During the playing of a bowed string instrument, the rosin-coated bow hair is drawn against the string, causing the string to repeatedly stick to and be suddenly released by the hair, a phenomenon known as stick-slip oscillation. It is widely accepted among players that different bows have different tonal properties, but despite nearly a century of study, how the different tonal qualities of violin bows are related to their physical properties is poorly understood. A test that violin players can perform to assess the characteristics of a violin bow is called the Salchow test, which involves holding the bow at the frog in one hand and tapping the bow hair on the knuckle of the other hand, feeling the resulting vibrations in the bow using the bow hand. We built a device for performing a quantitative version of the Salchow test and examined the pattern of vibrations and how they depend on the velocity of the bow, the location of the tap on the bow, and how they vary with different bows.

We hypothesized that the Salchow test excites the first lateral bending mode of the bow and that different bows have different decay lifetimes of vibration.

We concluded that the Salchow test is a measurement of the fundamental bending mode and that it showed clear differences in vibrational pattern among different contact points and different bows as well as clear power differences among different drop heights. Every test condition showed a consistent spectral peak in the fundamental frequency between 42-54 Hz and variation in the ratio of fundamental frequency to total frequency for each bow. Though there were vibrations in other frequencies, we did not study them because they were less consistent.

Different bows (fiberglass, carbon fiber, wooden) exhibited different higher order frequency excitations. We also saw that power in vibration increased linearly with drop height.

This study revealed tapping at the tip showed the greatest vibrational lifetime in the fundamental frequency. There was a higher ratio of power at the fundamental frequency to total power for bow 1 (carbon fiber) as compared to 2 (fiberglass) or 3 (wood), as well as a higher fundamental frequency peak width for the less expensive bow 2 compared to the most expensive bow 3, going against the Salchow Test hypothesis. Future research will compare physical properties of the bow with subjective evaluation of their playing or tonal properties.