Physics of the Piano

9722031使用实验测量和理论分析相结合的方法来研究钢琴产生音乐音调的过程。一个目标是开发一个理论模型，描述钢琴响板在音乐上重要的频率范围(~50-104赫兹)内的振动。之前关于振动弦的工作将被扩展，然后与我们的响板模型相结合，以产生弦-响板组合的理论图像。由于几何的复杂性和涉及的非线性，这些模型将在很大程度上是数值的。它们将通过与真实钢琴响板和琴弦的详细实验研究进行比较来进行测试和改进，这些测量也将作为该项目的一部分进行。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. ***