Room simulator

How do you use the tool?

Set the room dimensions (L × W × H), drag the sources S1/S2/S3 on the plan and place the receivers R1…R9, which read C50, C80, EDT, T30 and STI. Choose the materials of the six surfaces (α per band) and the metric, which drives both the α chart and the heatmap; save the state to compare the Δ after a treatment.

1. Set the room dimensions (L × W × H). The plan is the top view of the z_r plane; the four walls are marked N/S/E/W.
2. Drag the sources S1/S2/S3 on the plan (each with its own height and level). S2/S3 — off by default and placed at the edges — are a distributed voice system: enable them to see the effect.
3. The 9 receivers R1…R9 are on a grid (Restore / Clear all); each shows C50/C80/EDT/T30/STI at its point. They share the z_r height.
4. Choose the materials of the six surfaces from the library (per-octave-band α). Floor, ceiling and the four walls can have very different materials.
5. Choose the metric (C50/C80/EDT/T30/STI): it drives both the α chart and the heatmap. The α chart is the central element; the heatmap is a secondary spatial view.
6. Save the state, add absorptive panels to the walls (or enable S2/S3) and observe the Δ for each receiver.

Why the ISM is exact on a shoebox

The Image Source Method replaces each wall reflection with an “image” source, mirrored across that wall. In a rectangular room the images form a regular, infinite lattice: every image is reachable in a straight line, no edge can hide it. There is no need to enumerate and validate each path against a mesh, no visibility (in-triangle) test: the computation is a pure nested triple sum over the indices (i, j, k) of the three axes. This regularity is what makes the method exact, not approximate.

On a real geometry — a slanted wall, an alcove, a stage — the lattice breaks: some images become hidden behind an edge, others must be validated one by one. That requires meshes, BVH and ray casting. This is why the tool is shoebox-only by construction.

The meaning of i — with an example

On an axis of side L with the source at coordinate s, the image of index i is at:

$$\begin{array}{rl}i\text{even}& \to x_i=iL+s\\ i\text{odd}& \to x_i=(i+1)L-s\end{array}$$

Example with L = 8 m, s = 2 m. Image i = 1 (one reflection off the wall at x = L) is at x₁ = (1+1)·8 − 2 = 14 m: the mirror of the source beyond the back wall. Image i = 2 (a reflection off the back wall then the front one) is at x₂ = 2·8 + 2 = 18 m. The number of reflections on each of the two sides of the axis is counted separately — crucial when floor and ceiling have very different α: for i > 0 the far wall takes ⌈i/2⌉ reflections, the near one ⌊i/2⌋; for i < 0 the roles swap. Each image carries an energy Π (1−α)^(reflections) / dist², summed band by band.

Diffuse tail: why Eyring beats Sabine at high α

Beyond the early reflections the field becomes diffuse and energy decays exponentially. The two classic T60 formulas are:

$$\begin{array}{rlrl}\text{Sabine:}& T_{60}=\frac{0.161V}{A}& A& =\sum _i{S}_i{\alpha }_i\\ \text{Eyring:}& T_{60}=\frac{0.161V}{-S\ln (1-\bar{\alpha })}& \bar{\alpha }& =\frac{A}{S}\end{array}$$

Sabine assumes energy dissipates continuously and overestimates T60 when absorption is high: in the limit ᾱ → 1 (a fully absorptive room) Sabine still gives a finite T60, which is physically absurd. Eyring instead starts from the per-reflection decay off a wall of mean absorption ᾱ: in the limit ᾱ → 1 the term −ln(1−ᾱ) → ∞ and T60 → 0, as it must. This is why the tool uses Eyring as the reference to calibrate the tail; the two converge when ᾱ is low. Beyond the last discrete reflection an e^(−k·t) decay is extended with k = 13.8/T60, calibrated on the energy density of the last images.

How do you read C50 and C80?

C50 and C80 are clarity indices: the ratio in dB between the energy arriving early and that arriving late, with a 50 ms window for speech (C50) and 80 ms for music (C80). A C50 above +2 dB indicates good intelligibility; negative values a room too reverberant. For music a good C80 sits around −2…+2 dB.

