Quasilossless acoustic transmission in an arbitrary pathway of a network

Acoustic metamaterials have exhibited extraordinary potential for manipulating the propagation of sound waves. To date, it has been a challenge to control the propagation of a sound wave through arbitrary pathways in a network. Here, we design a symmetry-breaking, cross-shaped metamaterial comprising Helmholtz resonant cells and a square column. The square column is eccentrically arranged. The sound wave can be transmitted in a quasilossless manner through the channels along the eccentric direction with compressed spaces, which breaks through the general transmission phenomenon. This exotic propagation characteristic is verified by the band structure and the mode of the metamaterial. Two acoustic networks, including a $2\ifmmode\times\else\texttimes\fi{}2$ network and an $8\ifmmode\times\else\texttimes\fi{}8$ network, demonstrate the quasilossless propagation of the sound wave along various arbitrarily shaped pathways, which include a Great Wall shape, a stairway shape, and a serpentine shape, by reconfiguring the eccentric directions. This ability opens up a new method for routing sound waves and exhibits promising applications ranging from acoustic communication to energy transmission.