Physics of the Piano

9722031佐丹奴钢琴产生乐音的过程将结合实验测量和理论分析进行研究。 目标之一是开发一个理论模型，描述钢琴音板在整个音乐重要频率范围（~50 - 104 Hz）的振动。 先前关于振动弦的工作将被扩展，然后与我们的音板模型相结合，以产生弦-音板组合的理论图。 由于几何形状的复杂性和所涉及的非线性，这些模型将主要是数值的。 将通过与真实的钢琴音板和琴弦的详细实验研究进行比较来测试和改进它们，这些测量也将作为本项目的一部分进行。 在这项工作的最后阶段，他们将扩展建模，以计算他们的数字钢琴产生的声音。 ***

9722031 Giordano The process through which a piano generates musical tones will be investigated using a combination of experimental measurements and theoretical analysis. One goal will be to develop a theoretical model which describes the vibrations of the piano soundboard throughout the musically important frequency range (~ 50 - 104 Hz). Previous work on vibrating strings will be extended and then combined with our soundboard model to produce a theoretical picture of the string-soundboard combination. Due to the complexity of the geometry and the nonlinearities involved, these models will be largely numerical. They will be tested and refined by comparison with detailed experimental studies of real piano soundboards and strings, and these measurements will also be carried out as part of this project. In the final stage of this work they will extend the modeling to calculate the sound produced by their numerical piano. ***