C50 and C80 are clarity indices: the ratio, in dB, between the energy that arrives “early” and that which arrives “late”.

$$\begin{array}{rlrl}{C}_{50}& =10{\log }_{10}\frac{{\int }_0^{50\text{ms}}{p}^{2}dt}{{\int }_{50\text{ms}}^{\infty }{p}^{2}dt}& & \to \text{speech}\\ C_{80}& =10{\log }_{10}\frac{{\int }_0^{80\text{ms}}{p}^{2}dt}{{\int }_{80\text{ms}}^{\infty }{p}^{2}dt}& & \to \text{music}\end{array}$$

Our hearing “integrates” reflections arriving within ~50 ms with the direct sound: they reinforce speech instead of blurring it. Beyond that threshold they become reverberant tail that masks the following syllables. For speech, a C50 > +2 dB indicates good intelligibility; negative values flag a room too reverberant to be understood well. For music C80 is used (80 ms window): typical values of a good concert hall sit around −2…+2 dB — too high sounds “dry”, too low “muddy”.

Why a panel on a reflective wall raises C50

The late reflections are the ones that bounced many times along long paths: they are dominated by the diffuse tail. Putting an absorptive panel on a reflective wall cuts mostly that late energy (lowers ᾱ → T60 → tail), while the few early reflections that reinforce speech remain. The E_early/E_late ratio grows: C50 rises, intelligibility improves. This is the principle behind treating speech rooms, discussed in the speech/music rooms chapter of the book “Acustica per chi progetta”. Try it in the tool: save the state, assign an absorptive panel to the four walls and watch the Δ C50.

Total vs Room effect (heatmap). Clarity at a point is made by geometry and materials — the walls, the absorption, the tail — not by the mere distance from the source. The “Total” view includes the direct sound and so near S is dominated by the 1/dist² ramp (it essentially draws the distance from S); the “Room effect” view removes the direct sound and isolates the room’s acoustic effect, showing where reflections help or degrade listening. It is a diagnostic view for pre-dimensioning, not a standard metric — the receiver values always stay the real (total) ones.

Governing clarity: the α chart

In a rectangular room C50 and C80 vary little and regularly as the listener moves: position matters less than one would think. The real lever is the absorption of the surfaces — this is why the α chart, not the heatmap, is the central element. It shows how the metric at the receiver changes as you raise the absorption of one wall, leaving the others fixed.

How to read it: the slope of the curve is the sensitivity of clarity to the absorption of that wall — the steeper it is, the more a panel there pays off. The knee is the point beyond which the curve flattens: adding more absorption does ever less (diminishing returns), and it is often better to treat another surface. The vertical marker is the current α: it tells you where you are and how much headroom is left.

Which wall to treat first? The one that reflects energy toward the listener over the shortest paths — typically the surfaces near the source and listener (a low ceiling, the wall behind the source). A panel there intercepts reflections that would otherwise arrive late and degrade C50. This is the reasoning of the speech/music rooms chapter of “Acustica per chi progetta”: you treat where the late reflections are born, not at random.

Two levers: absorption and source distribution

Intelligibility is governed by two independent levers. The first is absorption (the α chart): it cuts the reverberant tail and raises C50/STI. The second is source distribution: two or three loudspeakers near the listeners reduce the average source-listener distance, bringing more direct energy everywhere — C50 and STI rise and, above all, become more uniform across the plan than a single powerful speaker at the back of the room can achieve. This is the principle of distributed voice systems.

Try it: with the metric on STI, enable S2 and S3 (at the edges) and watch the heatmap become greener and flatter; disable them and it goes back to being dominated by distance from the single source. Sources are summed in energy (incoherent): more loudspeakers always add energy, but the net clarity gain depends on how much direct energy they add relative to the reverberation. It is the same reasoning as the speech/music rooms chapter of “Acustica per chi progetta”.

