Dynamic mass density and acoustic metamaterials

The mass density of a composite is generally taken as the volume－averaged value of the components′ densities. Moreover, the same volume－averaged mass density is usually used to calculate the wave speed in the long wavelength limit, i.e., where the wavelength is much larger than the size of the inhomogeneities. In this paper we show via rigorous derivation that the dynamic mass density used in the calculation of (long wavelength) wave speed can differ significantly from the static volume averaged value. This recognition is shown to yield an excellent explanation of some recent experimental data, providing a basis for the realization of acoustic metamaterials. The physical reason for the difference between the two mass densities is attributed to the relative motion between the components. That is, the implicit assumption——that all components in a composite must move uniformly in the long wavelength limit——can be violated in the limit of large acoustic impedance contrast between the components. The dynamic mass density can even be negative for the locally resonant sonic materials, as demonstrated both experimentally and theoretically. The implications of this finding, in the context of acoustic metamaterials, are discussed.