Sound field modeling in streets by a diffusion equation

The transport theory of sound particles is applied to the sound field modeling in an empty street canyon with partially diffusely reflecting facades. A diffusion equation is then derived to predict the sound field distribution and the sound decay in the street. The main parameter, namely the diffusion coefficient, is a function of the street width and the acoustic reflection laws of both building facades. For a single rectangular street, analytical solutions can be found. For more complex urban spaces, a finite-element based approach is proposed. Several numerical examples are given, like the sound propagation in a street with a nonuniform cros section, and in street intersections, for point and line sources. In comparison with ray-tracing-based models, the diffusion model requires less computation time and could be applied to the calculation of a sound map for large urban areas. However, at the present time, the diffusion coefficient can be calculated only for simple building reflection laws, like the Lambert’s one.

In recent years, the use of data-driven methods in sound field analysis has advanced rapidly. These approaches often require a large number of observations, which are scarce in acoustics. Hybrid approaches offer a promising alternative by integrating computational techniques with sound field models and theoretical considerations, thereby restricting the solution space. This work introduces a Bayesian framework for sound field reconstruction that incorporates general acoustic constraints through prior distributions. The framework presents a modular design, whereby multiple sound field models (plane waves, spherical waves and diffuse kernel) can be used, as well as regularization in both time and frequency domains. Additionally, the Bayesian formulation enables cross-frequency information sharing by selecting the appropriate frequency covariance matrix. The framework’s performance is evaluated in two different real-life scenarios, including interpolation and extrapolation from the measurement array. This comparison highlights that the optimal sound field model is contingent on the characteristics of the observed sound field. The outcome of this study is twofold: first, it presents a modular framework that merges classical sound field reconstruction methods with a Bayesian inference formulation; second, it evaluates the performance of different reconstruction methods in different experimental scenarios.

Sound fields in realistic rooms were simulated by different kinds of computational methods, and comparisons were conducted. One is based on the wave acoustics and the other is based on the geometrical acoustics, i.e., the finite-element method (FEM) and the conical beam method (CBM). As for the software applied here, the authors have developed their own FEM code, namely LsFE-SFA, to conduct FEM computations, and they employed commercial software, i.e. raynoise, to conduct CBM computations. First, theoretical basis of LsFE-SFA was given briefly. Next, sound-pressure distributions in a reverberation room with the volume of 165 cubic meters were computed by both methods to compare the agreement with measured sound-pressure levels. The boundary conditions due to the sound absorption were changed to examine the relation between the absorbent condition and the agreements. The agreement between FEM and measurement were found to be better throughout the examination. Next, both FEM and CBM were applied onto the analysis of large-scale sound fields in a multipurpose hall with the volume of 37<th>000 cubic meters to discuss the agreement and difference in detail.

The eigenmode and free‐wave models of steady‐state reverberant sound field in rooms are sometimes mistakenly believed to be unrelated representations. These two models are shown to coincide for the case of rectangular rooms, for which the axial, tangential, and oblique modes can be decomposed into two, four and eight travelling plane waves, respectively. (This was pointed out by Morse and Bolt [Rev. Mod. Phys. 16 (2), 85 (1944)].) Above the frequency of modal overlap, therefore, the reverberant sound field in a rectangular room may be viewed as an ensemble of many plane waves arriving from many directions in space. This provides justification for use of the free‐wave model.

In order to study the problem that the array manifold of conformal arrays deviates from the ideal value due to the sound scattering caused by the rigid baffles of arrays, in this paper, the influence of the scattering phenomenon caused by the rigid baffle on the receiving response of array is analyzed by using sound field prediction method based on a conformal array-semi-cylindrical volume array. The sound field distribution of conformal array at different angles is calculated by using the sound field modeling and simulation. Based on the above distribution, an actual array manifold is constructed under consideration of rigid barrier, and its variation under the influence of scattered sound is analyzed. The variation is described by two physical quantities defined in this paper: the first-order response composed of amplitude and phase and the second-order response composed of cross-correlation. Simulation shows that compared with the ideal model, the scattered signals generated by rigid baffles on conformal array varies with the azimuth and signal-to-noise ratio(SNR), which further leads to the deviation of each hydrophone of conformal array. The experimental data verifies that the simulation results are basically consistent with the actual situation. The effect of the scattering on the conformal array should be considered when designing and performing in practice.

