Acoustic eigenfrequency analysis of some musical instruments

• Main Author: Kua, Li Shan.
• Other Authors: Ang Whye Teong
• Format: Final Year Project
• Language: English
• Published: 2012
• Subjects: DRNTU::Engineering::Mechanical engineering
• Online Access: http://hdl.handle.net/10356/50331
• Institution: Nanyang Technological University

This project deals with the acoustic eigenfrequency analysis of some musical instruments. There are two parts for this project: The first part of this project deals with the computation of eigenfrequencies of some musical instruments. The instruments considered include string instruments (e.g. guitar) and woodwind instruments (e.g. flute, horn, clarinet etc.) governed by the one-dimensional wave equation, and percussion instruments (e.g. circular drum, cymbals) governed by the two-dimensional wave equation. Analytical formulae for the eigenfrequencies of the guitar and the woodwind instruments can be found using the mathematical method of ‘Separation of Variables’. For the circular drum and cymbals, their eigenfrequencies have to be computed by solving equations which involve Bessel functions. A MATLAB program is written to extract these eigenfrequencies. The second part of this project deals with the construction and analysis of a simple three-stringed instrument and a set of panpipes. These instruments are constructed based on the eigenfrequency formulae obtained in the first part. Their frequency characteristics can be determined by a sound analyser software called the ‘Real-time Analyser’. Sounds produced by these instruments are first picked up and measured by an external microphone and their frequency waveforms are displayed later.