Violin sound synthesis from first principles
Gabriel Weinreich · The Journal of the Acoustical Society of America · 1983
A simple computer model of a violin has been constructed. It consists of two arrays carrying the forward and backward waves on the string, appropriate reflection rules at the bridge and finger, a bow of finite width, and a combination of parallel two-pole filters to simulate the radiativity of the violin body. The string is assumed to be nondispersive, although an equivalent amount of dispersion can be included in one or both of the boundary conditions. The instantaneous force exerted by the bow on the string is formulated as a single-valued function of their relative velocity. The output signal can be converted into sound. The model has been used to study a number of phenomena, including the dynamic changes in the Helmholtz motion when the bow velocity changes, and in particular the starting transients.