  This work is devoted to the resolution of the Helmholtz equation $-(\mu u')'
- \rho \omega^2 u = f$ in a one-dimensional unbounded medium. We assume the
coefficients of this equation to be local perturbations of quasiperiodic
functions, namely the traces along a particular line of higher-dimensional
periodic functions. Using the definition of quasiperiodicity, the problem is
lifted onto a higher-dimensional problem with periodic coefficients. The
periodicity of the augmented problem allows us to extend the ideas of the
DtN-based method developed for the elliptic case. However, the associated
mathematical and numerical analysis of the method are more delicate because the
augmented PDE is degenerate, in the sense that the principal part of its
operator is no longer elliptic. We also study the numerical resolution of this
PDE, which relies on the resolution of Dirichlet cell problems as well as a
constrained Riccati equation.
