Going nuts: Measuring free-fall acceleration by analyzing the sound of falling metal pieces

Galilei presented the kinematics of a one-dimensional accelerated motion with ease and in terms of elegant geometry. Moreover, he believed, “Philosophy [i.e. physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it.” In classroom practice, however, it can be difficult to reveal this mathematical heart of nature; free fall and other accelerated motions often get obscured by friction or other sources of errors. In this paper, we introduce a method of analyzing free-fall motion indirectly by evaluating the noise of freely falling metal pieces. The method connects a deeper understanding of the mathematical structure of accelerated motion with the possibility to derive a numerical value for the free-fall acceleration g.