Prediction of sound fields in rooms using statistical energy analysis

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

Guidance on efficient methods is needed for the practical application of modeling the sound field from broadband sources such as vessels, seismic surveys, and construction activities. These sound field models are employed for estimating how changes in the soundscape will affect marine life. For efficiency, acoustic propagation modeling is often performed in bands (decidecade or 13-octave), where propagation loss modeled for central frequency is assumed to represent an average propagation loss in the band. This shortcut comes at the expense of accuracy, which can be rectified by averaging the propagation loss across many frequencies in the band. Alternately, the equivalence of range and frequency averaging was shown by Harrison and Harrison [J. Acoust. Soc. Am. 97, 1314-1317 (1995)]. However, when and how to apply range averaging required further investigations. A simple environment with a flat sandy bottom and an isovelocity water-column sound speed profile was considered to test the agreement between the range and frequency averages for decidecade bands typically considered in soundscape modelling (10-1000 Hz). The optimal range smoothing window is a Gaussian window with a width of 10%-16% of the range from the source that switches to a width fixed beyond 20 km distance from the source.

Scattering coefficients (SCs) are crucial for modeling room sound fields in rooms. Due to the lack of SCs on many practical surfaces and room objects, this study aims to derive a relation between surface SCs and the angulardependent<br/>SCs obtained by a spherical receiver array in the room. The work is based on a computational approach. The sound field at a spherical receiver array is computed for a room with and without surface scattering at the room<br/>boundaries. A hybrid model of the Image Source Model and the Radiosity Model is used for this purpose. The sound field on the spherical receiver is then decomposed into plane waves, leading to ambisonic impulse responses<br/>(IRs). Then, the angular-dependent SCs are derived from these ambisonic IRs in both scenarios with a coherence method. Results show that angular-dependent SCs vary significantly depending on the apparent area of scattering<br/>surfaces as seen from the receiver, and a qualitative relationship between surface SCs and angular-dependent SCs is observed. This approach offers a promising framework for quantifying the scattering properties of room boundaries<br/>based on spherical array receivers.

Eigenfrequencies are found in sound fields in rooms by analyzing wave equations for a rectangular room surrounded by hard walls. The relationship between eigenfrequencies and eigenfunctions holds well for the wave equations as well as for linear equations. It might be quite rare to see a perfectly rectangular room in our daily life, but, room acoustics in rectangular rooms provide a good fundamental basis for better understanding of room acoustics in general. Representation of an impulse response and its frequency characteristics can be derived using the Green function in a rectangular room. Consequently, the wave theoretic representation of a sound field is derived from the expression in terms of geometric acoustics, such as the mirror image theory. Finally, a general solution form of the wave equation is presented using an integration formula in three-dimensional space.

The use of image and ray tracing methods (and variations thereof) for the computation of sound fields in rooms is relatively well developed. In their regime of validity, both methods work well for prediction in rooms with small amounts of diffraction and mostly specular reflection at the walls. While extensions to the method to include diffuse reflections and diffraction have been made, they are limited at best. In the fields of illumination and computer graphics the ray tracing and image methods are joined by another method called luminous radiative transfer or radiosity. In radiosity, an energy balance between surfaces is computed assuming diffuse reflection at the reflective surfaces. Because the interaction between surfaces is constant, much of the computation required for sound field prediction with multiple or moving source and receiver positions can be reduced. In acoustics the radiosity method has had little attention because of the problems of diffraction and specular reflection. The utility of radiosity in acoustics and an approach to a useful development of the method for acoustics will be presented. The method looks especially useful for sound level prediction in industrial and office environments. [Work supported by NSF.]

