RaySound: the room-acoustics engine

RaySound is the enclosed-space acoustic simulation engine developed by ST-LINE. This note describes what it does and what it makes possible in a room-acoustics commission. It does not describe how it is implemented: the internal architecture, the numerical schemes and the implementation choices are ST-LINE know-how and remain confidential.

The professional service that derives from it is described in room-acoustics design.

The problem it solves

Room acoustics is ceasing to be an accessory requirement. Italy’s Minimum Environmental Criteria for construction set thresholds on reverberation and speech intelligibility that it is no longer enough to promise: they have to be demonstrated with a prediction, and that prediction ends up in a file someone can challenge.

Established tools answer one question well: given the room and given the materials, how will it sound. That is extremely useful for verifying a design already made. But a designer starts from the other end: they have a target — a reverberation time, a clarity threshold, an intelligibility index — and must find the surface treatment that reaches it. Prediction alone leaves you guessing: change a material, run the calculation again, look at the result, repeat.

And there is a second question that stays uncovered, subtler and more awkward. When a model is calibrated against a room measurement, is that data enough to determine what you want to determine? Or will the calculation return a number anyway, one that looks precise and does not survive real scrutiny? It is the question nobody asks until a dispute arrives.

The three things it can do

Prediction. From the surveyed geometry of the room and the materials of its surfaces, the specified descriptors per frequency band: reverberation time, clarity, speech transmission index. The geometry is the real one — a surveyed mesh, with balconies, raked seating, sloped ceilings and communicating volumes — not an equivalent box of matching volume.

The descriptors are not generic labels: they are defined by standard. Clarity C₅₀, for instance, is the ratio in decibels between the energy arriving in the first 50 milliseconds and all the energy arriving after it,

$$C_{50}=10{\log }_{10}\frac{{\int }_0^{50\mathrm{ms}}{p}^2(t)\mathrm{d}t}{{\int }_{50\mathrm{ms}}^{\infty }{p}^2(t)\mathrm{d}t}$$

and it measures how far the first arrival prevails over the reverberant tail: it is the quantity that decides whether words are understood at the back of a classroom. For speech the window is 50 ms, for music 80.

Inverse design. From target to treatment. The engine looks for which surfaces to treat and by how much, to bring the descriptors inside the required limits. It is not a hand-guided loop of attempts: the target drives the search directly, and the result is a sizing — this surface at this absorption — rather than a general direction.

Identifiability diagnosis. Before calibrating materials against a measurement, the engine establishes whether that measurement holds enough information, and how many degrees of freedom of the design are actually constrained by the data. It is the capability that lets you sign a figure knowing what it rests on.

The last two steps are the ones established simulators do not cover, and that is where the engine’s value sits.

Why it is a hybrid engine

An enclosed space has two acoustic regimes, separated by the Schroeder frequency, and this is not a convention: it is computed from the room’s volume and its reverberation time,

$$f_{\mathrm{S}}\approx 2000\sqrt{\frac{T_{60}}{V}}$$

with the volume in cubic metres and the time in seconds. A 250 m³ classroom with one second of reverberation has its transition around 125 Hz; a 10 000 m³ auditorium with two seconds has it around 28 Hz. It is the same reason a small room “sounds” so different from a large hall: the part of the spectrum governed by modes is far wider.

Below that frequency the room’s resonances are few and individually distinguishable: the field is modal, and it must be handled by solving wave propagation. Above it, the resonances crowd together until they overlap and the field becomes statistically diffuse: there it is better handled by geometrical methods, which are efficient precisely where the wave approach would become impractical.

In the diffuse regime, reverberation is estimated in closed form from the room’s volume and surface area. Sabine’s formula, and the Eyring correction that holds also when mean absorption is not small, are

$$T_{60}=\frac{0.161V}{S\bar{\alpha }}\text{and}{T}_{60}=\frac{0.161V}{-S\ln (1-\bar{\alpha })+4mV}$$

where S is the total surface area, ᾱ the mean absorption and m the air attenuation coefficient. These formulas describe the field as though it were perfectly diffuse: above the Schroeder frequency that is a good approximation, below it is not, because there the modes are few and each one counts.

Neither approach covers the full spectrum of a room well, and that is not an implementation limitation but a physical fact: it is the reason the engine is hybrid, with a wave branch at low frequencies and a geometric branch at mid and high frequencies, and a transition between them built so that no energy is lost or double-counted at the junction.

