Investigations of the coupling of doubled mandolin strings using high-speed video

Abstract

The mandolin has four courses of doubled strings and in each pair the strings are tuned in unison. By using a macro lens on a quality high-speed camera, we are able to study the bridge-coupled motions of the strings in exquisite detail. We use an angled mirror to allow monitoring of the vertical and horizontal motions of both strings in a pair. With small colored tags on each string, we have automated the amplitude vs. time measurements using the Tracker Video Analysis tool. We observe clear evidence of coupling including the exchange of energy between the four modes. There is a strong tendency for the two strings to anti-correlate, while the vertical and horizontal modes of one string usually differ in phase by 90 degrees. We clearly observe the double-decay phenomena noted in Weinreich’s study of piano strings. The coupling thus serves to add richness to mandolin tones and also increases the sustain. We compare the experimental results to a Runge-Kutta coupled oscillator model implemented in Matlab. Matching the observations requires the model damping constants to be slightly larger than the coupling constants and a slight detuning of the strings is necessary to produce the observed anti-correlated behavior.