Abstract: The present invention provides processes and apparatus for selectively dissolving and removing unwanted solid and semi-solid materials and the like, within a highly localized region utilizing ultra-high energy acoustical waves having a frequency in the range above 50 MHz, for example from about 50 MHz to about 100 GHz. The invention apparatus includes a piezoelectric transducer that is modified to increase the amplitude of acoustical waves of a given frequency without increase in power to the system. The invention and apparatus have important applications in surgical procedures for the treatment of atherosclerotic plaque, prostate disorders, cancers, orthopedic and cosmetic surgery, various types of orthopedic surgery, including atheroscopic surgery, and the like. The present invention is also useful in a wide variety of non-surgical applications, including industrial processes, wherein materials are desired to be selectively removed in a very localized region.