Determining the temperature dependence of Young’s modulus using a tuning fork

Abstract

We describe a simple experiment that illustrates the use of acoustic resonance to determine the temperature dependence of an elastic constant. Instead of a traditional crystal that has been carefully cut and polished to provide a high Q, the specimen is an ordinary tuning fork. The resonant frequency of a tuning fork changes with temperature because of changes in Young’s modulus [D. W. Schindel et al., J. Acoust. Soc. Am. 102, 1296–1308 (1997)]. In the stainless steel fork used in a previous undergraduate research study [L. Bates et al., J. Undergrad. Res. Phys. 18, 9–13 (1999)], the resonant frequency decreased by 0.018<th>54 Hz for each 1°C increase in temperature. That experiment was carried out over a range of temperature from 25<th>°C to 80<th>°C using a simple oven. As the frequency change is not very dramatic, it is very important to have either a method of very precisely measuring the resonant frequency or one must extend the temperature range to get a sufficiently large total shift in frequency. We describe several options for tracking the resonant frequency.