A one-dimensional mathematical model is derived for the speed and attenuation of sound in a dense, non-cohesive uniform granular material. The model uses permeability to describe viscous air drag, a frictional term resulting from wall friction, a contribution from internal friction, assumes isothermal conditions, and ignores shear effects. Two dilational waves are derived-one associated with the solid, and one with air. In fluidized systems, the wave associated with air is always faster. In unfluidized systems, the air wave is faster at high frequencies, but at sufficiently low frequencies. the solid wave becomes faster. Low frequency wave speeds are matched to experimental fluidization data on voidage. and explain the rapid decrease in speed just above the fluidization point, where speeds drop from up to 30 to about 12 m/s. As the voidage increases further, the speed increases due to voidage changes, and eventually, another increase in speed occurs as the air compressibility changes from isothermal to adiabatic conditions. The theory predicts that for zero solid friction, and at low frequencies, the fastest wave speed is essentially constant. and then increases to the isothermal sound speed of about 278 m/s. Initially. the corresponding attenuation increases quadratically with frequency, but then reduces to a square root increase with frequency. and eventually becomes constant as the corresponding sound speed becomes constant. However, the theory also predicts that for non-zero wall and/or inter-particle friction, at low frequencies, the sound speed is non-monotonic in frequency, due to the solid acting as a high pass filter to sound waves, and such non-monotonic behaviour is evident is some recent experimental data.