  The paper deals with the generic problem of two waveguides coupled by
perforations, which can be perforated tube mufflers without or with partitions,
possibly with absorbing materials. Other examples are ducts with branched
resonators of honeycomb cavities , which can be coupled or not, and splitter
silencers. Assuming low frequencies, only one mode is considered in each guide.
The propagation in the two waveguides can be very different, thanks e.g. to the
presence of constrictions. The model is a discrete, periodic one, based upon
4th-order impedance matrices and their diagonalization. All the calculation is
analytical, thanks to the partition of the matrices in 2nd-order matrices, and
allows the treatment of a very wide types of problems. Several aspects are
investigated: the local or non-local character of the reaction of one guide to
the other; the definition of a coupling coefficient; the effect of finite size
when a lattice with n cells in inserted into an infinite guide; the
relationship between the Insertion Loss and the dispersion. The assumptions are
as follows: linear acoustics, no mean flow, rigid wall. However the effect of
the series impedance of the perforations, which is generally ignored, is taken
into account, and is dis- cussed. When there are no losses, it is shown that,
for symmetry reasons, the cutoff frequencies depend on either the series
impedance or the shunt admittance , and are the eigenfrequencies of the cells
of the lattice, with zero-pressure or zero-velocity at the ends of the cells.
