Sound Energy Decay Research Articles

Revision of Sabine's and Eyring's reverberation theories

Sabine's and Eyring's reverberation theories are still the most important theoretical frameworks for room acoustics. The important physical quantities derived from these theories are the average sound pressure level (sound energy density) and the reverberation time (sound energy decay). Eyring revised Sabine's theory to become the reverberation time zero in the perfect absorption condition. However, Eyring's theory has contradictions regarding the sound energy density in a steady state and the energy decay from the steady state. In this study, in order to resolve these contradictions, the theoretical framework for the consistent system is presented introducing the new concept of the average impulse response in a room, and the contradictions in the current room acoustic theory are clarified. Based on the theoretical framework, Sabine's reverberation theory is revised by a different way of Eyring's theory. The reverberation time of the revised theory is shorter than that of Sabine's theory and longer than that of Eyring's theory. Finally, ray-tracing computer simulations were performed to verify the revised theory. Results of sound ray tracing simulations were in better agreement with the values calculated using the revised theory rather than those calculated using Sabine's and Eyring's theories.

The acoustical characterization of clay pots in Ottoman architecture through experimental and numerical analysis.

In medieval age, clay pots are utilized as multi-functional building elements serving not only for structural and ventilative purposes but also for the improvement of the acoustic qualities of the space. Although the medieval usage of acoustic pots is vaguely connected with the acoustic vessels of Vitruvius, their employment is also interpreted as cavity resonators as in the case of Süleymaniye Mosque. The 16th century edifice designed by Sinan the Architect Laureate is a significant example among its European counterparts with 224 clay pots embedded into its central dome. The present work aims to discuss the contribution of clay pots in acoustics of historical edifices focusing on Süleymaniye Mosque. In this study, a clay pot sample employed in the mosque is reproduced and impedance tube measurements are held. The results are then compared with finite element model simulations carried out to examine the effective frequency range of the clay pots. Finally, the data acquired from numerical simulations and the experimental measurements are applied in ray tracing simulations. The final results reinforce the contribution of clay pots on the improvement of sound energy decay rate measured after the final restorations within the mosque with repaired pots.

The effects of stage house coupling on multipurpose auditorium acoustics

The current scientific research on coupled spaces has augmented the design applications of reverberation chambers and stage house-coupling in music venues in the last couple of decades, and vice-versa the halls that incorporate room acoustics coupling has attracted attention of researchers in the field. Most of the cases, depict the room acoustics coupling from a positive perspective, as the non-exponential energy decay aids clarity and reverberance, which are two simultaneous requirements to satisfy in a music hall. However, not many studies discuss the negative effects of a potential non-exponential energy decay in an auditorium, or a multi-function hall, if not intentionally and carefully utilized. This study aims to highlight the importance of stage tower design in an auditorium, which is aimed to be used dominantly for speech-oriented activities and occasionally to host recitals. The paper initially introduces the acoustical design phases of the auditorium that is within the Ted Ankara Foundation College Performance Art Center. Acoustical simulations are utilized during design phase. The selected auditorium has multiple construction phases, including pre and post acoustical treatment within the stage. Accordingly, field tests are held before and after stage tower acoustical interventions. Collected impulse responses are analyzed by Bayesian decay parameter estimations, in both stages of construction. The discomfort caused by the surplus sound energy within the stage tower, specifically the excessive late coming low frequency sound energy -boomy sound-, are validated by the double-slope sound energy decay within the hall. The desired acoustical comfort could only be provided when the multi-slope sound energy decays are overcome by sound absorptive treatment applications in stage tower and its auxiliary side and back spaces.

Neural network for multi-exponential sound energy decay analysis.

An established model for sound energy decay functions (EDFs) is the superposition of multiple exponentials and a noise term. This work proposes a neural-network-based approach for estimating the model parameters from EDFs. The network is trained on synthetic EDFs and evaluated on two large datasets of over 20 000 EDF measurements conducted in various acoustic environments. The evaluation shows that the proposed neural network architecture robustly estimates the model parameters from large datasets of measured EDFs while being lightweight and computationally efficient. An implementation of the proposed neural network is publicly available.

