Longitudinal vibrations in violin strings

Abstract

We report the observation of longitudinal vibrations in violin strings excited by bowing. These vibrations are detected from the rocking motion of the top of the bridge in the direction longitudinal to the strings, with the aid of a photoelectric device. The frequencies of these waves are approximately three octaves above the respective fundamental frequencies of the transverse string vibrations, in line with expectation. It is found that stable oscillations are difficult to sustain in which both the transverse and longitudinal motions can coexist in comparable strength. Essentially pure longitudinal oscillations can be excited by bowing at a forward angle. These modes are difficult to identify in the normal bowing spectrum, and are substantially absent in pizzicato tones, except in the initial transients.

The Physics of Musical Instruments

“…Longitudinal vibrations of the string give rise to sounds that are easily noticed, since their frequencies are not harmonically related to the main transverse vibrations and they lie in a frequency range (1-5 kHz) of high sensitivity for hearing. Lee and Rafferty (1983) observed longitudinal modes with frequencies of 1350 Hz and 2700 Hz for the G and D strings, respectively, of a violin. Longitudinal and transverse vibrations are difficult to excite simultaneously in the same string, however.…”

A low-cost high-precision measurement method of string motion

“…Another optical method, less intrusive, expensive and cumbersome, consists in catching the shadow of the string by using an integrated opto-sensor [13], a photo-Darlington [14], or an analog position sensing detector [15], as well as an optoswitch system including an infrared emitting diode coupled to a photo-transistor [16]. The latter system has been used to measure the transverse [17,18] and longitudinal [19,20] string vibrations to analyse, for instance, nonlinear free vibrations [21] as well as chaotic vibrations [22] of a string. This system/sensor seems to be appropriate to measure the string displacement regardless of its material.…”