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Recent fundamental results concerning the ultimate performance of electromagnetic absorbers were adapted and extrapolated to the field of sound waves. It was possible to deduce some appropriate figures of merit indicating whether a particular structure was close to the best possible matching properties. These figures of merit had simple expressions and were easy to compute in practical cases. Numerical examples illustrated that conventional state-of-the-art matching structures had an overall efficiency of approximately 50% of the fundamental limit. However, if the bandwidth at -6 dB was retained as a benchmark, the achieved bandwidth would be, at most, 12% of the fundamental limit associated with the same mass for the matching structure. Consequently, both encouragement for future improvements and accurate estimates of the surface mass required to obtain certain desired broadband properties could be provided. The results presented here can be used to investigate the broadband sound absorption and to benchmark passive and active noise control systems.