Aplicação da série de Fourier como análise acústica de instrumentos musicais

Abstract

Music has always been part of the history of humanity, its origin was sensorial and rhythmic. Later, because of a systematic and logical organization of the sounds, the musical notes were invented. For centuries, the study of sound has gained more and more space through the physical properties of sound waves and mathematical theories, especially the Fourier series. Thus, this work aims to perform a bibliographic research about sound waves, definitions and convergence of the Fourier series and Fourier analysis. As an application, an acoustic analysis of the musical instruments will be presented. Audios of a violin and a flute were recorded. To analyze the violin's acoustic box, the audio was recorded from a monochord, this one built specifically to simulate the violin without its acoustic box. After that, their Fourier series were calculated to represent the approximations of the waves in trigonometric functions and the timbre of the instruments was analyzed through the spectrum graphs. In addition, we sought to decrease audio noise by means of experimental methods. Thus, it was found that the series and the Fourier analysis indicated an efficient method to characterize sound timbre.