Reverberant Sound Field Research Articles

Interlaboratory comparison of ISO 354 sound absorption coefficient measurements for four sound absorbing materials

Sound absorption coefficients are among the most important acoustic parameters of building materials. The coefficients are measured in reverberation chambers using the ISO354 measurement procedure. The complex reverberant sound field that builds up in such facilities is closely related to the concept of the diffuse sound field and is difficult to characterize experimentally. Due to the limited quantitative assessment of the sound field, there is no general agreement in the scientific community on how to improve the method of measuring sound absorption coefficients, although significant differences have been reported between the results of different laboratories. To address part of this challenge, we investigate how specific the variations between laboratory results are for a particular material. In our investigation, we evaluated four different sound absorbing materials in five independent acoustics laboratories. Four of the reverberation chambers used suspended diffusers, while the complex shape of one chamber was designed to achieve a diffuse sound field. The results show that the interlaboratory deviations are not very specific to the material tested, while general differences between the facilities can be observed. Furthermore, the meticulous geometric design of the chambers can be seen as an alternative to the use of suspended diffusers.

Simulated analysis and experimental validation of sound field distribution regularity for a large-scale non-anechoic harbor pool

The large-scale underwater space, such as large water pool or large-scale harbor pool can provide a good experimental environment for the measurement of the underwater radiated noise of vessel. However, it's not as simple as measuring the sound power of a small machine in the air, the measurement and evaluation of the low frequency mechanical noise and radiated sound power of vessel requires a specific reverberation environment in the large-scale underwater space. Therefore, in this paper, the reverberant sound field characteristics of large-scale underwater space are simulated and calculated by finite element analysis, and experimental measurements are carried out in the large-scale harbor pool. It was found the cut-off frequency of large-scale underwater space depends on the depth of the water pool, and the lower limit frequency depends on the volume of the water pool. The dock door does not reduce the spatial average sound pressure in the reverberation sound field, the floating box platform does not effect on the cut-off frequency but has an effect on the sound energy of the reverberant sound field. It is possible to select the appropriate underwater experimental environment for the measurement and evaluation of different mechanical noise sources. The sound pressure level obtained by calculating the sound source at different locations in the reverberation area is basically the same, and in a 16 × 22 hydrophone arrays, more than 160 array elements are selected, each between 0.25 m and 1 m, a stable sound pressure level can be obtained through spatial averaging. Through experimental measurement verification in the large-scale harbor pool, low-frequency sound sources are emitted from 6 different positions, three hydrophone arrays data are collected, and the measured sound pressure level error is within 1.4 dB. These conclusions are conducive to the actual measurement and evaluation of noise sources of vessel.

Key comparison CCAUV.W-K2: features of hydrophone calibration

The results of key comparison are the most convincing and objective indicator of confirmation of the correctness and accuracy of the newly developed measurement method. The results of comparison and measurement methods applied at the second key comparison of national standards of the unit of sound pressure in water CCAUV.W-K2, organized by the Consultative Committee for Acoustics, Ultrasound and Vibration of the International Committee for Weights and Measures, are described. A feature of the comparison is that the calibration range has been expanded into the low frequency region by two octaves compared to the first key comparison CCAUV.W-K1. The results of the CCAUV.W-K2 comparison were considered successful. Important scientific results of participation in the comparison were confirmation of: the correctness of the hydrophone free-field calibration methods developed at VNIIFTRI (at ultra-low frequencies for a sound-reflecting water tank and in the noise reverberant sound field of the water tank), the equivalence of the calibration results when radiating signals of various types: chirp, noise and ton-burst. In the process of performing control calibrations, the pilot laboratory discovered violations of the stability of the reference hydrophone of comparison. When comparing the results obtained by participants, there was an increase in the discrepancy between the results in the frequency range 60–100 kHz, which is considered the least problematic.

Reverberant Sound Field Analysis of a Rectangular Room by Modal Synthesis Method

It is well known that the reverberation time within an enclosed space is dominated by its boundary surface absorption. The absorption can then be interpreted as averaged damping ratio of acoustical modes or a loss factor. The damping ratio can be determined during steady state excitation or during the transient decay or reverberation process. In this paper, acoustical reverberant field is considered as a synthesis of independent acoustical modes with their corresponding damping ratios. Each damping ratio is calculated from the absorption coefficient of the enclosed space considering the wavenumber vector. It is suggested that the consideration for the wave travelling direction in determining the modal decay rate give better results for a simple rectangular room.