The basics of the computational model

The equations are the ones any room-acoustics textbook gives. They are worth writing down, because they say precisely what the engine computes in each of the two regimes.

The modal regime. Acoustic pressure obeys the wave equation, and the behaviour of the walls enters as a boundary condition: a wall is neither perfectly rigid nor perfectly absorbing, but has an impedance that depends on frequency,

$$\frac{{\partial }^{2}p}{\partial t^2}=c^{2}abl{a}^{2}p,\frac{\partial p}{\partial n}=-\frac{h{o}_0}{Z(\omega )}\frac{\partial p}{\partial t}$$

where Z(ω) is the complex surface impedance. That Z is complex and frequency-dependent is the point: it means the wall does not merely attenuate but shifts the phase of the reflection, and at low frequencies that shift moves the room’s resonances. A model replacing Z with a single real absorption coefficient loses that information.

Where the modal regime ends. The number of modes contained in a band can be computed: Weyl’s law, in the complete form that includes the surface term, gives the modal density

$$\frac{\mathrm{d}N}{\mathrm{d}f}=\frac{4\pi V{f}^2}{c^3}+\frac{\pi Sf}{2c^2}$$

which grows with the square of frequency. From it follows how many modes overlap within each one’s bandwidth: while they are few the field is modal and the individual modes are visible; when they become many the field is diffuse. It is this calculation, and not a threshold chosen in advance, that says where the transition lies in a specific room.

The diffuse regime. Above the transition the field is handled in terms of energy that propagates, reflects and is lost. The contribution of a sound path decays with spherical spreading and loses a fraction of its energy at each reflection,

$$p\propto \frac{1}{4\pi r}{E}_n=E_0\prod _{i=1}^n(1-{\alpha }_i(f))e^{-m(f)r}$$

where the product runs over the surfaces met, α is each one’s absorption coefficient and m the air attenuation, which depends on temperature and humidity per ISO 9613-1. The 4π factor is not cosmetic: some implementations use 1/r and lose a constant factor of 22 dB on the absolute level.

Why design is an inverse problem. Put in these terms, sizing a treatment means choosing the surface coefficients α so that the computed descriptors D land on a target D*. It is a minimisation problem,

$$\underset{\mathbf{\alpha }}{\min }\Vert \mathbf{D}(\mathbf{\alpha })-{\mathbf{D}}^{\ast }{\Vert }_W^2$$

with weights W reflecting the tolerances in the specification. Written this way it is also clear why the identifiability question has an operational consequence: if the problem is ill-posed — if several different combinations of α give the same descriptors within the measurement uncertainty — the minimum exists but is not unique, and only one of those solutions would be returned as though it were the answer.

What changes, in a commission

For a client, the difference is between a document saying “the reverberation time will be 0.7 seconds” and one saying “it will be 0.7 seconds, here is which wall to treat to get there, and here your data does not support saying more”. In a tender the second is a defensible figure; the first is a prediction to be accepted on trust.

The sizing says which surface, not only how much area. At equal square metres of absorbing material installed, the position of the treatment changes the result: what counts is which surfaces the sound field meets most often. It is a real, measurable effect on independent data, not a theoretical refinement.

The result is a map, not a number. Clarity and intelligibility change from seat to seat in the same room, while reverberation time is a property of the volume. A prediction that returns a single clarity value for a three-hundred-seat hall is averaging away exactly the information needed to decide where to seat the audience and where to put the treatment.

The difficult cases are not hidden. Two communicating spaces — a foyer open onto a hall, a canteen on two levels — do not have a single decay: they have two, one local and faster and one sustained by the other volume. A single-tail model cannot reproduce that by construction, and the reference benchmark’s public round robin saw every geometric algorithm under comparison stop on that case.

The regulatory context

What brings room acoustics into public tendering in Italy is the Minimum Environmental Criteria for construction, in the version of Ministerial Decree 24/11/2025, in force since 1 February 2026, which repealed Decree 256/2022 and the corrective Decree of 5 August 2024. The criteria require predictions of reverberation time, clarity and speech intelligibility, and introduce BIM as a structural requirement.

The descriptors and measurement methods come from ISO 3382-1 (reverberation time, clarity, early decay time) and from IEC 60268-16 for the speech transmission index. The target values for Italian educational and shared spaces are in UNI 11532, parts 1 and 2.

