Evidence of two-dimensional magic clusters in the scattering of sound

We present experimental evidence of two-dimensional (2D) magic clusters consisting of N solid rods hexagonally distributed in air that scatter sound as fluidlike cylinders with parameters (density and sound speed) equal to those obtained by homogenization of the corresponding infinite periodic lattice. Our simulations reveal magic sizes at $N=7$, 19, 37, 61, 85, 121, and 163, for which the contribution of triple scattering events presents minima. Here, the magic cluster $N=7$ is used as a building block in the construction of a crystal slab, whose experimental characterization shows an acoustic response similar to that of a slab made of fluidlike cylinders with parameters determined by homogenization of the underlying lattice in the magic cluster. We conclude that magic clusters represent a class of 2D fluidlike metamaterials whose acoustical properties can be tailored within certain limitations.