Effect of reference value and ensemble size on perception of reverberation in simulated listening environments

Reverberation time is an important metric characterizing one of the key differences between performance venues caused by various furnishing, materials, and geometry within such spaces. To justify alterations to a venue, architects and acousticians refer to the just-noticeable-difference (JND) of reverberation time, cited in the ISO 3382-1 room acoustics standard as 5% of the reference value. This JND was determined experimentally using impulsive noise with varying reverberation. In real performance venues, overlapping and simultaneous sounds are more common than isolated impulses. As such, the JND noted in literature may not provide a complete picture of perceived reverberation for persons listening to live performed music. For this study, multiple test methods were evaluated by using different reference reverberation times as well as using a variety of instrumentation and genres for musical signals. Results were generated using test participants who were asked to listen to multiple virtual soundfields and provide subjective evaluation. Reverberant soundfields were recreated in an anechoic listening environment and auralizations were produced using ODEON room acoustics software. Results indicated statistically significant mean differences in perceived reverberation across instrumentation subsets, genre subsets, as well as through different testing configurations. [Work supported by The Paul S. Veneklasen Research Foundation.]

Experimental reconstruction of sound fields over large spatial domains

This talk discusses sensing methods and reconstruction techniques for characterizing sound fields over large spatial domains. We focus specifically on reconstructing reverberant soundfields in rooms and enclosures. Two complementary approaches are presented in the talk: on the one hand, we present a method that leverages on modeling the spatio-temporal and statistical properties of enclosed sound fields via wave expansions, enabling to estimate the sound field over a large volume of space. On the other hand, we present a Physics Informed Neural Network, which learns the governing wave equation using a small set of measured data and enables to meaningfully interpolate and extrapolate the sound field to any position where no observations are available. Experiments in real rooms are presented, including an opera hall and an auditoria for oral communication. The experiments successfully demonstrate the volumetric acquisition and three-dimensional characterization of the sound fields. The presented techniques can be of relevance in applications pertaining to immersive and navigable audio, architectural acoustics and heritage preservation.

A modal expansion method for simulating reverberant sound fields generated by a directional source in a rectangular enclosure

The prediction of reverberant sound fields generated by a directional source is of great interest because practical sound sources are not omnidirectional, especially at high frequencies. For an arbitrary directional source described by cylindrical and spherical harmonics, this paper developed a modal expansion method for calculating the reverberant sound field generated by such a source in both two-dimensional and three-dimensional rectangular enclosures with finite impedance walls. The key is to express the modal source density using the cylindrical or spherical harmonic expansion coefficients of the directional source. A method based on the fast Fourier transform is proposed to enable the fast computation of the summation of enclosure modes when walls are lightly damped or rigid. This makes it possible to obtain accurate reverberant sound fields even in a large room and/or at high frequencies with a relatively low computational load. Numerical results with several typical directional sources are presented. The efficiency and the accuracy of the proposed method are validated by the comparison to the results obtained using the finite element method.

Bayesian selection of plane-wave decomposition models.

Plane-wave decompositions, whereby a measured sound field is described as a superposition of plane waves, are central to many applications in acoustics and audio engineering. This letter applies a Bayesian probabilistic inference framework to the plane wave decomposition problem and examines the Deviance Information Criterion (DIC) for selecting the optimum number of waves in the decomposition. The framework learns the model directly from the data and, as such, adapts to the wavefield under study. The DIC is applied to data measured in two reverberant sound fields (highly-reverberant and lightly-damped) to determine the simplest models providing the preferred fit to the data.

Effect of musical instrumentation on perception of reverberation in simulated listening environments

The reverberance of a performance venue is often characterized by an important metric, reverberation time. In order for architects, acousticians, and performers to better understand the value of knowing and predicting the reverberation time in different spaces, the just-noticeable-difference (JND) is often cited. The established JND for reverberation time is approximately 5% of the reference reverberation, noted in the standard ISO 3382-1. This value was determined using impulsive sound, meaning it may not provide a complete picture for applications related to music. This study aimed to evaluate several elements of musical performance that may alter the perception of reverberation in a simulated listening environment. Primarily, the effect of instrumentation was investigated, including the use of solo, small ensemble, full orchestra, and vocal recordings for comparison. Results were generated using test participants listening to multiple soundfields and providing subjective evaluation. Reverberant soundfields were created in an anechoic listening environment and auralizations were produced using ODEON room acoustics software. Results indicated statistically significant mean differences in reverberation perception between musical instrumentation groups used during experiments. [Work supported by The Paul S. Veneklasen Research Foundation.]