In 1939, Dr. Dah-You Maa presented a paper entitled "The Distribution of Eigentones in a Rectangular Chamber at Lower Frequency Ranges" [D. Y. Maa, J. Acoust. Soc. Am. 10, 258 (1939)]. Since then, his interest in room acoustics has not diminished. More than six decades later, Maa proposed an idea of adding a monopole solution to the normal modal expansion to improve the accuracy in simulating the near-field sound field in rooms [D. Y. Maa, Acta Acust. (Beijing) 27, 385-388 (2002)]. Following this idea, a hybrid model that combines the free field Green's function and a modal expansion has been proposed by the authors based on a rigorous mathematical derivation [B. Xu et al, J. Acoust. Soc. Am.128, 2857-2867 (2010)]. The hybrid modal expansion can be further extended for complex sound sources by introducing the multipole expansion to the solution. In this paper, the theoretical derivation of the hybrid modal expansion will be reviewed, followed by examples demonstrating the use of the hybrid modal expansion in real-world applications.

In the Bergeron method [Shimoda et al., Trans. Inst. Electron. Commun. Eng. Jpn., Part A 72, 1–11 (1989); English transl., 1989 Electron. Commun. Jpn., Vol. 72; Scripta Technica, Inc. (Wiley, New York, 1990)], sound reflection surfaces in rooms are modeled by the simple resistances corresponding to the rigid walls. And the low-frequency responses for a middle scale of auditorium are agreed preferably with the real fields [K. Nakagawa and H. Shimoda, ASVA 97]. However, for big absorption acoustic models such as recording studios, or mixing rooms, the surfaces in rooms must be modeled by the impedance reflections. In this paper, the basic treatments for the impedance reflection models in the Bergeron method are investigated, and the wideband time-stretched pulses are used to simulate one-dimensional sound fields. The feasibility of numerical simulations using the Bergeron method are confirmed by supposing a simple surface impedance reflection model.

در این پژوهش میکروکپسول جدیدی تحت عنوان میکروکپسول آلژینات- پروتئین آب پنیر حامل دی استیل تهیه و خصوصیات آن تعیین گردید. رهایش دی استیل در شرایط شبیه سازی شده دهانی در سطوح مختلف بزاق به میکروکپسول (0:1، 1:4 و 1:8) و نیروهای برشی متفاوت (0، 50 و 100 معکوس ثانیه) مورد بررسی قرار گرفت و ضریب نفوذ با کمک معادله فیک تخمین زده شد. هدف اصلی این پژوهش توسعه مدلی به منظور پیش بینی فرآیند رهایش و نیز تخمین ضریب نفوذ از میکروکپسول جدید ابداعی بوده تا بتوان به کمک آن رهایش کنترل شده عطر و طعم در شرایط دهانی ایجاد نمود. نتایج این تحقیق نشان داد که مدل حاصله می تواند با ضریب همبستگی بالای 95 درصد رفتار رهایش را پیش بینی نموده و علاوه بر این مدل مذکور به خوبی قادر به تخمین میزان ضریب نفوذ می باشد. نتایج همچنین نشان داد که اعمال نیروی برشی بطور معناداری سبب افزایش ضریب نفوذ شده درحالیکه تغییر میزان بزاق تاثیر معناداری بر آن ندارد.

The effects of the irreversible boundary reaction and the particle drag on mass transfer are studied analytically in concentric annulus flows. The solution of mathematical model, based on the generalized dispersion model brings out the mass transport following by the insertion of catheter on an artery in terms of the three effective transport coefficients, viz., the exchange, convection and diffusion coefficient. A general expression is derived which shows clearly the time dependent nature of the coefficients in the dispersive model. The complete time dependent expression for the exchange coefficient is obtained explicitly and independent of velocity distribution in the flow; however it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large time evaluations are made for the convective and diffusion coefficients, but these are sufficient to give the physical insight into the nature of the problem of the effects of drag and absorption parameters. It is found that as absorption parameter increases exchange and convection coefficients will be enhanced, but diffusion coefficient will be reduced. After certain period of time exchange coefficient will be constant for different values annular gap. As the drag parameter increases convection and diffusion coefficients will be reduced. With the enhancement of catheter radius i.e., the annular gap will be reduced then the convection and diffusion coefficients will be decreased.