Geometrical Acoustics Research Articles

Computationally-efficient rendering of diffuse reflections for geometrical acoustics based room simulation

Geometrical acoustics is well suited for real-time room acoustics simulation and is often implemented using the image source model (ISM). One drawback of the ISM is its limitation to specular reflections, while sound scattering plays an important role in real environments. Here, computationally-efficient, digital-filter approximations are proposed to account for effects of non-specular scattered reflections in the ISM. For scattering at large surfaces such as room boundaries, each reflection is energetically split into a specular and a scattered part, based on the scattering coefficient. The scattered sound is coupled into a diffuse reverberation model. Temporal effects of the underlying surface scattering for an infinite ideal diffuse (Lambertian) reflector are derived and the resulting monotonic decay is simulated using cascaded all-pass filters. Effects of scattering and multiple (inter-) reflections caused by larger geometric structures at walls, and by objects in the room are accounted for in a highly simplified manner. A single parameter is used to quantify deviations from an empty shoebox room. The cumulated temporal effect of scattering along a reflection path is mimicked using cascaded all-pass filters adjusted to obtain a gamma-distribution-shaped envelope. The proposed method was perceptually evaluated with both music and pulse stimuli against dummy head recordings of real rooms. The results show a better agreement between the recording and the simulation for transient stimuli. In a technical evaluation, the temporal evolution of echo density showed a comparable profile for the suggested method and real rooms.

Adaptation and evaluation of Pyroomacoustics for auralization purposes

An open-source room simulation software that relies on geometrical acoustics - Pyroomacoustics - was used to compute Binaural Room Impulse Responses (BRIRs) of existing rooms that are modeled in the Benchmark for Room Acoustical Simulation (BRAS). Modifications were made to the software to investigate the impact of the scattering model on the acoustic parameter values. A comparison with the acoustic parameter measurements showed that the values of EDT, C80 and D50 were found to be closer when using the Vector-Mixing method in comparison with the original scattering method. Overall, the alternative method reduced by 95% the mean squared error on the acoustic parameter values. The sound source directivity was also considered in the simulations to quantify its influence on the perceived auditory scenes. A listening test was then conducted to compare binaural renderings derived from measured and simulated BRIRs. Results showed that ratings of the modified versions of the software were either not significantly different or significantly higher than those of the original version depending on the room and sound source. Including the source directivity significantly improved the perceptual ratings, which is thought to be due to the reduction of spectral and loudness differences with the measured reference.

Retro-diffraction - importance for the calculation of road traffic noise

In geometric acoustics, "retro-diffraction" describes the loss of energy when reflected at the upper edges of noise screens. By bending the sound beam against the direction of propagation under consideration, reflected energy of the mirror sound source is reduced by up to 5 dB in addition to the absorption. This effect becomes particularly effective if the sound beam is blocked by a noise screen in the direction of propagation under consideration, meaning that diffraction also occurs in this direction. Sound attenuation by retro-diffraction can be found in the French standard NF S 31-133, an alternative method to ISO 9613-2 for calculating sound propagation outdoors. It was incorporated into the French noise forecasting procedure NMPB in 2008. We also take it into account by using it in the procedure for calculating environmental noise (European: CNOSSOS; German: BUB). This paper attempts to determine the impact of considering retro-diffraction in sound propagation. First, the equations from ISO 9613-2 and BUB regarding retro diffraction are compared in a simple geometric model. The level differences calculated in commercial sound propagation software are compared with those from measurements on a 1:20 scale model. An estimate of the relevance of retro-diffraction in calculating sound propagation is given.

Comparing outdoor sound propagation simulations based on geometrical and numerical methods

Conventional simulations of outdoor noise propagation often rely on geometrical acoustic methods such as ray tracing or mirror sources. Especially for low frequencies, these methods deliver physically implausible results due to their inherent approach not resolving the properties of the acoustic field. In this contribution, the results of a conventional noise propagation simulation software based on geometrical acoustics are compared to numerical results originating from solving the Helmholtz equation with the Finite Element Method (FEM). A 2.6 km long cross-section through an alpine valley with a railway line is considered as an exemple. In comparison with the FEM results, the shortcomings of geometrical acoustic methods are demonstrated, which underline the need for powerful and computationally efficient numerical approaches for outdoor noise propagation.

