A ray-tracing semiclassical (RTS) geometrical method was developed to model the sound field in a room. The method relies on the construction of the Green's function of the amplitude equation by employing the semiclassical propagator. Available commercial applications of geometrical methods in room acoustics are restricted to energy methods and therefore limited to higher frequencies. RTS is classified as a phased geometrical method capable of modeling interference effects, and can be thus used also in the lower frequency range which was as well the goal of this study.
In RTS, sound rays are emitted from a point source in random directions. They reflect specularly on the boundaries and are detected in a spherical region. In this way the frequency response is constructed, giving a complete insight into the acoustic properties of a room. The frequency response in a rectangular room has been compared to the analytical solution derived as a perturbation for the case of weak damping. This presented a rigorous test of the method which provided good results. The RTS method was tested also for a set of more complex boundary conditions (resonator, porous material) for which the frequency response and 1/3 octave band reverberation time were compared to the finite element method. A systematic agreement is observed.
Furthermore, the RTS results were compared to measurements performed by the specially developed multi-microphone measurement technique. Both methods can correctly identify room resonances and visualize modal shapes.
In geometrical methods diffraction is excluded by definition, therefore I attempted to directly extend the RTS method to trajectories in the form of broken straight lines, which can propagate in the geometric shadow. For the infinite edge case the frequency response was compared to the finite element method and qualitative agreement was observed. Moreover, I theoretically reviewed the possibility of constructing the Green's function with the summation over non-classical trajectories. From this viewpoint, I again suggested the use of broken trajectories. In their proximity the variation of the action was examined and important aspects of the numerical implementation were introduced.