Sound Absorbers Share One Hidden Rule: A Gradual Rise in Acoustic Resistance

Engineers have long chased a deceptively simple goal: a sound absorber that swallows nearly all incident acoustic energy across a wide range of frequencies, rather than only in a narrow band around a single resonance. Microperforated panels, thin sheets punctuated with millimetric or sub-millimetric holes, are among the most attractive candidates because they contain no fibrous material, can be wiped clean, hold their shape over decades, and slot neatly into prefabricated walls, ceilings and façades. Yet designing a stack of these panels that absorbs broadband sound near-perfectly has remained more art than science, with researchers relying on heavy numerical optimization that often produces solutions specific to whichever algorithm they happen to use. A new study published in Results in Physics argues that the field has been optimizing the wrong variables, and that a single, geometry-independent quantity holds the real key to broadband absorption.

The research, carried out by Yi Yang, Yujie Qian, Xiaodong Shi and Dawei Li, tackles a persistent ambiguity in the multilayer microperforated panel literature. When different teams report that shrinking hole diameters layer by layer, reducing the perforation ratio, or thickening panels toward the back of a stack all improve absorption, it has been unclear whether any particular geometric trend is physically essential, or whether these apparently different recipes are merely alternative ways of satisfying the same underlying acoustic condition. The authors suspected the latter. Within the standard lumped description of a microperforated panel, its response to sound is captured by just two quantities: a dissipative acoustic resistance, which converts sound energy into heat through viscous friction in the tiny holes, and an effective acoustic inertance, the mass-like reactance of the air oscillating in and near those apertures. Many different combinations of hole diameter, panel thickness and perforation ratio can produce the same pair of values, meaning the mapping from geometry to acoustics is fundamentally many-to-one.

To test this idea rigorously, the team ran four independent global optimization algorithms, namely a Genetic Algorithm, a Grey Wolf Optimizer, an Artificial Immune Algorithm and a Multi-Start Local Search Algorithm, on both three-layer and six-layer panel stacks. The three-layer designs were optimized for the band from 100 to 6000 hertz under a total cavity depth of 50 millimetres, while the six-layer designs targeted 500 to 12000 hertz within 100 millimetres. The objective function was the band-averaged normal-incidence absorption coefficient, a metric that rewards flat, high absorption across the whole band rather than isolated peaks. All four algorithms delivered excellent performance, with band-averaged coefficients around 0.908 for the three-layer case and 0.983 for the six-layer case, but the optimized geometries told a surprising story.

Contrary to the widespread assumption that hole size or perforation ratio should decrease monotonically through the stack, neither parameter showed a consistent gradient. In several three-layer solutions the front panel actually had a substantially larger aperture than the layers behind it, and in the six-layer case near-perfect absorption was achieved even with completely uniform hole diameters and perforation ratios across all layers. The only geometric trend that appeared consistently was a monotonic increase in panel thickness along the direction of wave propagation, but the authors caution against reading too much into this. When they relaxed the lower bound on hole diameter from 0.1 millimetres to 0.01 millimetres, allowing ultra-microperforations that dramatically widen the accessible resistance design space, even that thickness trend vanished. The apparent geometric rules, it turned out, were artifacts of the constraints imposed on the search, not physical necessities.

The decisive insight emerged when the researchers stopped looking at geometry and instead computed the layer-wise acoustic impedance of each optimized design. Across every algorithm, every layer count and every constraint set, the same pattern appeared: the relative acoustic resistance increased monotonically from the front layer facing the incident sound to the back layer near the rigid backing, while the acoustic reactance stayed comparatively stable. This graded resistance is what allows sound waves to enter the structure progressively instead of being reflected at the front surface, a condition known as impedance matching. When the total relative resistance approaches unity and the total reactance approaches zero, the absorber becomes acoustically indistinguishable from open air, and the absorption coefficient approaches one. The overlapping resonances of the multiple panel-cavity stages then fill in the spectral valleys between individual absorption peaks, producing the smooth, near-unity response that the band-averaged objective explicitly demands.

