THE FREQUENCY CALCULATION FOR A LOADED TUNING FORK

The frequency is calculated of a loaded tuning fork so as to acquire a deep understanding of its frequency variation and be able to control the frequency accurately. The frequency equation for the loaded tuning fork is derived and the first three partials of the normal vibration are calculated; The characteristic curves showing the variation of the frequency with the position of the concentrated mass is also given.
It is found that as the position of the concentrated mass varies, the fundamental frequency is a decreasing function of its distance from the boution of the fork while the frequecies of overtones fluctuate with the position, in which some maxima and minima appear. It is also indicated that when different concentrated masses are put on the tuning fork, all the maxima of the overtones of the same order almost approach to the limit frequency of that order and are hardly affected by the magnitude of the mass.