In this study, we examine effective modes of acoustic waves in periodic solid layers embedded in ideal or viscous fluids. In particular, at the long-wavelength limit, a three-scale homogenization analysis is developed to derive the effective group velocities in analytical forms for the shear-vertical (SV) waves as well as for the longitudinal-shear-horizontal (P-SH) waves. It is found that propagating modes, i.e., modes with real group velocities, may be supported even if the fluid phase is viscous. A criterion for the existence of a vanishing effective viscosity is derived based on composite medium constants and the filling ratio of the fluid phase. The critical filling ratios at which an evanescent mode changes to a propagating mode are given for various solid-water systems. Finally, we would like to acknowledge that the analysis presented here benefited greatly from the article drawn attention to the first author by Prof. Mei some ten years ago: “C. Mei, J-L. Auriault, and C. O. Ng (1996) Some Applications of the Homogenization Theory, Advances in Applied Mechanics, Vol. 32, edited by J. Hutchinson and T. Y. Wu, Academic Press, New York.”

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