Experience with coupled spaces: From theory to practice

It has been more than a couple of decades since the interest in coupled volume systems started to grow rapidly among researchers. Basically, due to their increasingly popular applications in music halls for providing a rich acoustical environment either to fulfill the competing criteria of clarity and reverberance or simply to tune the auditoriums for multi-functional use. A lifelong experience with coupled spaces is the main motivation behind this paper. The journey starts with further developing the theoretical knowledge through scale model experiments. The results of which are utilized to observe the effects of the aperture size and shape on non-exponential sound energy decay by applying Bayesian analysis. The investigations have continued by field tests of real-size architectural monuments, specifically, worship spaces with multi-volume and domed typology. The relation of non-exponential energy decay and architectural parameters, for different scenarios or original uses of historical buildings, are searched through energy flow decays by applying the diffusion equation model. Simultaneously, all of these findings from academic research have been a source to produce acoustical design solutions for either small sized recording studios or large-scale multi-purpose auditoria in landmark buildings, all of which are briefly exemplified within this study.

On the acoustics of coupled volumes in the safavid architecture—Comparison of computer-modeled objective parameters of two historic buildings

One of the typical architectural prototypes in the Safavid era is the utilization of nested rooms for creating assembly spaces with spatial connectivity. Varied in geometry and size, each volume contributes differently to the acoustical environment. Shah Mosque prayer hall and Ali Qapu Palace music room are the two rooms that employ this organization system in their planning. Various simulations have been performed on 3D models of these architectural entities to study the mechanism of sound energy exchange and the impact of each volume on the perceived acoustic characteristics. The objective parameters were collected for both rooms and compared in various configurations to understand each cluster of space's impact on the overall acoustic experience. Furthermore, materials' properties, proportions, and architectural features are discussed as contributing factors to the sonic landscape. The result shows that the sound energy decay behaves differently mainly due to the two rooms' differences in scale and sound absorptive properties. The comparative analysis verifies some of the previous research on coupled volumes in which these two precedents exhibit a similar non-exponentialsound energy decay.

Theoretical analysis on structure of sound energy field decay of acoustical radiosity model with finite initial excitation.

The acoustical radiosity model (ARM) is a typical algorithm in geometrical acoustics to simulate the sound field in a room of ideally diffusely reflecting boundary. Even in such a room, the sound field decay is a complex process, as the relaxation of the sound field observed in simulations has shown. Based on the Laplace transform of the acoustical radiosity equation, this paper gives a set of properties of the ARM. It shows the system has a series of real or complex conjugate L-eigenvalues and corresponding L-eigenfunctions. Under the relaxation condition, the sound energy decay on the room boundary, generated by finite initial excitation, can be expanded as a summation of decay components, which are composed of real and/or complex conjugate decay modes. Each decay mode is a decaying and oscillating L-eigenfunction corresponding to an L-eigenvalue. The real part of the L-eigenvalue is the exponential decay rate, and the image part is the angular frequency of the oscillation. The reverberant sound field inside the room space has a similar decay structure to the boundary. As an example, the decay structure in a sphere is analyzed. The relaxation of the sound field is explained by the geometrical significance of the sound field decay.

Factors influencing scattering coefficient measurement accuracy in scaled reverberation room

The method described in ISO 17497-1 standard has been worldwide adopted to measure the random-incident scattering coefficient of irregular surfaces either in a full-size reverberation room or in a scale model. In practical measurements, the sound energy propagation and decay at high frequencies (over 10 kHz) are easily affected by small operating errors and by tiny changes in the measurement conditions. It is difficult to obtain the same accuracy of results in the scale model as that in a full-size reverberation room while maintaining the same setup in both tests as suggested in the standard. This study performed a series of experiments in a 1:10 scale reverberation room to investigate the influence of several practical aspects on measurement accuracy. A maximum length sequence diffuser, with a design frequency of 1700 Hz (full-size value), was used as the specimen. All results obtained in the scaled reverberation room were compared to the reference values measured in a full-size reverberation room. Five factors were studied, which included different recording methods (double-channel and eight-channel), number of source positions (one and four), number of receiver positions (one, two, four and eight), turntable rotation conditions (full-turn or half-turn rotation during T3 and T4 measurements), and numbers of averages (24, 36 and 72). The results show that the first three factors above have greater impacts on the measurement accuracy of the scale model experiments than the remaining factors. When the multichannel recording method and four source positions were used in the scaled tests, the measured scattering coefficient values were more reliable, appearing much closer to the reference data over the whole frequency range. Furthermore, applying a half-turn of the turntable (in reference to the measurements of the axisymmetric diffusers) and a 36-impulse coherent average can greatly reduce the test duration without decreasing the measurement accuracy.

