  We report on an observation of propagating compression waves in a
quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow
of air. The collective wave speed is an order of magnitude faster than the
speed of the particles. This gives rise to anomalously large number
fluctuations dN ~ $N^{0.72 \pm 0.04}$, which are greater than ordinary number
fluctuations of N^{1/2}. We characterize the waves by calculating the
spatiotemporal power spectrum of the density. The position of observed peaks,
as a function of frequency w and wavevector k, yields a linear dispersion
relationship in the long-time, long-wavelength limit and a wavespeed c = w/k.
Repeating this analysis for systems at different densities and air speeds, we
observe a linear increase in the wavespeed with increasing packing fraction
with no dependence on the airflow. Although air-fluidized rods self-propel
individually or in dilute collections, the parallel and perpendicular
root-mean-square speeds of the rods indicate that they no longer self-propel
when propagating waves are present. Based on this mutual exclusivity, we map
out the phase behavior for the existence of waves vs self-propulsion as a
function of density and fluidizing airflow.