Optimizing a small room for critical listening with Treble

This work presents a detailed validation of new software Treble launched in 2023 that hybridizes the discontinuous Galerkin method and pressure-based geometrical acoustics methods. We investigated a small studio for voice productions both through physical measurements and treble's room acoustic simulations. By employing a dense measurement grid with a spacing of 25 cm at the ear level, a comprehensive validation of the room acoustic simulation was conducted in terms of room impulse responses, transfer functions, ISO 3382 acoustic parameters and sound pressure level distribution. Treble's simulation successfully predict the room modes, ISO 3382 acoustic parameters as well as the sound level distribution. The study demonstrates the impact of speaker positions, particularly regarding their interaction with boundary surfaces and how this can be planned with the simulation.

Geometrical acoustic modelling of occupied acoustic conditions in mosques: Application to a case study

Geometrical acoustic modelling of occupied acoustic conditions in mosques: Application to a case study

Using ray tracing modeling tools for room acoustics

When designing a venue (new construction or remodel) with specific acoustics requirements, acousticians usually rely on room acoustics software for the prediction of specific parameters to match a set of predefined goals. This presentation will discuss the benefits and drawbacks of using geometrical acoustics software for room acoustics and best practices for defining appropriate settings and evaluating the reliability of predictions.

Framework for real-time computation and streaming of soundscapes

The auralization of dynamic soundscapes brings significant computational challenges, as multiple often moving sources have to be considered simultaneously. Making such auralizations interactive rules out pre-rendering, requiring the underlying computations to be performed in real-time instead. The “Virtual Acoustics” (VA) framework allows for such real-time applications by leveraging geometrical acoustics and efficient multi-threading. Delivering these simulations to a larger audience, however, has proven difficult, as they still require a lengthy setup and possible simulation complexity is highly dependent on available hardware. When also including high-fidelity 3D visualization, hardware requirements rise further, hindering remote deployment. We present a web-based approach that executes simulations on a server and streams the result in real-time, offloading heavy calculations to a sufficiently powerful machine. 3D graphics are rendered by Unreal Engine and streamed using Pixel Streaming. VA auralization is transmitted via WebRTC audio streams. Both visualization and auralization are ultimately aggregated in a single website for platform-independent access. User input is gathered by the website and relaid back to the server, making the experience interactive. Thereby, this approach can deliver high-fidelity virtual environments with minimal setup and hardware requirements for the user. The approach will be demonstrated by streaming an interactive city park soundscape.

Employing reflection and diffraction signals around a wedge to determine the wedge angle.

In the present study the acoustic field around rigid wedges is investigated. The acoustic field consists of diffraction contributions (from the edge) and of geometrical acoustics contributions (the incident signal and signals reflected on the wedge faces). A new depiction, called the polarity plot, is proposed that depicts the polarity of the diffracted impulse response, as well as the number of the geometrical acoustics contributions around a given wedge. Based on the observed patterns of the polarity plots, a set of measurements around a wedge is described which (if experimentally feasible) could be used in order to determine the wedge angle.

ON THE POSSIBILITY OF ESTIMATING THE RADIUS OF A CYLINDRICAL REFLECTOR BY THE TIME OF THE DELAY OF THE PULSE OF THE PASSING WAVE IN RELATION TO THE MIRROR-REFLECTED PULSE OF THE SHEAR WAVE DURING ULTRASONIC METAL INSPECTION BY AN ANGLE PROBE

Modeling of the electro-acoustical channel of an angle probe for a side drilled hole type reflector made it possible to calculate the forms of the run round pulse generated by the radiation of a surface Rayleigh wave propagating along a concave cylindrical cavity and the wave pulse when reflected in the geometric acoustics approximation (mirror) for different radii of the hole and to obtain estimates of the ratio of the amplitudes of these pulses and the difference in their registration time. Comparison of the experimental results with those obtained by calculation for holes with radii of 2 and 3 mm showed their quite good qualitative and satisfactory quantitative coincidence. Estimates of the radius of a cylindrical hole are given based on the experimental delay time of the run round pulse and the Rayleigh wave velocity for a flat surface using a simple ratio; the range of the ratio of the diameter of the hole to the length of the transverse wave in the medium in which such an assessment is advisable is indicated, and an example of the values of the lag time in this range is given.