To confirm that the gradient itself, rather than some other feature of the optimized stacks, was responsible, the team repeated the optimization with all panel parameters forced to be identical across layers, so that every layer had the same acoustic resistance. The result was unmistakable. Uniform-resistance stacks showed noticeably fluctuating absorption curves and fell short of the smooth near-perfect characteristics of their graded counterparts, with band-averaged coefficients dropping to about 0.875 for the three-layer case and 0.952 for the six-layer case. The comparison also cast new light on earlier work by Qian and colleagues, who had reported that dual-gradient panels, with both hole diameter and perforation ratio decreasing layer by layer, outperformed single-gradient designs. The new analysis suggests that this superiority reflected the favourable impedance profile generated by that particular parameter combination, not any intrinsic magic of dual gradients.

The demonstration was strikingly quantitative. When the researchers compared the published dual-gradient configuration against three single-parameter alternatives, one grading only the aperture diameter downward, one grading only the perforation ratio downward, and one grading only the panel thickness upward, all four designs produced essentially identical absorption. For the three-layer absorber the band-averaged coefficient fell between 0.9936 and 0.9937 across all four routes, and for the six-layer absorber it was 0.9969 in every case. In other words, the strong performance previously credited to a dual geometric gradient can be fully reproduced by much simpler single-parameter designs, provided those designs generate an equivalent resistance progression. This is the central practical payoff of shifting the design objective from geometry to resistance: it collapses a high-dimensional search space into a lower-dimensional, transferable rule.

Equivalent absorption does not mean all geometric routes are equally convenient, however. Because panel thickness and perforation ratio scale both the resistive and the inertial parts of a layer’s impedance, using either variable alone to create a large resistance contrast also tends to create a pronounced reactance contrast that can detune the broadband matching. Aperture diameter, which enters the viscous perforation constant and the end corrections differently, offers strong leverage over resistance while producing a comparatively smaller spread in layer reactance. The numerical results therefore favour aperture-dominated grading as the most robust implementation route within the explored design space, though the authors stress this is a practical preference, not a universal ranking. Manufacturing resolution, clogging tolerance, mechanical strength and allowable porosity may all shift the preferred route in a given application.

Crucially, the claim was not left untested. The team fabricated both unconstrained full-parameter designs and deliberately restricted single-parameter gradient designs as three-layer and six-layer specimens, with the microperforated layers produced by a MEMS microfabrication process and the backing cavities made by 3D printing. Measurements were performed in a 30-millimetre impedance tube using the standing-wave-ratio method according to ISO 10534-1, over the 1500 to 6500 hertz range where the tube supports clean plane waves, with each specimen measured three times and calibrated against a piston-phone reference. The experimental spectra agreed well with theory in both trend and level, and both the unconstrained and single-parameter designs achieved similarly smooth, near-perfect absorption, with average absorption coefficients exceeding 0.96, exactly as the graded-resistance picture predicts. Across the target band the measured total resistance hovered near unity and the reactance near zero, confirming stable impedance matching with air.

The study’s limitations are clearly acknowledged: the validation covers normal incidence only and a specific frequency band, so diffuse-field and low-frequency performance remain open questions, and the deeper numerical benchmarks should not be read as practical thickness recommendations. Even so, the contribution is significant for anyone designing quiet rooms, vehicle cabins or industrial enclosures. Instead of trusting an optimizer to stumble upon a working stack of panels, engineers can now aim directly at a monotonic resistance gradient from front to back while keeping layer-to-layer reactance variation controlled, and then choose whichever geometric parameter, aperture diameter chief among them, best realizes that target under their manufacturing constraints. The geometry, in the end, is negotiable; the resistance profile is not.

Subject of Research: Graded acoustic resistance as a geometry-independent design principle for broadband sound absorption in multilayer microperforated panels

Article Title: Graded acoustic resistance as a design criterion for broadband absorption in multilayer microperforated panels

Article References: Yang, Y., Qian, Y., Shi, X., & Li, D. (2026). Graded acoustic resistance as a design criterion for broadband absorption in multilayer microperforated panels. Results in Physics, Article 108763. https://doi.org/10.1016/j.rinp.2026.108763

Image Credits: AI Generated

DOI: Not provided

Keywords: microperforated panels, acoustic resistance, impedance matching, broadband sound absorption, acoustic metamaterials, optimization algorithms, gradient structures, impedance tube, MEMS fabrication, noise control, acoustic impedance, multilayer absorbers