Effects of dynamic Young’s modulus and geometric parameters on vibration duration of tuning forks

Tuning forks are used in a variety of fields, including music, medicine, and healing. Considering the purpose of a tuning fork, its fundamental tone should persist as long as possible. However, parameters that are expected to directly affect vibration duration — such as the geometry of the tuning fork and material properties like dynamic Young's modulus — have not been rarely examined. In this study, we investigated the effects of tuning-fork shape parameters and material properties, such as dynamic Young’s modulus, on vibration duration. Dynamic Young's modulus was calculated by measuring the sound emitted when the tuning fork was struck, along with shape and material parameters such as width, thickness, length, mass, volume, and density. The results showed that vibration duration generally decreased as dynamic Young's modulus increased. Also, vibration duration tended to increase as volume and length increased, and to decrease as density increased. These findings suggest that vibration duration can be roughly estimated by measuring the dynamic Young's modulus during the manufacturing process. It is also suggested that parameters such as volume, density, and tuning fork length may have a particularly strong impact on vibration properties of tuning forks.