The propagation of a normally incident plane acoustic wave through a three-dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes A and B, the wavelength , and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only

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... on the transmission coefficient, 0 , of an infinitely long slab with the same configuration. The determination of 0 requires the solution of an infinite set of algebraic equations. These equations are approximately solved by exploiting the small parameter D / ͱ AB. Remarkably, this structure is transparent at certain frequencies and opaque for all others. Such a structure may be useful in constructing narrow-band filters and resonators.