Acoustic metamaterial exhibiting four different sign combinations of density and modulus

We fabricated a double negative acoustic metamaterial which consisted of Helmholtz resonators and membranes. Experimental data on the transmission and dispersion relation are presented. The system exhibits three frequencies where the acoustic state makes sharp transitions from density negative ({\rho} -NG) to double negative (DNG), modulus negative (B-NG), and double positive (DPS) in sequence with the frequency. We observed a wide range of negative refractive index from -0.06 to -3.7 relative to air, which will allow for new acoustic transformation techniques.