Bow response to the string it is bowing

Abstract

The force that a bowed string exerts on the bow can be reconstructed from the forces on the string’s termination. By using one or more accelerometers attached to the bow, the response of the bow to that reconstructed force can be recorded. Bow responses will be shown that were obtained using a bowing machine. At some harmonic frequencies of the string the signal from the longitudinal standing wave excited on the bow hair allows determination of the velocity of propagation of that wave. The consequence of the variable excitation of various harmonics of the standing wave as the bow stroke progresses is a rapidly changing excitation of the bows various normal modes. Three data channels, requiring at least a 128 kHz sampling rate for E-strings, are required for bow force reconstruction and motion detection of the bow. The validity of substituting the force of the string on the bridge instead of the reconstructed bow force is explored. That allows a reduction of the minimum number of data channels from three to two, a reduction in the necessary sampling rate, and use of a bow stroke by a player instead of a bowing machine.