Acoustical Impact of Architectonics and Material Features in the Lifespan of Two Monumental Sacred Structures

Hagia Sophia and Süleymaniye Mosque, built in the 6th and 16th centuries, respectively, are the two major monuments of the İstanbul World Heritage Site. Within the context of this study, sound fields of these two sacred multi-domed monumental structures are analyzed with a focus on their architectonic and material attributes and applied alterations in basic restoration works. A comprehensive study is undertaken by a comparative analysis over acoustical field tests held in different years and over an extensive literature review on their material and architectural characteristics. Initially, the major features of Hagia Sophia and Süleymaniye Mosque are presented, and later, basic alterations in regard to function and materials are provided. The methodology includes the field tests carried both within the scope of this research as well as the published test results by other researchers. Acoustical simulations are utilized for comparison of unoccupied versus occupied conditions and also for discussion on original materials. The impact of historical plasters on the acoustics of domed spaces is highlighted. Common room acoustics parameters as of reverberation time and clarity are utilized in comparisons. The formation of multi-slope sound energy decay is discussed in light of different spiritual and acoustical needs expected from such monumental sacred spaces.

Archaeoacoustic Examination of Lazarica Church

The acoustic analysis provides additional information on building tradition and related indoor practice that includes sound, thus deepening our understanding of architectural heritage. In this paper, the sound field of the Orthodox medieval church Lazarica (Kruševac city, Serbia) is examined. Lazarica is a representative of Morava architectural style, developed in the final period of the Serbian medieval state, when also the chanting art thrived, proving the importance of the aural environment in Serbian churches. The church plan is a combination of a traditional inscribed cross and a triconch. After the in situ measurement of acoustic impulse response using EASERA software, we built a computer model in the acoustic simulation software EASE and calibrated it accordingly. Following the parameters (reverberation time (T30), early decay time (EDT) and speech transmission index (STI)), we examined the acoustic effect of the space occupancy, central dome and the iconostasis. In all the cases, no significant deviation between T30 and EDT parameter was observed, which indicates uniform sound energy decay. Closing the dome with a flat ceiling did not show any significant impact on T30, but it lowered speech intelligibility. The height of iconostasis showed no significant influence on the acoustics of Lazarica church.

Diffusion equation modeling for sound energy flow analysis in multi domain structures.

This study investigates reliable models and methods to be applied in sound field analysis of multi-domain structures. The case structures are two monuments, namely, Süleymaniye Mosque and Hagia Sophia in İstanbul. These are both multi-volume spaces with many smaller sub-volumes coupled to each other by coupling apertures in form of arches. A key concern of the study is to examine energy flow decays and understand the mechanism of multi-slope sound energy decays. The methodology involves diffusion equation model (DEM) application in a finite-element scheme for sound energy flow analysis. Energy flow decays, energy flow dips, and spatial flow vectors are examined for single versus multi-domain DEM solutions. It is concluded that specification of different domains with individual diffusion coefficients is a critical setting such that, if not assigned correctly, may mislead the results. The energy flow vector analysis has enabled us to comprehend the architectural features in relation to such energy flow decay dip occurrence. The computational efficiency of DEM is also discussed. The DEM application in this study has proved to be a powerful and practical method in room acoustics applications, specifically for multi-rate decay investigations.

