Experimental analysis of two-dimensional vibration of a piano string measured with an optical device
Hideyuki Tanaka, Keinosuke Nagai, Koichi Mizutani · The Journal of the Acoustical Society of America · 1999
It is well known that a piano string vibrates in the direction not only perpendicular to the soundboard but also parallel to it. The sound decays rapidly at first and then it decays slowly. A change in the predominant direction of vibration of the string from perpendicular to parallel contributes to the compound decay rate [G. Weinreich, Sci. Am. 240, 118–127 (1979)]. In this paper, two-dimensional vibration of a piano string is measured with handmade equipment consisting of two phototransistors. Just after the string was struck with a hammer, it vibrates perpendicularly to the soundboard. Then it vibrates gradually in the direction parallel to the soundboard. As a result, a point of the string moves on an elliptic trajectory. It was found that the fundamental resonant frequency of the perpendicular vibration of the E1 string, for example, which is about 40 Hz, is 0.07 Hz lower than that of parallel vibration. This causes the change of rotating direction of the string every 7 s. The discrepancy of the resonant frequencies is also found in the vibration of the D♯1 string.