Abstract
When a piano string is struck by a hammer, it begins to vibrate vertically, i.e., in a plane perpendicular to the soundboard. After the vertical vibration has begun, the string then begins to rotate owing to 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. In this article, we describe the modeling and theoretical analysis of the two-dimensional motion of a piano string. To this end, the string and soundboard are represented by an equivalent mechanical circuit. The string with two-dimensional movement is divided into two independent strings, each with one-dimensional movement. The vertical and horizontal motions are initialized to have the same frequency and are connected by a bridge that is represented as an ideal transformer. A soundboard is attached to the vertically vibrating string. Once the circuit is excited, the two strings vibrate at slightly different frequencies.