Directional reverberation time and the image source method for rectangular parallelepipedal rooms.

The image source (IS) method is a commonly used geometrical acoustics simulation technique in room and virtual acoustics. In particular, it has been used in the analysis of room reverberation under different choices of geometry and wall conditions. Under a simple rectangular parallelepipedal geometry, reverberation time is known to be dependent on the direction of arrival of reflections relative to the room axes. In this article, a closed-form expression for the directional energy decay and reverberation time is derived, which is valid in the late response, and may be used in the case of either angle-independent or angle-dependent reflection. The expression reduces to an easily evaluated formula in the case of an omnidirectional energy decay curve (EDC). Various numerical results are presented, including the validation of the closed-form expression against EDCs and late reverberation times drawn directly from the IS method.

Filter-based first- and higher-order diffraction modeling for geometrical acoustics

Geometrical acoustics (GA) offers a high computational efficiency, as required for real-time renderings of complex acoustic environments with applications in, e.g., hearing research, architectural planning, and entertainment. However, the assumed ray-like sound propagation does not account for perceptually relevant effects of diffraction. In indoor environments, diffraction at finite objects and apertures such as tables, music stands, and doors is of interest for computationally efficient rendering. Outdoors, buildings and barriers are relevant. Here, we extend the recent physically-based universal diffraction filter approximation (UDFA) for GA to approximate spectral effects of higher-order diffraction and apply it to a flat finite object and a double edge. At low frequencies, such effects predominantly occur when sound is diffracted repeatedly at the edges of a finite object, and at high frequencies when sound is propagating around subsequent edges of, e.g., buildings or sound barriers. In contrast to existing methods, the suggested filter approaches and topology offer spatially smooth infinite impulse response implementation for modelling higher-order diffraction at flat objects for arbitrary geometrical arrangements. For double diffraction at a three-sided barrier, errors are considerably decreased in comparison to a state-of-the-art sequential approach. Both suggested methods are computationally highly efficient and scalable depending on the desired accuracy.

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain.

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. These results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

Interpolation of scheduled simulation results for real-time auralization of moving sources

A central part of auralization is the consideration of realistic sound propagation effects. This can be achieved using computationally efficient physics-based simulations based on the principle geometrical acoustics. When considering complex effects, e.g. curved propagation due to atmospheric refraction, those simulations can be computationally demanding. This can become the bottleneck for real-time auralizations, as the run-time exceeds the duration of one audio block even for large block sizes. A solution is to schedule the simulations into a separate thread. However, this leads to an irregular update rate which is lower than the rate of the audio blocks. Consequently, the output signal can contain audible artifacts. This especially holds when considering the Doppler effect for dynamic scenarios with fast moving sources, like aircraft. This paper introduces a method for interpolating, and thereby upsampling, the results of scheduled simulations in an auralization context in order to avoid such artifacts. The method is applied to an aircraft flyover auralization considering curved sound propagation in an inhomogeneous, moving atmosphere. Using this method, it is possible to auralize such scenarios in real time.

Pressure dynamics of an internal shock wave emission inside a water droplet and potential cavitation

Shock reflected by a spherical interface is involved in shock-droplet interaction. Here, we investigate the pressure dynamics of an internal spherical shock wave and the potential cavitation inside a spherical water droplet. We conduct hydrodynamic simulation and employ the linear geometrical acoustics approximation to analyze the negative pressure and the wavefront at different intervals d between the source point of the shock and the droplet surface. Studies indicate that the negative pressure at a very large d is primarily attributed to the focusing effect of the droplet surface, whereas the collision of the reflected waves contributes to negative pressure at a small d. The caustic, which is the locus of the cusps (singular points) on the shock wavefront is determined by the parametric equations. Notably, the caustic also has singular points owing to the off-axis reflection. Finally, we evaluate the cavitation inside the droplet. Cavitation occurs on the opposite side of the droplet and moves away from the surface with d increasing, which agrees with previous experimental results. Additionally, we demonstrate that cavitation can occur with less damage to the droplet compared to a planar shock impact on a water droplet.