How it is validated

The bench is the public BRAS benchmark of the Technische Universität Berlin: real rooms with surveyed geometry, materials characterised per surface and measured impulse responses. The engine receives geometry and materials and produces the prediction, with no recalibration — no parameter is adjusted to move closer to the measurement.

On the benchmark’s two performance spaces the measured reverberation time is reproduced to within 1.1 % and 1.3 % over the core band, and the spatial pattern of clarity correlates with the measurement at +0.89 and +0.68, with a level residual of −0.17 and +0.70 dB. The room-by-room, band-by-band detail, with the methodology and the complete tables, is in the documents below.

Those figures must be read for what they are, and the report is the first to draw the distinction. The 1.1 % and 1.3 % are the agreement of the analytical diffuse T60 — Eyring on measured volume and surfaces, with the benchmark’s coefficients: an agreement those coefficients partly impose, being obtained by inverting Eyring on the same volume-to-surface ratio. The independent prediction is the ray-tracer’s, and over the same bands it sits at 17.1 % and 11.5 %: that is the figure to compare against a commercial simulator. The C50 correlation too comes with its uncertainty: five positions per room give a very wide 95 % confidence interval, ±3.6.

Taken together these figures demonstrate the coherence of the chain geometry → materials → descriptors with known materials: the benchmark’s coefficients are declared inputs, not an unknown the engine guesses.

The benchmark’s two remaining rooms serve a different purpose, and are perhaps the most characteristic result. On CR2, an acoustically rigid room, material identifiability is negative: the inverse problem is rank-deficient — three informative directions out of five — and the engine flags it instead of returning an indefensible estimate; below the Schroeder frequency the modal observable separates wall orientation where the energetic one is blind (rank 3/6 against 1/6). On CR1, the benchmark’s only coupled-room, double-slope scene, the clarity of the coupled field closes with no fit at all.

Where it sits in the literature

Each of the two families of methods has a known boundary, and it is the literature that fixes it. Geometrical methods lose validity below the Schroeder frequency, where the high-frequency assumption breaks down: they do not capture diffraction, interference or phase — the canonical review by Savioja and Svensson (2015) argues this method by method. Wave methods have the opposite boundary, and it is not one of modelling but of cost. To resolve up to a maximum frequency the discretisation step must go as 1/f, the time step follows through the stability condition, the number of cells in three dimensions grows as f³ and the number of steps as f: the total cost therefore goes as

$$\mathcal{C}\propto f_{\max }^4$$

Doubling the maximum frequency costs sixteen times the computation. That is why, above a few hundred hertz in a large room, wave methods become impractical even on high-end hardware — and it is the economic reason, not only the physical one, for the hybrid approach.

Hybridisation has therefore become standard practice over the last decade, and the crossovers the literature adopts fall in the 200–500 Hz range.

The differentiable frontier

The most active strand of 2023–2025 is differentiable acoustic simulation: carrying into acoustics what graphics did with differentiable rendering, that is, making the simulator differentiable with respect to its parameters and designing by optimisation instead of by trial and error. Zhi and Sharma (2023) demonstrated feasibility on an image-source model; Finnendahl et al. (2025), at SIGGRAPH, brought time-resolved backpropagation to acoustic path tracing; DART (2025) made acoustic radiance transfer differentiable, and DSDN (2025) did the same for scattering delay networks.

There is a trait common to all of this work, and it defines the space RaySound occupies: it is single-method. Either it is purely geometrical — and then it is blind below the Schroeder frequency, which is precisely where the acoustics of a classroom or a medium-sized hall is decided — or it is a reverb network, which does not solve the propagation equation. A hybrid engine that can be designed in reverse, with a material description consistent across both regimes, is the position RaySound holds.

The open problem the engine is built around

The applied literature of 2024–2025 has a recurring theme: the step from absorption coefficients to impedance. Coefficients measured in a reverberation room per ISO 354 are not directly usable as input to a wave model, and even between different geometrical simulators the “right” values do not agree. A study on a historic hall quantifies that step: significant low-frequency discrepancies between different input data, with a reduction of up to 45 % in the absorption coefficient before conversion. On the calibration side, recent work proposes constrained methods for estimating the coefficients from measurement.

This is why, in a real commission, the absorption values of existing surfaces come from a field survey rather than from a table — and why alongside calibration you need a diagnosis that says beforehand whether that survey is enough.

The three technical documents

The detail of the validation — room by room, band by band, with the methodology and the complete tables — lives in three downloadable documents, written in Italian.

