  We study temporal oscillations, known as dynamical beats, developed by a
propagating pulse due to its interaction with a near-resonant collective medium
of $^{133}$Cs atoms randomly captured by a nanofiber-based optical lattice. A
phenomenological theory provides an intuitive explanation and quantitative
predictions, which are improved by an input-output theory considering
multiple-scattering between the atoms. The results deepen our understanding of
light propagation in waveguide QED, essential in time-frequency analysis and
light engineering for probing, manipulating, and exploiting many-body quantum
systems.
