  We investigate the scattering of elastic waves off a disordered region
described by a one-dimensional random-phase sine-Gordon model. The collective
pinning results in an effective static disorder potential with universal and
non-Gaussian correlations, acting on propagating waves. We find signatures of
the correlations in the wave transmission in a wide frequency range, which
covers both the weak and strong localization regimes. Our theory elucidates the
dynamics of collectively-pinned phases occurring in any natural or synthetic
elastic medium. The latter one is exemplified by a one-dimensional array of
Josephson junctions, for which we specify our results. The obtained results
provide benchmarks for the array-enabled quantum simulations addressing the
dynamics in broader and yet-unexplored domains of individual pinning and
quantum Bose glass.