The scientific-technical report (2 September 2026) is forty pages: the method and the physical justification of the two regimes, validation on the benchmark’s four rooms, the per-position maps, external validation on other public benches, and an appendix of methodological notes — which coefficients are inputs, which regime holds for which band, what each validation label means.

The technical note on validation and method (22 June 2026) is seven pages on four points: validation of the modal regime against measured frequencies in two real rooms, with an error below 1 %; the limit of the stitching between the two regimes, localised at the 500 Hz band and shown not to be a specular- order problem; guaranteed-coverage prediction intervals on the ISO descriptors; and a criterion for building a modal test bench that can actually discriminate.

The GenDARA Room_0 stress test (25 August 2026) is three pages on a real room from the ICASSP 2025 challenge, and it answers two questions: whether the modal spectrum of an arbitrary room can be recovered stably as the model is refined, and whether the materials of a small room with contrast are identifiable from the data — they are, with six degrees of freedom out of seven.

• Scientific-technical report · PDF, 40 pages, 7.5 MB
• Technical note on validation and method · PDF, 7 pages, 343 kB
• GenDARA Room_0 stress test · PDF, 3 pages, 237 kB

References

Wave methods and numerics

• J. S. Hesthaven, T. Warburton (2008). Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer. DOI 10.1007/978-0-387-72067-8.
• B. Hamilton, S. Bilbao (2017). FDTD methods for 3-D room acoustics with high-order accuracy. IEEE/ACM TASLP 25(11).
• K. S. Yee (1966). Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14(3).
• S. Bilbao (2009). Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics. Wiley.
• B. Hamilton, S. Bilbao, C. J. Webb (2015). Revisiting implicit finite difference schemes for 3D room acoustics simulations on GPU. DAFx-15.
• B. Hamilton (2016). Finite Difference and Finite Volume Methods for Wave-based Modelling of Room Acoustics. PhD thesis, University of Edinburgh.
• M. Aretz (2009). Combined wave and ray based room acoustic simulations of small rooms. PhD thesis, RWTH Aachen.

Geometrical acoustics, image sources, diffraction

• J. B. Allen, D. A. Berkley (1979). Image method for efficiently simulating small-room acoustics. JASA 65(4). DOI 10.1121/1.382599.
• U. P. Svensson, R. I. Fred, J. Vanderkooy (1999). An analytic secondary source model of edge diffraction impulse responses. JASA 106.
• L. Savioja, U. P. Svensson (2015). Overview of geometrical room acoustic modeling techniques. JASA 138(2).
• R. Scheibler, E. Bezzam, I. Dokmanić (2018). Pyroomacoustics: a Python package for audio room simulation and array processing algorithms. IEEE ICASSP.
• R. Thomas (2017). Wayverb: a hybrid waveguide/geometric room acoustics simulator. Thesis, University of Huddersfield.

Differentiable simulation and learned methods

• Y. Zhi, D. Sharma et al. (2023). A differentiable image source model for room acoustics optimization. IEEE.
• U. Finnendahl, M. Worchel, J. Jüterbock, S. Wujecki, F. Brinkmann, S. Weinzierl, M. Alexa (2025). Differentiable geometric acoustic path tracing using time-resolved path replay backpropagation. ACM TOG 44(4), SIGGRAPH 2025.
• DART — Differentiable Acoustic Radiance Transfer (2025). arXiv 2509.15946.
• DSDN — Differentiable Scattering Delay Networks (2025). DAFx-25, Ancona.
• A. Luo, Y. Du et al. (2022). Learning neural acoustic fields. NeurIPS 2022, arXiv 2204.00628.
• N. Borrel-Jensen, A. P. Engsig-Karup, C.-H. Jeong (2021). Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries. JASA Express Letters 1(12).
• S. Schmid et al. (2025). Physics-informed neural networks for modal wave field predictions in 3D room acoustics. Applied Sciences 15(2):939.
• J. McCarthy, X. Zhang, S. A. Verburg, W. F. Jenkins, P. Gerstoft (2025). Machine learning in acoustics: a review and open-source repository. npj Acoustics 1:18.

