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.     

An oscillation phenomenon of low frequency reverberation in the shallow water and its physical explanation

~~An oscillation phenomenon of low frequency reverberation in the shallow water and its physical explanation1 Zhang, R.. Jin. G. Normal-mode theory of average reverberation intensity in shallow water, Journal of Sound and Vibration, 1987 19(2):215-223 2. Ellis, D. D., A shallow-water normal-mode reverberation model, J. Acoust. Soc, Am., 1995, 97(5): 2804-2814. 3. McDaniel, S. T., Seafloor reverberation fluctuations, J. Acoust. Soc. Am., 1990, 88(3): 1530-1535. 4. Abraham, …     

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.     

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.     

Indirect measurement of acoustic power into a small room at low frequencies

An essential step towards improving sound insulation is a reliable means of quantifying the performance. However, for various reasons sound insulation measurements at low frequencies are associated with relatively high uncertainty and wide variance values. The objective of this research is to develop a method of sound insulation measurement which complements the standard ISO 140 measurement methods by providing improved accuracy at low frequencies. In this paper part of the problem is considered, namely the measurement of power radiated into the receiver room. The ‘peak envelope method’ is based on mode theory and the measurement employs a pair of microphones in the receiver room and a calibrated volume velocity source. No reverberation time measurements are required. The theory is outlined and computer simulations and trial measurements are carried out in order to validate the theory. Good agreement in numerical and experimental validation is demonstrated. We conclude that the peak envelope method is suitable for the measurement of radiated sound power at modal frequencies where ISO 140 methods are poorly adapted. In order to obtain transmission loss, a measure of incident power in the source room will also be required, which will be the subject of future works.     

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.     

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.     

Room acoustical model of external reverberation

A theory of external reverberation in urban built-up environments is developed, based on a classical room acoustical model. In the model, external reverberation is analyzed as a special limiting case of internal reverberation in rooms. Explicit formulae are deduced for the statistical value of the external reverberation time, and the spatial distribution of the external sound field amplitude with distance from a fixed, constant power, sound source, for which comparison with published experimental results is possible. Predictions of the theory compare reasonably well with the experimental values. It is found that the external reverberation time in a built-up area depends chiefly on the average building height, and to a lesser extent on the packing fraction, and the ratio of surface area to cross-sectional area of buildings which make up the built-up environment, apart from the absorptive properties of the building and ground plane surfaces. For the spatial distribution of the steady state sound field amplitude in a built-up environment, it is found that the diffuse field amplitude attenuates with distance from a fixed, constant power source exponentially faster than the inverse square law.     

On the steady-state and the transient decay methods for the estimation of reverberation time

The discrepancy between reverberation times of an enclosed sound field measured by the steady-state method and by the transient decay method is well-known. So far, no clear explanation has been obtained. In this paper, the steady-state bandlimited energy in an enclosure and bandlimited power flow into modally reactive boundaries are derived to describe the energy balance relationship and thus the reverberation time in a frequency band. This reverberation time is then compared to that obtained from the transient decay of the sound field based on the modal analysis. The comparison provides an understanding of the discrepancy mentioned above as well as the physical interpretations of the reverberation times estimated by both methods.     

Sound power measurements in a reverberant room

This paper describes and discusses the ASHRAE standard test procedure for measuring the sound power output of mechanical equipment in reverberation room [1]. Particular attention is given to the qualification test required of a facility for the measurement of pure tones.     

Nonexponential sound decay in concert halls

The paper presents acoustic measurement results for two concert halls in which nonexponential sound decay is observed. Quantitative estimates are given for how the obtained decay laws differ from exponential. Problems are discussed that arise when using reverberation time to assess the quality of room acoustics with nonexponential sound decay.     

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.     

The effect of loudness on the reverberance of music: reverberance prediction using loudness models

This study examines the auditory attribute that describes the perceived amount of reverberation, known as "reverberance." Listening experiments were performed using two signals commonly heard in auditoria: excerpts of orchestral music and western classical singing. Listeners adjusted the decay rate of room impulse responses prior to convolution with these signals, so as to match the reverberance of each stimulus to that of a reference stimulus. The analysis examines the hypothesis that reverberance is related to the loudness decay rate of the underlying room impulse response. This hypothesis is tested using computational models of time varying or dynamic loudness, from which parameters analogous to conventional reverberation parameters (early decay time and reverberation time) are derived. The results show that listening level significantly affects reverberance, and that the loudness-based parameters outperform related conventional parameters. Results support the proposed relationship between reverberance and the computationally predicted loudness decay function of sound in rooms.     

