Optimal sound-absorbing structures

The causal nature of the acoustic response dictates an inequality that relates the two most important aspects of sound absorption: the absorption spectrum and the sample thickness. We use the causality constraint to delineate what is ultimately possible for sound absorbing structures, and denote those which can attain near-equality for the causality constraint to be "optimal.'' Anchored by the causality relation, a design strategy is presented for realizing structures with target-set absorption spectra and a sample thickness close to the minimum value as dictated by causality. By using this approach, we have realized a 10.86 cm-thick structure that exhibits a broadband, near-perfect flat absorption spectrum starting at around 400 Hz, while the minimum sample thickness from the causality constraint is 10.36 cm. To illustrate the versatility of the approach, two additional optimal structures with different target absorption spectra are presented. This "absorption by design'' strategy would enable the tailoring of customized solutions to difficult room acoustic and noise remediation problems.