Matter to be treated by mediated electrochemical redox reaction is mixed with electrolyte containing ions of an electrochemically re-generable primary oxidising or reducing species. The mixture is subjected to ultrasonic and/or sonic insonation directly to enhance the respective oxidation or reduction interaction between the ions and the matter. In this process the primary oxidising or reducing species is reduced or oxidised respectively and is re-generated by electric potential applied in an electrochemical cell.