  A generalized macroscopic nonlocal theory of sound propagation in
rigid-framed porous media saturated with a viscothermal fluid has been recently
proposed, which takes into account both temporal and spatial dispersion. Here,
we consider applying this theory capable to describe resonance effects, to the
case of sound propagation through an array of Helmholtz resonators whose
unusual metamaterial properties such as negative bulk moduli, have been
experimentally demonstrated. Three different calculations are performed,
validating the results of the nonlocal theory, relating to the
frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode,
for 1D propagation in 2D or 3D periodic structures.
