Induced Current Measurement of Rod Vibrations

The longitudinal¹ normal modes of vibration of rods are similar to the modes seen in pipes open at both ends. A maximum of particle displacement exists at both ends and an integral number (n) of half wavelengths fit into the rod length. The frequencies f_n of the normal modes is given by Eq. (1), where L is the rod length and V is the wave velocity:

Many methods have been used to measure the velocity of these waves. The Kundt's tube method commonly used in student labs will not be discussed here. A simpler related method has been described by Nicklin.² Kluk³ measured velocities in a wide range of materials using a frequency counter and microphone to study sounds produced by impacts. Several earlier methods^4,5 used phonograph cartridges complete with needles to detect vibrations in excited rods. A recent interesting experiment⁶ used wave-induced changes in magnetization produced in an iron rod by striking one end. The travel time, measured as the impulsive wave reflects back and forth, gave the wave velocity for the iron rod. In the method described here, a small magnet is attached to the rod with epoxy, and vibrations are detected using the current induced in a few loops of wire. The experiment is simple and yields very accurate velocity values.

Contents

• BODY OF ARTICLE
• Appendix: Details and an Added Experiment
• REFERENCES
• About the Author
• FIGURES