The sound-assisted fluidized bed combustion of powders of tyre derived fuel (TDF) and of a biomass (Robinia Pseudoacacia) has been studied to assess the benefits deriving from the application of an acoustic field on the performance of the combustor. Experiments consisted of steady combustion, either ordinary or sound-assisted, of TDF and Robinia fine particles. High intensity acoustic fields of 120Hz reduce carbon elutriation rates by a factor of about 1.5, increasing the fixed carbon conversion efficiency by 5-8% and 2-3% for TDF and Robinia respectively. Sound frequencies either lower or higher than 120Hz reduce the effectiveness of sound, approaching the performances of ordinary fluidized bed combustors. Results have been analyzed assuming that fine particles are present in the bed either freely moving in the interstices of the bed (free fines) or attached onto coarse inert bed particles (attached fines). Accordingly the inventory of carbon under steady state conditions in the bed depends on the competition between the following processes: elutriation of free fines, adhesion of fines onto bed material, attrition of fine-coarse aggregates and combustion of fine particles. In this framework, acoustic fields have the property of enhancing the formation of fine-coarse aggregates.