Measurement and numerical simulation of two-dimensional vibration of a single piano string
Daisuke Naganuma, Hideyuki Nomura, Tomoo Kamakura · The Journal of the Acoustical Society of America · 2016
A piano string begins to vibrate vertically as soon as a hammer strikes it. After the vertical vibration has begun, the string then starts to rotate owing to the generation of horizontal vibration. The rotation direction changes several seconds later, which suggests that the frequencies of the vertical and horizontal components of the vibration are slightly different. We previously reported an equivalent mechanical circuit model for physically elucidating such two-dimensional movements of the string. In this presentation, we show the verification and validation of the equivalent model by comparing with experiments. The movements of a string in low frequencies were observed using a high-speed camera and a mirror. In order to increase the measurement accuracy of displacement, interpolation technique was applied to the correlation of recorded images. It was noted that the frequency of a partial vibration of the string in the vertical direction is higher or lower than that in the horizontal direction to the soundboard. The rotation directions and the rotation change periods suggest how the soundboard acts on the generation of the partial vibration as mass-dominated or stiffness-dominated control at the string end, and to what extent does the soundboard affect the partial vibration of the string.