Dynamical Theory of String Excitation by Bowing

The kinematics of the bowed string have already been observed and mathematically described by H. von Helmholtz. For the present investigation we need to know the energy supply at the location of bowing and the energy loss in the vibrating system. A self‐excited mechanism is used to create the energy supply between bow and string. To analyze string excitation at that point investigations were made of: characteristic of friction between bow and string; influence of the normal force between string and bow on the steady vibration; longitudinal impedance of the bow hair; influence of the eccentric excitation on the string, which also introduces torsional waves. The steady state of the bowed string was calculated with regard to the characteristic of the friction force and a complex impedance at the end of the string corresponding to the bridge, taking into account the modes of the body and all energy losses. Results explain the influence of the normal force between bow and string on the steady vibration. Result...