Newfound sound wave scattering rule may lead to less bulky, more effective soundproofing

June 8, 2026 report Newfound sound wave scattering rule may lead to less bulky, more effective soundproofing Krystal Kasal Author Gaby Clark Scientific Editor Robert Egan Associate Editor Researchers in China recently uncovered a quantum-inspired rule governing how sound is scattered by certain physical properties of a material. Their research, published in Physical Review Letters, may lead to the ability to design materials with optimal, broadband sound blocking. Rules governing acoustic metamaterial engineering The mass law in acoustics says that the denser a wall is, the more effectively it blocks sound waves. More specifically, for every doubling of mass per unit area, the sound transmission loss increases by approximately 6 decibels. However, this law doesn't always hold. Acoustic metamaterials can manipulate sound in ways that break the traditional mass law, enabling applications like sound cloaking and perfect absorption. Acoustic metamaterials are engineered to manipulate, direct and control sound waves in ways that are not possible with natural materials. These materials are designed at the subwavelength scale using periodic "unit cells" to achieve exotic properties, like negative mass density or a negative refractive index, allowing for extreme noise cancellation and sound routing. "In essence, metamaterials can concentrate modes within a specific band of interest, to create a large range of dynamic properties, by leveraging the density of states from other frequencies. This enables exciting applications such as wave focusing, cloaking, imaging, tweezing and perfect absorption. However, the mass law disregards the causal dispersion of materials and could be inapplicable at excessively low frequencies (stiffness control region) or excessively high frequencies (where higher-order modes emerge)," the authors of the new study wrote. Because metamaterial engineering often relies on resonance, there are inherent restrictions on performance across frequencies. In particular, there was not a known universal rule connecting the physical properties of a material to its ability to block or scatter sound across all frequencies. An acoustic analogy of a quantum rule The researchers wanted to find out how improving the performance of a metamaterial in one frequency range would affect another range of frequencies. To do this, they derived a sum rule governing acoustic scattering, which served as an analogy of the Baldin sum rule from quantum physics. The Baldin sum rule relates the "stiffness" or polarizability of subatomic particles to how they absorb radiation over all possible frequencies, and indicates that a nucleus can only scatter a set amount of photons. When a nucleus scatters more photons in one range of frequencies, it must scatter fewer photons in other frequency ranges. The acoustic version showed that the total ability of a material to scatter sound waves is fundamentally limited by its static mass and stiffness. This meant that if more acoustic waves were scattered in one range of frequencies, less were scattered in another. The team also validated the results with numerical simulations of classic acoustic metamaterial designs, including Helmholtz and dipole resonators, and then with experimental tests on three types of resonators in air ducts. For the experiments, they measured sound transmission and compared to predictions from the sum rule. These measurements and predictions matched up, confirming that the sum rule works and also showing broader sound-blocking bandwidth than traditional designs. "The acoustic Baldin sum rule serves as a predictive tool: By maximally suppressing the low-frequency σext, scattering resources are redistributed to higher frequencies, broadening the operational bandwidth," the study authors explain. Although the study focuses on one-dimensional sound propagation, the researchers say the framework can be extended to 2D and 3D systems, potentially impacting an array of acoustic technologies. Potential applications of the work are wide-ranging, including improved soundproofing materials for buildings, vehicles and industrial settings, more efficient and compact silencers for ventilation systems or even use in medical ultrasound or sonar technologies. Written for you by our author Krystal Kasal, edited by Gaby Clark, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you. Publication details Sichao Qu et al, Acoustic Analogy of Quantum Baldin Sum Rule for Optimal Causal Scattering, Physical Review Letters (2026). DOI: 10.1103/dbs8-g68w. On arXiv: DOI: 10.48550/arxiv.2601.02630 Journal information: Physical Review Letters , arXiv © 2026 Science X Network