Abstract: An acoustic metamaterial structure acts as a sound reducing filter in that the level of sound that exits the structure is much less than the magnitude of sound that enters the structure. In forming the structure, modular stages of a given geometry are stacked upon one another to create a cell. Each stage of the cell is provided with a nozzle that is acoustically connected to the nozzles of other stages of the cell. The stages have chambers that are positioned radially or laterally outside of the respective nozzles, with the chambers of the cell being acoustically connected to one another. An amalgamation of cells are arranged in an adjacent formation, with chambers of the cells being acoustically connected to one another for purposes of protecting items, components and people from destructive levels of sound. The geometry of the nozzles and chambers are designed for economical additive manufacture with acoustic infills.