Measuring Young’s modulus the easy way, and tracing the effects of measurement uncertainties

Abstract

The speed of sound in a solid is determined by the density and elasticity of the material. Young’s modulus can therefore be calculated once the density and the speed of sound in the solid are measured. The density can be measured relatively easily, and the speed of sound through a rod can be measured very inexpensively by setting up a longitudinal standing wave and using a microphone to record its frequency. This is a simplified version of a technique called ‘impulse excitation’. It is a good educational technique for school pupils. This paper includes the description and the free provision of custom software to calculate the frequency spectrum of a recorded sound so that the resonant peaks can be readily identified. Discussion on the effect of measurement uncertainties is included to help the more thorough experimental student improve the accuracy of his method. The technique is sensitive enough to be able to detect changes in the elasticity modulus with a temperature change of just a few degrees.