A method for effectively degrading and destroying many pharmaceutical and personal care compounds in aqueous solutions. The method includes providing an aqueous solution containing at least one pharmaceutical or personal care compound (e.g., estrogene hormone, antibiotics, and the like) to a reactor. A source of ultrasound is provided having a predetermined energy and intensity. The aqueous solution is sonicated in the reactor to degrade and destroy the at least one pharmaceutical or personal care compound. Further provided is a related method for degrading and destroying many pharmaceutical and personal care pollutants in aqueous sludge while simultaneously enhancing the biodegradability and dewaterability of the aqueous sludge. Still further provided is a related method for predicting the first order ultrasound-induced degradation rate constant of any estrogen compound present in an aqueous solution based on the rate constant of estrone.