Binaural effects and rendering of edge diffraction in geometrical acoustics

Virtual acoustic environments have many applications in entertainment, architectural planning, and hearing research. Geometrical acoustics (GA) is commonly used, offering high computational efficiency by assuming ray-like sound propagation. However, GA does not account for wave-related effects such as edge diffraction, leading to perceptually dissatisfactory results or discontinuities, e.g., when a sound source is occluded. GA can be extended by constructing edge-diffracted sound paths. Recently, we have suggested the universal diffraction filter approximation (UDFA) to model the spectral effects of diffraction from infinite and finite edges and objects composed thereof using highly efficient recursive filters. This contribution investigates how edge diffraction affects the spatial perception of a sound source in conditions where a flat plate occludes the direct sound or produces a reflection. Binaural recordings were obtained with a head and torso simulator at discrete points of a sound source trajectory in the vicinity of a flat plate, including conditions near the incident and reflection shadow boundary. In a listening test, the perceived source location was matched for conditions with and without plate. Differences in localization were observed, and an approach for binaural rendering of simulated diffraction in the GA context is suggested, replicating the localization results obtained for the dummy-head recordings.

Sound scattering at building façades

The state-of-the-art models of soundscape planning and noise mapping are based on geometrical acoustics. Numerical wave models are possible but they exceed acceptable computation times for acoustics in practice by orders of magnitude. In geometrical acoustics, the sound is propagated either assuming Lambert’s diffusion or specular reflections, which applies to randomly corrugated surfaces and to flat surfaces, respectively. For specific architectural surface design, however, no appropriate simplified sound reflection model exists. In this paper, architectural façade shape typologies are categorized, and a directional scattering coefficient concept will be introduced and applied in an example simulation and auralization of complex sound scattering phenomena.

Filter-based solutions for finite and infinite edge diffraction

Sound diffraction occurs at (building) corners, objects and openings, prominently affecting occluded and reflected sounds. Here, a physically-based, parametric filter model for diffraction at arbitrary wedges is presented. The model connects existing high-frequency asymptotic and exact solutions in geometrical acoustics using up to four half-order low-pass filters. Compact expressions for the transfer function and impulse response of the singly diffracted field are derived, with errors below 0.1 dB. A filter modification is suggested to account for the exact solution at low frequencies. The filter solution is further simplified to approximate the spectral effects of diffraction from finite wedges and objects composed thereof, referred to as universal diffraction filter approximation (UDFA). A computationally highly-efficient recursive filter implementation is presented and it is demonstrated that diffraction from flat finite objects like plates or apertures can be closely approximated. To account for effects of higher-order diffraction at the object, a heuristic filter extension is suggested. The presented filter-based diffraction solution is suited for the prediction and simulation of sound propagation including non-specular reflections in architectural acoustics. For virtual acoustics, UDFA provides an efficient and accurate approximation of edge diffraction to account for perceptually relevant frequency-dependent attenuation, extendable to arbitrary objects.

Influence of ground blocking on the acoustic phase variance in a turbulent atmosphere.

Sound propagation through atmospheric turbulence is important in many applications such as localization of low flying aircraft, sonic boom disturbances, and auralization of aircraft during takeoff and landing. This article extends an isotropic turbulence model in the atmospheric boundary layer to account for ground blocking of buoyancy-produced velocity fluctuations. The extended, anisotropic turbulence model is needed to correctly predict the effect of the largest velocity eddies on the statistical characteristics of sound signals. This model and geometrical acoustics are then employed to derive a closed-form expression for the variance of the phase fluctuations of a spherical sound wave for vertical and slanted propagation, without the use of the Markov approximation. A numerical analysis of this expression indicates significant anisotropy of the phase variance due to the buoyancy-produced velocity fluctuations with ground blocking such that it decreases in the vertical direction and increases in the near-horizontal directions. The newly formulated phase variance is compared with data from an outdoor experiment on vertical and slanted sound propagation. By accounting for ground blocking, much better agreement is obtained between the theoretical predictions and experimental data.

Numerical geometric acoustics: An eikonal-based approach for modeling sound propagation in 3D environments

Numerical geometric acoustics: An eikonal-based approach for modeling sound propagation in 3D environments