In a model-based sound synthesis we create the time function of a musical instrument's sound by modelling and simulating its physical parameters and the mechanism of sound production. The process is helpful in musical instrument manufacturing, because the effects of the physical parameter changes become audible.
In the thesis we create the sound of a marimba bar struck with a mallet in free space observation points. We overview the physics and mathematics of strings and rods, and we solve the equations analytically based on the principle of modal superposition. The presence of excitation can't be handled analytically, thus we have to use a discretized numerical method, the finite difference method.
After determining the excited rod's vibrations, we overview the acoustic field formalism. We get the acoustic pressure values in the free space using the boundary element numerical method in frequency domain. We can hear and see the results by a MATLAB implementation.