  A chain of small Josephson junctions (aka superinductor) emerged recently as
a high-inductance, low-loss element of superconducting quantum devices. We
notice that the intrinsic parameters of a typical superinductor in fact place
it into the Bose glass universality class for which the propagation of waves in
a sufficiently long chain is hindered by pinning. Its weakness provides for a
broad crossover from the spectrum of well-resolved plasmon standing waves at
high frequencies to the low-frequency excitation spectrum of a pinned charge
density wave. We relate the scattering amplitude of microwave photons reflected
off a superinductor to the dynamics of a Bose glass. The dynamics at long and
short scales compared to the Larkin pinning length determines the low- and
high-frequency asymptotes of the reflection amplitude.