Field theory, descriptors, uncertainty

• W. C. Sabine (1922). Collected Papers on Acoustics. Harvard University Press.
• C. F. Eyring (1930). Reverberation time in “dead” rooms. JASA 1(2A). DOI 10.1121/1.1915175.
• M. R. Schroeder (1962). Frequency-correlation functions of frequency responses in rooms. JASA 34(12). DOI 10.1121/1.1909136.
• M. R. Schroeder (1965). New method of measuring reverberation time. JASA 37(3). DOI 10.1121/1.1909343.
• J.-D. Polack (1993). Playing billiards in the concert hall: the mathematical foundations of geometrical room acoustics. Applied Acoustics 38(2–4). DOI 10.1016/0003-682X(93)90054-A.
• J. S. Abel, P. Huang (2006). A simple, robust measure of reverberation echo density. AES 121st Convention, paper 6985.
• M. Vorländer (2008). Auralization: Fundamentals of Acoustics, Modelling, Simulation, Algorithms and Acoustic Virtual Reality. Springer. DOI 10.1007/978-3-540-48830-9.
• H. Kuttruff (2016). Room Acoustics, 6th ed. CRC Press. DOI 10.1201/9781315372150.
• A. Lundeby, T. E. Vigran, H. Bietz, M. Vorländer (1995). Uncertainties of measurements in room acoustics. Acustica 81(4).
• A. Tarantola (2005). Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM. DOI 10.1137/1.9780898717921.

Materials and boundary conditions

• B. Mondet, J. Brunskog, C.-H. Jeong, J. H. Rindel (2020). From absorption to impedance: enhancing boundary conditions in room acoustic simulations. Applied Acoustics 157, 106884. DOI 10.1016/j.apacoust.2019.04.034.
• Y. Miki (1990). Acoustical properties of porous materials — modifications of Delany–Bazley models. J. Acoust. Soc. Jpn. (E) 11(1). DOI 10.1250/ast.11.19.
• J. F. Allard, N. Atalla (2009). Propagation of Sound in Porous Media, 2nd ed. Wiley.
• G. Fratoni, D. D’Orazio (2025). Boundary conditions for hybrid simulations in a rectangular environment with sound-absorbing ceiling. Applied Acoustics 240, 110933. DOI 10.1016/j.apacoust.2025.110933.
• S. D. Bellows et al. (2025). Constrained least-squares and maximum-likelihood calibration of absorption coefficients. Acta Acustica 9:25.

Benchmarks and validation data

• L. Aspöck, F. Brinkmann, D. Ackermann, S. Weinzierl, M. Vorländer (2020). BRAS — Benchmark for Room Acoustical Simulation, v3. Technische Universität Berlin. DOI 10.14279/depositonce-6726.3.
• F. Brinkmann et al. (2019). A round robin on room acoustical simulation and auralization. JASA 145(4).
• F. Brinkmann et al. (2021). A benchmark for room acoustical simulation. Applied Acoustics 176.
• D. Di Carlo et al. (2021). dEchorate: a calibrated room impulse response dataset.

Italian room acoustics

• D. D’Orazio, G. Fratoni, M. Garai (2020). Sound energy distribution in Italian opera houses. Applied Acoustics.
• M. Cingolani et al. (2021). MPP sound absorbers and FDTD acoustic simulations in a lecture hall. Applied Sciences 11(6):2445.
• D. D’Orazio, G. Fratoni, E. Rovigatti, B. Hamilton (2019). Numerical simulations of Italian opera houses using geometrical and wave-based acoustics methods. 23rd International Congress on Acoustics.
• G. Fratoni, B. Hamilton, D. D’Orazio (2021). Rediscovering the acoustics of a XII-century rotunda through FDTD simulation. I3DA 2021.
• G. Fratoni, B. Hamilton, D. D’Orazio (2024). Acoustic analysis of a well-preserved Renaissance music space: the Odeo Cornaro in Padua.
• D. D’Orazio, G. Fratoni (2025). The Renaissance theatre as a bridge between ancient and modern acoustics. J. Acoust. Soc. Am. 158.
• A. Tardini, G. Fratoni, D. D’Orazio (2025). A survey of national standards on classroom acoustics.
• D. D’Orazio, G. Fratoni, A. Tardini (2025). The applied meaning of UNI 11532-2 through Italian case studies.

Standards and regulatory references

ISO 3382-1 (descriptors), ISO 354 (absorption in a reverberation room), ISO 17497-1 (scattering), ISO 9613-1 (air absorption), IEC 61260-1:2014 (band filters), IEC 60268-16 (speech transmission index), UNI 11532-1/2 (indoor acoustics of confined spaces), Italian Ministerial Decree 24/11/2025 (2025 building CAM, in force since 1 February 2026).