Diffusion equation modeling in sound field analysis of disproportionate rooms and coupled spaces

This study discusses alternative models and methods to be applied in room acoustics estimations for specific room types including disproportionate rooms and rooms with coupled volumes. A recent prediction method, namely, diffusion equation model (DEM) in room acoustic applications is utilized in the methodology, and this method is compared to common models as of statistical theory, image-source or ray-tracing techniques. Both long enclosures as of subway stations and coupled volumes as of multi-domain monumental structures are special cases with specific interior sound fields. Statistical theory is not always reliable in such extraordinary room forms, while ray tracing may tend to over or under estimate certain acoustical parameters. Thus, the application of DEM in a finite element scheme for detailed sound energy decay and sound flow analysis are held over some case structures. The results are compared to field tested data and ray-tracing solutions. Pros and cons of DEM in comparison to different methods are searched in detail considering the efficiency in visualization, computational speed, and reliability of acoustical parameter results for specific room shapes.This study discusses alternative models and methods to be applied in room acoustics estimations for specific room types including disproportionate rooms and rooms with coupled volumes. A recent prediction method, namely, diffusion equation model (DEM) in room acoustic applications is utilized in the methodology, and this method is compared to common models as of statistical theory, image-source or ray-tracing techniques. Both long enclosures as of subway stations and coupled volumes as of multi-domain monumental structures are special cases with specific interior sound fields. Statistical theory is not always reliable in such extraordinary room forms, while ray tracing may tend to over or under estimate certain acoustical parameters. Thus, the application of DEM in a finite element scheme for detailed sound energy decay and sound flow analysis are held over some case structures. The results are compared to field tested data and ray-tracing solutions. Pros and cons of DEM in comparison to different methods...

Design of a multiple-slope sound energy decay system with string and block coupling methods

Design of a multiple-slope sound energy decay system with string and block coupling methods

Assessment of Acoustical Indicators in Multi-domed Historic Structures by Non-exponential Energy Decay Analysis

The key concern of this study is to discuss the reliable acoustical metrics for analyzing particular sound fields within monumental multi-domed sacred spaces with an emphasis on multiple sound energy decay formation. The potential of such structures in featuring non-exponential sound energy decay characteristics necessitates new formulation of sound decay indicators in understanding of their sound fields. The early and late energy decay components within non-exponential sound energy decays can have a unique contribution to the interior acoustic quality. These acoustical features can also provide the functional and spiritual acoustical needs of monumental sacred spaces. Suleymaniye Mosque and Hagia Sophia, two major monuments of Istanbul World Heritage Site, are examined in this regard. Field measurements are the main method of data collection. Over collected room impulse responses, relevant acoustical predictors including decay rates and decay times are computed by applying Bayesian decay parameter estimation. Analysis results disclose double or triple decay formations in both structures. Authors argue that, the detection of multiple sound energy decays in analyzed structures sets out a new vision for room acoustics studies of sacred spaces and for multi-domed monuments. Thus, implementation of new metrics, namely multiple slope decay parameters to replace classical room acoustics indicators, is recommended and discussed in light of the outcomes of this study.

Características arquitetônicas e o decaimento sonoro de salas acopladas: uma revisão da literatura

Nas últimas décadas, o crescente número de salas de concerto construídas com variabilidade acústica impulsionou o estudo acústico de salas acopladas. Esta variabilidade tem sido feita de diversas formas, sendo uma delas o acoplamento de câmaras reverberantes na sala principal de espetáculos. Salas acopladas propiciam um decaimento de energia sonora diferenciado, a energia decai de forma não exponencial. As características arquitetônicas do espaço têm influência direta na formação do decaimento não exponencial de energia sonora. Os objetivos deste trabalho são identificar e analisar, na literatura, as características e parâmetros arquitetônicos propostos ao longo dos anos que influenciam a formação de curvas de decaimento de energia não exponencial em salas acopladas. O trabalho foi desenvolvido empregando a revisão sistemática da literatura (RSL), realizada em três etapas: Planejamento, Condução da Revisão e Análise de Dados. Os resultados mostraram que a combinação de três características arquitetônicas são as responsáveis pela formação de curvas de decaimento não exponencial de energia. A relação entre estas características foi sistematizada em três parâmetros arquitetônicos, a saber: a Área de Acoplamento, que é a razão entre a área de abertura de acoplamento e a área total da sala principal, a Razão de Volumes, que é a razão entre os volumes da sala acoplada e da sala principal e a Razão de Absorção, que é a razão entre a absorção equivalente da sala acoplada e da sala principal. A RSL permitiu avaliar o estado da arte sobre o assunto, identificar o período de maior interesse nas pesquisas sobre salas acopladas e observar a aplicação da teoria de salas acopladas para compreensão da acústica de igrejas e catedrais. Foi possível encontrar lacunas em pesquisas relacionadas à psicoacústica de salas acopladas e dos parâmetros arquitetônicos razão de volumes e razão de absorção além de identificar a necessidade em pesquisas de acoplamento de caixa cênica em teatros. Os resultados deste trabalho fornecem subsídios para serem empregados na elaboração de projetos acústicos de ambientes que se utilizam de salas acopladas para sua adequação acústica.

