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, ΔN~N(0.72±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 ω and wave vector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed c=ω/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow.