Abstract The absorption of broadband sound waves is crucial for numerous engineering applications. In recent years, a specific integral bound on brown noise absorption has been derived and used as guidance for absorber design optimization. This study examines the physical factors that determine this bound and concludes that, while causality is always satisfied in any mechanical system, it is ultimately the system stiffness that determines the actual integral limit. Labeling the bound as the “causal limit” risks interpreting major design improvements as potentially “overcoming causality”. It is demonstrated theoretically and experimentally that, for an absorber filled with porous materials, this absorption can be raised by 40% when compared to an absorber with the same pure air cavity, due to the extra fluid compressibility when sound propagates isothermally in porous media. For incident sound with a finite pink noise spectrum, optimal mass and damping parameters exist. However, because a compact absorber’s peak performance remains dependent on system stiffness, research should prioritize creating negative effective stiffness to neutralize positive cavity fluid stiffness, rather than pursuing the upper-bound equality required for brown noise.
Zhang et al. (2026) studied this question.