Introduction to the Mechanics of Sound

The present paper is an attempt to explore the interesting properties of sound underlined by mathematical ideas. The first part of this study will be dedicated to understanding the basic properties of sound. Afterwards the reader will be introduced with the wave equation, which will be solved for two concrete examples illustrating the mechanics of the circular membrane, and that of the string, that aim to introduce him to the mechanics of the source of the sound and it also involves a small introduction to Bessel functions. This project aims to introduce a mathematician to music, and it therefore requires an audience with prior study in mathematical and physical sciences.