  Characterising spectral variability of radio sources is a technique that
offers the ability to determine the astrophysics of the intervening media,
source structure, emission and absorption processes. We present broadband
(0.072--10 GHz) spectral variability of 15 peaked-spectrum (PS) sources with
the Australia Telescope Compact Array (ATCA) and the Murchison Widefield Array
(MWA). These 15 PS sources were observed quasi-contemporaneously with ATCA and
the MWA four to six times during 2020 with approximately a monthly cadence.
Variability was not detected at 1--10GHz frequencies but 13 of the 15 targets
show significant variability with the MWA at megahertz frequencies. We conclude
the majority of variability seen at megahertz frequencies is due to refractive
interstellar scintillation of a compact component ~25 mas across. We also
identify four PS sources that show a change in their spectral shape at
megahertz frequencies. Three of these sources are consistent with a variable
optical depth from an inhomogeneous free-free absorbing cloud around the
source. One PS source with a variable spectral shape at megahertz frequencies
is consistent with an ejection travelling along the jet. We present spectral
variability as a method for determining the physical origins of observed
variability and for providing further evidence to support absorption models for
PS sources where spectral modelling alone is insufficient.

Astrophysics of Galaxies;High Energy Astrophysical Phenomena