Measuring Acoustic Normal Modes of a Rectangular and Cylindrical Geometry and Measurement of Speed of Sound

Christopher Spencer
Physics 180D
Professor Gary Williams
30 April 2014

Introduction

The purpose of the lab was to find the normal modes of rectangular and cylindrical geometries and using that data of these frequencies obtain the speed of sound. Before the lab was started the first 33 modes for the rectangular box were found theoretically up to the \((4,0,0)\) mode to compare to our results and the first 17 modes of the cylindrical up to the \((4,2,0)\). The physics used to to find the resonant frequencies of the box come from seperation of variables of the pressure wave equation and the frequencies for the cylindrical geometry were found seperating variables again but in cylindrical coordinates to the pressure wave equation and examining the zeroes of the deriviatives of the bessel function. For practial purposes, c was taken to be \(345 \frac{m}{s}\) to approximate resonant frequencies.