On the motion of the bowed violin string

Abstract

Oscillations with nodes at the bow point have been observed. For a typical violin string such oscillations exist for β > 0.08 (here β is the relative bow position along the string). For β > 0.18 the amplitude of this motion may become comparable to the Helmholtz motion if the bow force exceeds a critical value (2–40 g/wt. depending on the value of β). At the critical force and with β ≠ n−1 (n = 2, 3, 4...), the waveform can be well described analytically. The analytic expression consists of two terms, a sinusoid and the usual Helmholtz expression. It is used to calculate consecutive string shapes. At the critical bow force, the slip period of the string at the bow point is observably reduced to half the value given by the classical Helmholtz theory. However, this slip duration is given by the analytic expression. For bow forces much larger than the critical value the sinusoids of the waveforms (including the slip duration at the bow point) become narrower than the “predictions.” It is shown that this type of motion does not exist for β < 0.18 because it demands too high a bow force. The relationship between this motion and Raman's “higher types of motion” will be explained.