Applicability and reliability of an experimental method measuring underwater acoustic radiation efficiency of floating box-type plate structures in a reverberant water tank

This paper aims to investigate the applicability and reliability of an experimental method measuring the underwater acoustic radiation efficiencies of floating plate structures in a reverberant water tank. For the purpose, an experimental method for estimating the acoustic power of a source in a reverberant sound field has been introduced and applied to measure the acoustic radiation efficiencies of two floating box-type plate structures excited by a logarithmic sine sweeping force in a water tank. The validity of the adopted experimental method has been examined by the comparison with numerical results obtained by a fully coupled vibroacoustic analysis with an infinite radiation boundary condition for the structures. From the results, it is confirmed that the experimental method for measuring the underwater acoustic radiation efficiency of floating plate structures in a reverberant water tank is reliably applicable for high-frequency ranges above the Schroeder frequency of the water tank.

Acoustic analysis of a metasurface for normal and random incidence sound waves

This article proposes an acoustic metasurface (AMS) capable of effectively absorbing sound frequencies in the range of 100−800 Hz. The input and airborne impedances are combined considering incident normal and oblique sound waves, and the sound absorption capacity is presented analytically and numerically. Results of 99% sound absorption under normal incidence are obtained experimentally. Considering the radiation impedance of the Thomasson and Paris' models the analytical study of the sound absorption of different samples of the absorber in diffuse field is discussed. The results are coherent and confirm the influence of the sample area on its acoustic performance. This approach provides a practical and reliable procedure for evaluating the behavior of the AMS in a reverberant sound field.

Development of direct acoustic energy flow analysis (DAEFA) for ship cabin noise in the medium-to-high frequency range

Noise analysis from heating, ventilation and air conditioning (HVAC) elements in ship cabins is needed to satisfy the strict noise regulation for the ship cabin, and it is very important for their effects to be evaluated in the early stage of design. In this paper, a direct acoustic energy flow analysis (DAEFA) model is presented for the noise analysis of the ship cabin to reflect direct fields of the sources from an HVAC element. Total acoustic fields are considered by deriving the fundamental solution of the energy flow model for direct and reverberant fields in a closed space. Sound propagation in the direct field is implemented using the geometrical acoustics concept, and noise sources introduced into the reverberant sound fields are considered by using the relationship between direct fields and the closed space boundaries. For cabin noise analysis using DAEFA, interior boundaries of the cabin are discretized, and boundary integral formulations for each field are integrated. Noise analysis is performed for various cases with the DAEFA model to minimize cabin noise. The optimal design derived through the analysis was applied to an actual ship, and cabin noise measurement was conducted onboard the applied ship. Comparison of the analysis and measurement results confirms the effectiveness of the proposed design.

Time-frequency-dependent directional analysis of room reflections using eigenbeam processing and von Mises-Fisher clustering.

The knowledge of frequency-dependent spatiotemporal features of the reflected soundfield is essential in optimizing the perception quality of spatial audio applications. For this purpose, we need a reliable room acoustic analyzer that can conceive the spatial variations in a decaying reflected soundfield according to the frequency-dependent surface properties and source directivity. This paper introduces a time-frequency-dependent angular reflection power distribution model represented by a von Mises-Fisher (vMF) mixture function to facilitate manifold analysis of a reverberant soundfield. The proposed approach utilizes the spatial correlation of higher-order eigenbeams to deduce the directional reflection power vectors, which are then synthesized into a vMF mixture model. The experimental study demonstrates the directional power variations of early reflections and late reverberations across different frequencies. This work also introduces a measure called the directivity time-span to quantify the duration of anisotropic reflections before it decays into a totally diffused field. We validate the subband performance by comparing it with the eigenbeam multiple signal classification method. The results prove the influence of source position, source directivity, and room environment in the distribution of reflection power, whereas the directivity time-span behaves independent of the source positions.

Sound field reproduction using multilayer equivalent source method

Sound field reproduction aims to create or reproduce a desired sound environment, where both the audio content and the spatial property of the sound field are preserved. For a practical reproduction system which is usually placed in a real 'listening room', acoustic transfer function measurement of the loudspeaker array is a time consuming work. The equivalent source method is an option to interpolate loudspeaker array acoustic transfer functions over the target region in reverberant sound field and has been implemented in the preceding researches. However, the selection of the optimized distances of the equivalent sources remains a challenging problem, especially considering the complex acoustic environment in reverberant room. In this work, we apply a multilayer equivalent source method. A simulation is conducted in virtual listening rooms with different reverberation conditions to investigate the reproduction performance of the proposed method. The comparison with the conventional single layer equivalent source method is provided.

