Harmonics of <i>S</i> motion on bowed strings

Lossless bowed strings have usually been thought to possess a motion discovered by Helmholtz in 1863. However, it was shown [Acustica 44, 194-206 {1980)] by the author that a more complicated standing wave motion, the $ motion, exists on such strings provided both the bowing distance and bowing force are above certain minimum values. This paper explores S-motion harmonics which give arise to waveforms of considerable complexity on very thin strings. Equations are found which describe the experimentally determined waveforms as a function of bow position, bow velocity, and observation point. In the special case of square velocity waves at the bow point, the equations give quantized values for the bow/string sticking duration. That result agrees with Raman's [Proc. Ind. Assoc. Adv. Sci. 15, 1-158 {1918)] prediction. In general, however, the waveforms have rounded corners.