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We numerically analyze the performance of labyrinthine acoustic metamaterialswith internal channels folded along a Wunderlich space-filling curve to controllow-frequency sound in air. In contrast to previous studies, we perform directmodeling of wave propagation through folded channels, not introducing effectivetheory assumptions. As a result, we reveal that metastructures with channels,which allow wave propagation in the opposite direction to incident waves, havedifferent dynamics as compared to those for straight slits of equivalentlength. The differences are attributed to activated tortuosity effects andresult in 100% wave reflection at band gap frequencies. This total reflectionphenomenon is found to be insensitive to thermo-viscous dissipation in air. Forlabyrinthine channels generated by iteration levels, one can achieve broadbandtotal sound reflection by using a metamaterial monolayer and efficientlycontrol the amount of absorbed wave energy by tuning the channel width. Thus,the work contributes to a better understanding of labyrinthine metamaterialswith potential applications for reflection and filtering of low-frequencyairborne sound.

Labyrinthine acoustic metamaterials with space-coiling channels for low-frequency sound control