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。      

Sound strength and reverberation time in small concert halls

Sound strength and reverberation time measurements have been carried out in six small concert halls in Cambridge, UK. The sound strength G is a measure of the physical sound level in a concert hall and is closely related to the subjective sensation of loudness. It compares integrated impulse responses at a point in the measured room with that measured at ten metres distance in the free field.The aim of the measurements is to investigate the acoustic characteristics of the halls concerning sound strength and reverberation time. Furthermore the effect of the variable acoustics in the halls on these parameters is discussed in this paper. Especially for bigger ensembles it is often desirable to reduce the sound level in a small concert hall. The measurement results show that for a fixed hall volume, this can primarily be achieved by decreasing the reverberation time in the hall. However, with regard to the sound quality of a hall and the recommended reverberation times for chamber music, reverberation time cannot be reduced by an arbitrary extent. Therefore reverberation time and strength have to be balanced very carefully in order to obtain sufficient reverberation whilst at the same time avoiding excessive loudness. Finally the measured strength levels are compared to values derived from traditional and revised theory [Barron M, Lee L-J. Energy relations in concert auditoriums. J Acoust Soc Am 1988;84(2):618-28] on strength calculations in order to assess the accuracy of the theory for small chamber music halls. Possible reasons for the low measured strength levels observed are discussed with reference to related design features and objective acoustic parameters.     

低频混响信号中的简正波衰减系数提取方法

提出一种从低频混响信号中提取简正波衰减系数的方法。利用简正波过滤技术对垂直阵混响信号进行分析,获得单阶简正波混响声场。假设海底反向散射矩阵可分离,从单阶简正波平均混响强度中提取出有效海底反向散射矩阵元素,最后利用不同距离上的有效海底反向散射矩阵元素计算出简正波的衰减系数。利用该方法从混响信号中提取出的简正波衰减系数预报的声传播损失和相同海域实测声传播损失一致。该简正波衰减系数提取方法有效避免了海底散射衰减和简正波传播衰减耦合的问题,同时对海底参数反演和水声环境的快速评估也具有重要的意义。      

Sound radiation from an aperture in a rectangular enclosure under low modal conditions

This paper investigates both theoretically and experimentally the sound radiation from an aperture placed in an enclosure wall for the particular case of low modal sound field. The incidence field is composed of the enclosed sound field, which is calculated using the theoretical modal model presented. The transmitted sound is calculated by the Rayleigh radiation equation after continuity conditions have been applied in the aperture plane, assuming the condition of a thin wall. The model is experimentally validated by measuring the directivity and sound pressure radiated from an aperture in the side of a rectangular box. Because the walls of the enclosure are not rigid, an experimental procedure to determine its admittance is also presented. The experiments have been carried out for the first four modes of the enclosed sound field, and good agreement is found between the theoretical and experimental results. These results indicate that the admittance of the aperture, its radiation efficiency, and its directivity are all functions of the predominant mode shape, and the frequency, as well as the location and shape, of the aperture relative to the predominant enclosed mode shape.     

Spatially extended sound equalization in rectangular rooms.

The results of a theoretical study on global sound equalization in rectangular rooms at low frequencies are presented. The zone where sound equalization can be obtained is a continuous three-dimensional region that occupies almost the complete volume of the room. It is proved that the equalization of broadband signals can be achieved by the simulation of a traveling plane wave using FIR filters. The optimal solution has been calculated following the traditional least-squares approximation, where a modeling delay has been applied to minimize reverberation. An advantage of the method is that the sound field can be estimated with sensors placed in the limits of the equalization zone. As a consequence, a free space for the listeners can be obtained.     

Acoustics of courtyard theatres

The traditional Chinese theatre was often built with a courtyard. In such open-top space, the absence of a roof would mean little reverberation and non-diffused sound field. Acoustically the situation is quite different from that of any enclosed space. Therefore, the classic room acoustics, such as Sabine reverberation formula, would no longer be applicable due to the lack of sound reflections from the ceiling. As the parameter of reverberation time T30 shows the decay rate only, it would not properly characterize the prominent change in the fine structure of the echogram, particularly in case of a large reduction of reflections during the decay process. The sense of reverbrance in a courtyard space would differ noticeably from that of the equivalent 3D-T30 in an enclosed space. Based upon the characteristic analysis of the sound field in an open-top space, this paper presents a preliminary study on the acoustics of the courtyard theatres.     

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.