Numerical study on transient response of the bowed string

This study focuses on the transient response in a bowed string with the stick-slip vibration for the clear understanding of its behavior and tone at the beginning of playing. Helmholtz waves can be observed in a bowed string instrument such as a violin, and many researchers have studied the phenomenon, focusing on its unique movements and the mechanism of sounds. However, the transient response in a bowed string has not yet been completely clarified, and little research exists on it. Thus, this paper investigates multiple Helmholtz waves in the transient response occurring in a bowed string using numerical simulation. In the analytical model considered in this paper, the string is a damped free vibrating system of discretized masses connected by springs. The bow and the string are in contact at a single point, and the frictional characteristic is modeled as a function of the relative velocity between the bow and the string with a negative gradient to the velocity. It is confirmed that multiple Helmholtz waves can be observed as a transient response by calculating the behavior of the string using the analytical model, and that the multiple Helmholtz waves can be separated into several Helmholtz waves approximately. The number of Helmholtz waves induced by bowing and the process from the transient response to the steady state are examined by separating the original multiple Helmholtz waves into several Helmholtz waves.