Alternative sum rules and waterbed effects of Lorentz resonator system for sound absorption and transmission in a unidimensional waveguide

TL;DR

This paper develops new linear sum rules for passive acoustic systems using Herglotz functions, revealing fundamental constraints and the waterbed effect in broadband sound absorption within unidimensional waveguides with Lorentz resonators.

Contribution

It introduces alternative sum rules that avoid non-linear terms, providing clearer physical insights and predicting performance limits for broadband acoustic absorbers and isolators.

Findings

Sum rules effectively predict absorption constraints

Demonstrates the waterbed effect in resonator systems

Guides design of optimal broadband sound absorbers

Abstract

We investigate fundamental constraints on passive linear time-invariant acoustic systems through the developing alternative linear sum rules for sound absorption and transmission. Our approach, based on the Herglotz function method, yields integral identities without non-linear logarithmic terms or frequency weightings, providing clearer physical insights into system performance limits. The study focuses on unidimensional waveguides with Lorentz resonators, encompassing various practical acoustic structures. The developed sum rules are found to be particularly effective in predicting constraints on the average sound absorption coefficient for broadband absorbers operating in deep-subwavelength structures. Based on these rules, we demonstrate the waterbed effect in such systems, highlighting the inherent compromises between absorption efficiency, bandwidth, and device thickness. Through case studies of resonator arrays and membranes, we illustrate the practical implications of these new sum rules for designing optimal sound absorbers and isolators. The work concludes with a discussion on the challenges and future prospects in passive noise control, suggesting potential pathways to surpass current performance boundaries.