Simulating brass instrument sound with the solution of wave equation

Abstract

The principle of the sound produced by a brass instrument is the vibration and sound waves produced from the mouthpiece which will generate resonance in the closed tube Using the wave equation of partial differential equations the study investigates the boundary value condition of a mathematical model presented in the study The mathematical model is then used to simulate the tone of the brass instrument sound By the application of Visual Studio simulation is undertaken with C and C++ program languages and simulation output is produced in the form of a song with notations which may be saved as a document By Fourier transformation the document is transformed into a frequency map to facilitate observation As shown by the results of the study the tone of the sound produced by a brass instrument may be attributable to the vibration of the tube The resonance frequency of the tone is connected with the length of the tube The fingering of playing a brass instrument is aimed at changing the length of the tube so that the tube can meet the requirement for the resonance frequency of the tone The sound of the brass instrument depends not only on the length of the tube but on the type of the mouthpiece as well Hopefully the sound waves of different types of mouthpieces can be accurately simulated and exact brass instrument sound can be created by computer programs in the future research

Date of Award	2019
Original language	English
Supervisor	Shih-Yu Shen (Supervisor)