Investigations on sound energy decays and flows in a monumental mosque.

This work investigates the sound energy decays and flows in the Süleymaniye Mosque in İstanbul. This is a single-space superstructure having multiple domes. The study searches for the non-exponential sound energy decay characteristics. The effect of different material surfaces and volumetric contributions are investigated using acoustic simulations and in situ acoustical measurements. Sound energy decay rates are estimated by Bayesian decay analysis. The measured data reveal double- or triple-slope energy decay profiles within the superstructure. To shed light on the mechanism of energy exchanges resulting in multi-slope decay, spatial sound energy distributions and energy flow vectors are studied by diffusion equation model (DEM) simulations. The resulting sound energy flow vector maps highlight the contribution of a sound-reflective central dome contrasted with an absorptive carpeted floor in providing delayed energy feedback. In contrast, no multi-slope energy decay pattern is observed in DEM simulations with a bare marble floor, which generates a much more diffuse sound field than in the real situation with a carpeted floor. The results demonstrate that energy fragmentation, in support of the non-exponential energy decay profile, is due to both the sound absorption characteristics of materials and to their distributions, as well as to relations between the subvolumes of the mosque's interior.

Perceived suitability of reverberation in large coupled volume concert halls.

Large acoustically coupled volumes can be found in a variety of places such as churches, factories, train stations, and concert halls, where sound reverberation occurs. In recent decades, coupled volume concert halls have garnered increasing attention (Beranek, 2004) as the use of reverberation chambers can provide both sound clarity and reverberance due to the nonexponential temporal sound energy decay. Furthermore, variations of clarity and reverberance are essentially controlled by modifying the coupling area between the adjacent volumes. The present study focuses on the appreciation of changes in reverberation in terms of perceived suitability for different musical instruments or ensembles. Reverberation is often described in terms of reverberation time (reaction time [RT]), defined as the time required for the energy of a stopped sound to decay by 60 dB. However this metric does not provide a unique quantification of the decay profile and is therefore not sufficient to characterize nonexponential decays. To focus the study on physically possible variations of a given architectural space, the present study relies on variations of an architectural element, the coupling area, which embeds acoustical parameter variations, estimated from room impulse responses. Participants were asked to rate the suitability of reverberation settings for different instruments and ensembles. The sound stimuli were synthesized with an auralization method, providing control over the coupling area.Previous ResearchSingle volume concert halls have been widely studied while in comparison little research has been conducted on perceptual aspects of coupled volume concert halls. Perceptual thresholds, or just noticeable differences (JND), based on reverberation time have been estimated in large single volume rooms (Billon & Embrechts, 2012; Katz, 2004; Seraphim, 1958) and were found to lie between 5% and 10% of a given RT value (for RT 1.0 sec). In coupled volume concert halls, a recent study (Luizard et al., 2013; Luizard et al., 2015) based on an architectural parameter whose variations affect the room reverberance found a perceptual threshold of changes of 10% of a given open coupling area.Previous research has determined that although discrimination performance does not seem to depend on sound material (Frissen et al., 2010), reverberation preference, or evaluation, depends on the sound material (Frissen et al., 2010; Kuhl, 1954) proposed to the listeners. Preference for reverberation in the context of concert hall design has been previously studied (Ando et al., 1997) with the definition of four subjective criteria: sound level, initial time delay gap, reverberance, and interaural cross correlation; these acoustical parameters being defined in the ISO standard (ISO 3382-1, 2009). Another study (Ando et al., 1982) in single volume concert halls has shown that long reverberation times (around 2.7 sec.) were preferred for baroque music played with an orchestra, slow classical music required lower RTs (around 1.2 sec.) and preferred RTs for speech were 0.3 sec. However, another research group (Schroeder et al., 1974) has tested one of these classical music pieces using the characteristics of 11 concert halls and listeners preferred the stimuli corresponding to an RT 2.0 sec. This discrepancy can be explained by variations in stimuli parameters other than RT, such as initial time delay gap or interaural cross correlation, which are linked to spatial aspects and depend on the room geometry. Preference of reverberation in coupled volumes as compared to single-slope reverberation has been studied (Ermann, 2007) by means of listening tests with sound stimuli generated by ray-tracing software with no significant differences being observed between single-slope and double-slope reverberation.Preference of reverberation within coupled spaces has also been studied (Bradley & Wang, 2010) by means of geometrical acoustics simulations with participants preferring low to medium levels of decay curvature, as compared to high levels of curvature and classical linear slope exponential reverberation. …

