  We consider a waveguide modeled by the Laplacian in a straight planar strip.
The Dirichlet boundary condition is taken on the upper boundary, while on the
lower boundary we impose periodically alternating Dirichlet and Neumann
condition assuming the period of alternation to be small. We study the case
when the homogenization gives the Neumann condition instead of the alternating
ones. We establish the uniform resolvent convergence and the estimates for the
rate of convergence. It is shown that the rate of the convergence can be
improved by employing a special boundary corrector. Other results are the
uniform resolvent convergence for the operator on the cell of periodicity
obtained by the Floquet-Bloch decomposition, the two-terms asymptotics for the
band functions, and the complete asymptotic expansion for the bottom of the
spectrum with an exponentially small error term.
