  A theoretical investigation is made of acoustic wave propagation in a
periodically stubbed waveguide. In general the waveguide segments and stubs are
made of different materials. The acoustic wave in such a system has two
independent polarizations: out-of-plane and in-plane modes. The band structure
and transmission spectrum is studied for diverse geometries using a simple and
efficient version of the transfer-matrix method. For the same material between
the waveguide and symmetric stubs the width of some gaps can change, upon
varying the stub length or width, by more than one order of magnitude. A
further modulation can be achieved for different material between the stubs and
the main waveguide or if the stubs are asymmetric. The gaps in the band
structure of an infinitely long system correspond to those in the transmission
spectrum of the same system but with finite number n of units. For n finite i)
there exist pseudogaps that gradually turn into complete gaps with increasing
n, and ii) the introduction of defects gives rise to states in the gaps and
leads to transmission resonances.