EDT and T30: two times, two meanings

Both measure how long sound takes to decay, but over different stretches of the decay curve — and they tell different stories.

• T30 (and T60) — measured over the late part of the Schroeder curve (from −5 to −35 dB, then extended to 60 dB). It is the physical reverberation time of the room: a diffuse-field property, almost identical at every point. It answers “how reverberant is this room?”. T30 is the standard way to estimate T60 by measuring only 30 dB of decay (more robust to background noise) and extrapolating.
• EDT (Early Decay Time) — measured over the first 10 dB (from 0 to −10 dB) and multiplied ×6 to scale it to 60 dB. It weights the early reflections, which depend on where you are relative to the source and the surfaces. It is the reverberation the ear actually perceives. It answers “how reverberant does it sound at this spot?”.

In a perfectly diffuse field they coincide. They diverge when the early decay differs from the late: near the source the direct sound and early reflections are strong, EDT drops below T30 and the spot sounds “drier” and clearer than T30 would suggest; at distant or unfavourable spots EDT can exceed T30. This is why EDT is regarded as the best predictor of the sensation of reverberance, while T30/T60 is the most stable, repeatable measure of the room.

You can see it directly in the tool by switching the heatmap metric: EDT varies point to point (it follows the early-reflection geometry), while T30 is almost uniform and equals the Eyring T60 — a global property of the room, not of the single spot.

What are the tool’s limitations?

Rectangular geometries only: on real rooms the image lattice collapses. It is a geometric model, blind to waves and room modes below ~250 Hz. Sources sum in energy. STI uses the male α weights of IEC 60268-16:2020 over six octave bands 125–4000 Hz — the 8 kHz band is missing, 12.5 % of the weight — with no β redundancy factors and no masking or background noise: it matches the standard when the MTI is uniform across bands and departs from it as the spread grows. The α absorption coefficients are tabulated at random incidence and mostly unverified. It serves pre-dimensioning and teaching, it is not a validated solver.

• Rectangular geometries only. On a real room (slanted walls, alcoves, tiered seating) the image lattice collapses: it needs mesh + BVH + visibility tests. The tool is shoebox-only by construction, not by simplification.
• Do not extend to near-rectangular geometries. A “nearly” rectangular room is not rectangular: there the geometric model keeps producing plausible but wrong numbers — it lies silently. Use it only on true boxes.
• No waves below ~250 Hz. It is a purely geometric model (rays/images): the axial room modes of low frequencies are invisible to it. Below the Schroeder frequency the field is not diffuse and the 125 Hz values should be read as a trend, not data.
• Multiple sources summed in energy (incoherent). The model does not represent phase interference between loudspeakers (comb filtering, cancellations); it is the standard first-approximation assessment for distributed systems. STI is approximate (6 bands 125–4k, renormalised IEC male weights, no background noise): a relative value, not for expert reports.
• Random-incidence α. The library coefficients are tabulated, measured in a reverberation room (ISO 354): not an angle-dependent impedance. In situ, mounting, edges and backing cavities give different effective α.
• Unverified values. Almost all the library α have verified = false in materials.json: they are representative of the literature, not checked against the primary source. Do not use them for expert reports.
• Pre-dimensioning and teaching. It helps grasp orders of magnitude and the effect of treatments, it is NOT a validated solver. Design and compliance need dedicated software, in-situ measurements and a competent acoustic technician.

References

• Allen J.B., Berkley D.A. (1979) — Image method for efficiently simulating small-room acoustics. J. Acoust. Soc. Am. 65(4), 943–950.
• Eyring C.F. (1930) — Reverberation Time in “Dead” Rooms. J. Acoust. Soc. Am. 1, 217.
• Sabine W.C. (1922) — Collected Papers on Acoustics. Harvard University Press.
• ISO 3382-1/-2 — Measurement of room acoustic parameters (T30, EDT, C50, C80).
• ISO 354:2003 — Measurement of sound absorption in a reverberation room.
• Acustica per chi progetta — speech/music rooms chapter (clarity, treatment).

Learn more: Room simulator wiki →