Analytical Models

  • Richard Mark French

People have been studying the physics of musical instruments at least since the early Renaissance; Galileo, when he wasn’t busy with astronomy, optics and upsetting the Catholic Church, studied the motion of a vibrating string [64]. He clearly described the relationship between tension, length and frequency, taking one of the first steps toward putting stringed instrument design on a firm physical foundation.

Historically, stringed instruments have been designed empirically, and progress on describing them using mathematical models was slow until the mid 20th century. Stringed musical instruments pose a surprisingly difficult challenge to the would-be analyst. In order to completely characterize the sound produced, the mathematical model must include structural dynamics, acoustics and the interaction (coupling) between the two. If the results are to include sound quality, the model might also need to account for the physiology of human hearing and the psychoacoustics of how we...


Finite Element Model Resonant Frequency Boundary Element Method Frequency Response Function Helmholtz Resonator 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Richard Mark French
    • 1
  1. 1.Purdue UniversityWest LafayetteUSA

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