. It is necessary to develop acoustic characterization methods for these kinds of walls to predict the acoustic pressure cartography in the room in order to improve the acoustical treatment. However, this characterization is quite difficult because of the partially reverberant conditions. We developed a measurement system which determines in situ the sound scattering coefficients of relief surfaces. The measurement method, originally operating in free-field conditions, was adapted for indoor use. To overcome problems of parasite echoes coming from reverberation and from noisy sources present on the site, we developed a dedicated emission/reception system. An acoustic antenna with constant directivity over the full frequency range allows spatial filtering of the parasite echoes and an impulsive sound source enables the use of a broad temporal window, resulting in adequate time separation of the different signals received by the antenna. Measurements of the sound scattering coefficient of a corrugated panel were carried out for several incidence angles in free-field and in a noisy workshop and allowed the in situ validation of this system.     

Acoustical design of the multi-purpose ‘Hjertnes’ hall in Sandefjord

‘Hjertnes’ is a typical multi-purpose hall primarily intended for concerts. A three-dimensional ray tracing computer program was used to provide a picture of the sound energy distribution on the audience area of the hall, various room shapes being investigated. This resulted in tilted side walls and a convex ceiling. Variable acoustics have been obtained through the use of movable ceiling absorbing and diffusing elements. In addition, a demountable orchestra enclosure has been constructed within the stagehouse. Control measurements of pulse response and reverberation time are reported.