The goal of the proposed research is to develop theoretical predictions for the intensity and absorption of finite-amplitude sound waves. The intended application is to biomedical ultrasound as used for diagnosis, hyperthermia, surgery, and lithotripsy. We expect to obtain predictions for a wide variety of wave fields. signals, and media: 1. Fields - plane, spherical, and directional. Of most practical interest are focused and unfocused beams. 2. Signals - periodic, modulated, and transient. Both continuous waveforms and waveforms containing shocks are to be considered. 3. Media - thermoviscous fluids, relaxing fluids, and fluids having arbitrary (small-signal) absorption characteristics. The absorption will be computed from the relation alpha = -delta leads to I/2I, where the intensity I will have to be found from existing analytical and computational solutions. The only known analytical solutions are those based on weak shock theory (which is limited in application to one-dimensional waves, does not include diffraction or ordinary small-signal absorption, but may be used for signals of arbitrary waveform) and Burger's equation (for which the solution is known only for plane, periodic waves in thermoviscous media). However, computer solutions for one- dimensional waves in arbitrary media (diffraction not included) and for paraxial beams (parabolic approximation, arbitrary media, diffraction included) are known. It is thus felt that a sufficient range of theoretical tools are available to permit the goal to be reached.
