The ZAPPA project: designing better reverberation rooms

Before I worked on microphones, I worked on rooms. For a year at KU Leuven I worked full time on a project that ROCKWOOL, for reasons of their own, named Zappa, after Frank Zappa, who has nothing to do with acoustics. The question behind it sounds almost too simple: if you measure how much sound a material absorbs, why do two laboratories so often disagree?

The same material, two answers

Sound-absorbing materials are rated by a number per frequency band, the absorption coefficient $\alpha$, running from 0 (perfectly reflective) to 1 (perfectly absorbing). Architects and engineers choose materials from these ratings, so the ratings have to be trustworthy. They are measured in a reverberation room: a hard-walled room where you measure the reverberation time empty, lay a sample of the material on the floor, and measure again. The faster decay with the sample present tells you how much it absorbed. From the two reverberation times, Sabine's formula gives the diffuse absorption coefficient:

$$\alpha_\mathrm{d} = \frac{24\ln(10)}{c_0 \, S_\mathrm{abs}} \left( \frac{V_\mathrm{rs}}{T_\mathrm{s}} - \frac{V_\mathrm{re}}{T_\mathrm{e}} \right)$$

where $T_\mathrm{e}$ and $T_\mathrm{s}$ are the reverberation times of the empty room and of the room with the sample, $V_\mathrm{re}$ and $V_\mathrm{rs}$ the corresponding air volumes, $c_0$ the speed of sound, and $S_\mathrm{abs}$ the exposed sample area. The whole procedure is standardized as ISO 354. And yet round-robin tests, where the same product is sent from lab to lab, keep finding large disagreements, especially below 500 Hz.

It is the room, not just the material

The catch is that absorption is not a property of the sample alone. It depends on the sound field the sample sits in. Above a room's Schroeder frequency the field is approximately diffuse, a near-uniform mix of waves arriving equally from every direction, and measurements behave. Below it, only a handful of room modes are excited, the field depends on the specific shape of the room, and a large absorptive sample further destroys what diffusivity there was in its own neighbourhood. Finite samples add an "edge effect" that can even push the measured coefficient above 1. So a low-frequency number measured in one room can say as much about that room as about the material.

Two questions

ZAPPA split in two. The first question was fundamental: is there even a well-defined value to aim for at low frequencies? The answer, worked out mainly by Cédric Van hoorickx within the ERC VirBAcous project, is yes. If you average the absorption a finite sample shows across a diverse ensemble of rooms, and account properly for how the sample interacts with the field, that average converges to the theoretical diffuse absorption coefficient, even at low frequency. A Monte Carlo study over detailed room models confirmed it. So the diffuse coefficient is a legitimate target, and the problem becomes making a single real room measure close to it.

The second question was applied, and it was mine: how should you shape a reverberation room so that its measurements land on those reference values?

Simulating the measurement

You cannot optimize what you cannot compute quickly. I built a finite-element model of the absorption measurement in the low-frequency range (roughly 50 to 250 Hz), focusing on highly absorptive porous samples, which can be modelled accurately as equivalent fluids (Delany-Bazley-Miki). Rather than solve for the full sound field on every iteration, I estimated absorption through a power-balance approach, which is far cheaper. Validated against both real measurements and a much more expensive full finite-element solution, it agreed well, which is what made it usable inside an optimization loop. With it I could sweep room shape, source positions, and diffuser layouts and watch the measured absorption move.

Optimizing the shape

The optimization searched room geometries, from cuboid dimension ratios to skewed hexahedra, for the ones that minimize the distance between the simulated absorption and the theoretical diffuse value at low frequencies. Two findings stood out. First, certain shapes do bring measured absorption close to the diffuse reference, where standard cuboid rooms struggle. Second, in those same shapes the result is also less sensitive to where you place the sources and diffusers, which is exactly the robustness a measurement standard wants. I also checked that the good designs hold up across different sample types and small geometric inaccuracies.

What came of it

The practical output is a set of design guidelines for building new reverberation rooms, or retrofitting existing ones, to improve the reproducibility of ISO 354 at low frequency, plus concrete suggestions fed into the standard's ongoing revision. The work was published in Applied Acoustics (see publications), and the design ideas informed a real reverberation room later built at ROCKWOOL's headquarters in Hedehusene, Denmark.

Frank Zappa, still, had nothing to do with any of it.