Ondas mecânicas unidimensionais e modelagem matemática aplicadas à música

Abstract

Music, besides being an art appreciated by most human beings, is an area of knowledge that presents relationships with Mathematics and Physics. The structure of musical notes, in a harmonic scale, and the study of sound and its different characteristics can be performed through the use of computational tools and mathematical modeling, as the application of Fourier series, for example. Thus, the main objective of this research was to develop a physical-mathematical study of signals captured from sound waves emitted by musical instruments, making use of computer programs and mathematical modeling, by Fourier series. For that, it was sought to understand the process of construction of the musical scale and apparent initial failures and it was analyzed the main aspects of the studies of the sound in Physics, with the advent of the Ondulatory. Specifically, to obtain the results of the work, the sound signals (oscillatory) emitted by the note Sol of a recorder and a guitar were collected and decoded separately, using the free software Audacity and analytical and numerical methods were used to generate the Fourier series of these signals. The main results show that the Fourier series is an excellent tool to represent sound signals by means of mathematical equations and that, with a few harmonics of this series, it is possible to represent, with good approximation, musical note signals by means of simple mathematical models. Key-words: Mathematical Modeling. Music. Unidimensional Mechanical Waves. Fourier Series.