Investigations on acoustical coupling within single-space monumental structures using a diffusion equation model

Sound energy distributions and flows within single-space rooms can be exploited to understand the occurrence of multi-slope decays. In this work, a real-size monumental worship space is selected for investigations of non-exponential sound energy decays. Previous field tests in this single-space venue indicate multi-slope formation within such a large volume and the multiple-dome upper structure layout. In order to illuminate/reveal the probable reasons of non-exponential sound energy decays within such an architectural venue, sound energy distributions and energy flows are investigated. Due to its computational efficiency and advantages in spatial energy density and flow vector analysis, a diffusion equation model (DEM) is applied for modeling sound field of the monumental worship space. Preliminary studies indicate good agreement for overall energy decay time estimations among experimental field and DEM results. The energy flow vector and energy distribution analysis indicate the upper central dome-structure to be the potential energy accumulation/ concentration zone, contributing to the later energy decays.

Multiple-slope sound energy decay investigations in single space enclosures with specific geometrical and material attributes

Acoustical coupling until now has basically been studied to define the peculiar sound field within acoustically coupled enclosures in which multiple-slope energy decays can often be observed. The key concern of this study is to reveal the potential of multiple-slope energy decay formation in over-size single space structures with particular geometry and distribution of materials in different acoustical performance characteristics. Specifically, multiple dome superstructures, composed of one central dome supported by semi-domes and transitional elements, are selected for the case studies. The interpretation of the acquired data is carried in order to broaden the definition of “the coupled volume system” with an emphasis on invisible sources and apertures of acoustical coupling in a “single volume system.” The methodology of the research involves joint use of in-situ acoustical measurements, acoustical modeling/simulation methods, and computational analyses. Bayesian analysis approach is applied in quantify...

Energy decay analysis in coupled volumes using an acoustic wave simulator

The acoustics in coupled volumes present various challenges. For example, the sound energy decay curve is double-sloped indicating that a single reverberation time cannot be assigned to coupled volumes. Such a behavior depends on various factors like the aperture sizes between the coupled volumes, absorption coefficients of each volume, etc. Recently, many studies using computer simulation have been performed to better understand the acoustic behavior of coupled volumes. None of these studies perform full 3D acoustic wave simulation on coupled volumes as they are regarded as computationally expensive and limited to very small spaces. We perform acoustic wave simulation using a relatively new wave solver called adaptive rectangular decomposition (ARD). ARD is more accurate than geometric acoustics techniques. It has been demonstrated to provide reliable simulation results through comparison with measurement data in indoor and outdoor scenes. Furthermore, it is practical and can handle large acoustic spaces on a single desktop. In this study, we analyze energy decay curves in coupled volumes using ARD. We perform numerical simulation for various coupled volume configurations such as varying aperture sizes, absorption coefficients, etc., and present their decay curves for analysis.