Dynamic mass density and acoustic metamaterials

Mass density of a composite is generally taken as the volume-averaged value of 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 account of some recent experimental data, as well as to make possible the realization of acoustic metamaterials. Physical reason for the difference between 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.