A 2.5D acoustic finite element method applied to railway acoustics

Railway acoustic problems commonly have a constant cross-section and uniform properties in the longitudinal direction. To solve such 3D acoustic problems with reduced effort, a wavenumber domain acoustic finite element (2.5D acoustic FE) method is introduced in which the cross-section of the domain is meshed and the third dimension is represented by a wavenumber transform. The acoustic wavenumber is thereby decomposed into a combination of wavenumbers in the x direction and in the y-z plane. The method is extended to exterior noise problems by including a perfectly matched layer (PML) with bespoke absorption to prevent reflection of the sound waves at the boundary of the domain. The method as presented can be used with 2D finite element solutions from commercial software. To verify the application of the 2.5D acoustic FE method for interior acoustic problems, sound attenuation in a tunnel is predicted and compared with existing measurements. To verify the implementation for exterior acoustic problems, an example is given of the sound distribution on the side surface of a train due to a compact source below it. The comparison of the solutions obtained from the 2.5D acoustic FE models with measurements shows good agreement in the both validation cases. The method is then used to investigate the effect of the tunnel walls on the sound distribution on the train external surface by comparing the results with the case in the open field. A highly reverberant sound field is found in tunnels, which increases the sound pressure level on the train side-surface above 250 Hz by about 10 dB for a tunnel with a ballasted track and by about a further 6 dB for a slab track.

On the representation of wavefronts localized in space-time and wavenumber-frequency domains.

This Letter reports evidence suggesting a representation system for transient waves with band limited spectra, referred to here as localized waves in the space-time and wavenumber-frequency domains. A theoretical analysis with a transient monopole shows that the wavenumber-frequency pressure spectrum is distributed over hyperbolic regions of propagating waves and evanescent waves. An experimental analysis is performed, applying dictionary learning to reverberant sound fields measured with a microphone array in three rooms. The learned components appear to be related by analytical transformations in the spectra, suggesting a partitioning characterized by hyperbolic dispersion curves and multiple directions and times of arrival.

Perceptual implications of different Ambisonics-based methods for binaural reverberation.

Reverberation is essential for the realistic auralisation of enclosed spaces. However, it can be computationally expensive to render with high fidelity and, in practice, simplified models are typically used to lower costs while preserving perceived quality. Ambisonics-based methods may be employed to this purpose as they allow us to render a reverberant sound field more efficiently by limiting its spatial resolution. The present study explores the perceptual impact of two simplifications of Ambisonics-based binaural reverberation that aim to improve efficiency. First, a "hybrid Ambisonics" approach is proposed in which the direct sound path is generated by convolution with a spatially dense head related impulse response set, separately from reverberation. Second, the reverberant virtual loudspeaker method (RVL) is presented as a computationally efficient approach to dynamically render binaural reverberation for multiple sources with the potential limitation of inaccurately simulating listener's head rotations. Numerical and perceptual evaluations suggest that the perceived quality of hybrid Ambisonics auralisations of two measured rooms ceased to improve beyond the third order, which is a lower threshold than what was found by previous studies in which the direct sound path was not processed separately. Additionally, RVL is shown to produce auralisations with comparable perceived quality to Ambisonics renderings.

Isotropy in decaying reverberant sound fields.

A method of evaluating sound field isotropy in decaying reverberant sound fields is presented. The proposed method extends the experimental framework outlined in [J. Acoust. Soc. Am. 143(4), 2514-2526 (2018)] and analyzes the decaying sound field in a reverberation room. Spatio-temporal measurements of the sound field are obtained, and a wavenumber decomposition is performed as a function of time, which serves to examine the directional properties of the sound field and its angular symmetry. Experimental results are obtained in a reverberation room in four different configurations (the empty room, with an absorber on the floor, with panel diffusers, and without them). The results demonstrate how isotropy tends to increase or decrease as a function of time, depending on the disposition of the diffusing and absorbing elements. Diffusers are found to effectively redirect the energy in the room, although they do not succeed in generating a uniform incidence on the sample. The proposed approach makes it possible to analyze the specific processes occurring in a reverberation chamber and can provide valuable insights in the process of standardization to verify the directional properties found in each reverberation room.

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.

Two definitions of the inner product of modes and their use in calculating non-diffuse reverberant sound fields.

There are two definitions of the inner product of modal spatial functions used in the literature. Both definitions integrate the product of the modal spatial functions over a line, area, or volume. The only difference is that one of the definitions takes the complex conjugate of one of the modal spatial functions before multiplying the modes together. The definitions are the same if the modal spatial functions are real. If the modal spatial functions are complex, only the definition which takes the complex conjugate is an inner product. If the specific acoustic impedance of the boundaries has a real part, then the modes are only orthogonal with the definition which does not take the complex conjugate, although this definition is not strictly an inner product because the modal spatial functions are complex in this situation. However, this definition of "inner product" can be used to calculate the coefficients in the modal expansion of the system response. On the other hand, when it comes to calculating the mean pressure squared and the mean sound intensity, the modal spatial functions cross-products cannot be ignored because the modes are not orthogonal for the definition which takes the complex conjugate.