Time-domain simulation of the bowed cello string: Dual-polarization effect

Abstract

A detailed time-domain simulation is implemented to model the bowed cello string. Building on earlier simulation models, several new features have been added to make the model more realistic: in particular, both polarizations of the string motion are included, as well as the longitudinal vibrations of the bow hair. These additional features can be turned on and off in the model to evaluate their relative importance. In all previous simulations, the bow-hair was assumed stiff enough to suppress any motion of the string perpendicular to the bowing direction. High-speed video recordings, on the contrary, have suggested that the amplitude of this motion is not negligible compared to the motion of the string in the bowing direction. The major source of this motion is tracked down to the X-Y coupling through the bridge. Although this extra dimension of vibration may not necessarily contribute much to the radiated sound by itself, it can modulate the effective bow force and hence affect the stick-slip motion of the string. The longitudinal vibration of the bowhair is also included in our model. The compliance of the bow-hair was accounted for in previous studies in a crude way, but without enough detail to capture the difference between different bows.