The lowest frequency modes of the mandolin modeled as a coupled oscillator system

Abstract

The mandolin is an acoustically unique musical instrument with elements similar to the guitar and violin. Inspired by a classic guitar study by Christensen and Vistisen, we tested if the mandolin’s low-frequency response could be modeled as a simple 3-mass coupled oscillator system. We measured the response of the front plate, back plate, and air within thecavity from sinusoidal forcing of the front plate using microphones, accelerometers, and a force probe. We calculated the mobility (i.e., 1/impedance = v/F) and compared this to a theoretical model. To determine how the collective resonances are affected by the individual oscillators in the system, we added small masses to the front and back plates, and “collared” the f-holes to add mass to the moving air, thus lowering the resonances of the corresponding oscillator. We found clear evidence of coupling: by changing any one element, the resulting three resonant frequencies of the coupled system were affected. We also found the expected phase relations between the individual oscillators for each of the three resonances of the coupled system. From a detailed analysis, we found that a 3-mass coupled oscillator model can reasonably approximate the low-frequency behavior of the mandolin.