  We numerically analyze the performance of labyrinthine acoustic metamaterials
with internal channels folded along a Wunderlich space-filling curve to control
low-frequency sound in air. In contrast to previous studies, we perform direct
modeling of wave propagation through folded channels, not introducing effective
theory assumptions. As a result, we reveal that metastructures with channels,
which allow wave propagation in the opposite direction to incident waves, have
different dynamics as compared to those for straight slits of equivalent
length. The differences are attributed to activated tortuosity effects and
result in 100% wave reflection at band gap frequencies. This total reflection
phenomenon is found to be insensitive to thermo-viscous dissipation in air. For
labyrinthine channels generated by iteration levels, one can achieve broadband
total sound reflection by using a metamaterial monolayer and efficiently
control the amount of absorbed wave energy by tuning the channel width. Thus,
the work contributes to a better understanding of labyrinthine metamaterials
with potential applications for reflection and filtering of low-frequency
airborne sound.
