Sound speed and attenuation in dense, non-cohesive air-granular systems

A one-dimensional mathematical model is derived for the speed and attenuati on of sound in a dense, non-cohesive uniform granular material. The model u ses permeability to describe viscous air drag, a frictional term resulting from wall friction, a contribution from internal friction, assumes isotherm al 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. th e solid wave becomes faster. Low frequency wave speeds are matched to exper imental fluidization data on voidage. and explain the rapid decrease in spe ed just above the fluidization point, where speeds drop from up to 30 to ab out 12 m/s. As the voidage increases further, the speed increases due to vo idage 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 s ound speed of about 278 m/s. Initially. the corresponding attenuation incre ases quadratically with frequency, but then reduces to a square root increa se with frequency. and eventually becomes constant as the corresponding sou nd speed becomes constant. However, the theory also predicts that for non-z ero wall and/or inter-particle friction, at low frequencies, the sound spee d is non-monotonic in frequency, due to the solid acting as a high pass fil ter to sound waves, and such non-monotonic behaviour is evident is some rec ent experimental data. (C) 2001 Elsevier Science Ltd. All rights reserved.