  Fast magnetoacoustic wave is an important tool for inferring solar
atmospheric parameters. We numerically simulate the propagation of fast wave
pulses in randomly structured plasmas mimicking the highly inhomogeneous solar
corona. A network of secondary waves is formed by a series of partial
reflections and transmissions. These secondary waves exhibit
quasi-periodicities in both time and space. Since the temporal and spatial
periods are related simply through the fast wave speed, we quantify the
properties of secondary waves by examining the dependence of the average
temporal period ($\bar{p}$) on the initial pulse width ($w_0$) as well as the
density contrast ($\delta_\rho$) and correlation length ($L_c$) that
characterize the randomness of the equilibrium density profiles. For
small-amplitude pulses, $\delta_\rho$ does not alter $\bar{p}$ significantly.
Large-amplitude pulses, on the other hand, enhance the density contrast when
$\delta_\rho$ is small but have a smoothing effect when $\delta_\rho$ is
sufficiently large. We found that $\bar{p}$ scales linearly with $L_c$ and that
the scaling factor is larger for a narrower pulse. However, in terms of the
absolute values of $\bar{p}$, broader pulses generate secondary waves with
longer periods, and this effect is stronger in random plasmas with shorter
correlation lengths. Secondary waves carry the signatures of both the leading
wave pulse and background plasma, our study may find applications in MHD
seismology by exploiting the secondary waves detected in the dimming regions
after CMEs or EUV waves.
