- 一般社団法人 日本時計学会
- 日本時計学会誌 (ISSN:00290416)
- vol.40, pp.45-61, 1966-12-01 (Released:2017-11-09)
A theoretical method to obtain the vibration mode of the tuning fork is explained and some discussions are done relating to the obtained vibration mode. Here, the tuning fork is regarded as the one composed of three straight bars which are connected with each other at right angle to form the U-shape. Through the above method, the resonant frequencies n_j (j=1, 2, 3, .....) and the corresponding modes of vibration can be calculated. In the results, it is seen that, when j is odd, the bending motion of the two paralledl sides of the tuning fork are in the opposite direction, when j is even, however, those are in the same direction. Moreover, when two tuning forks are of the similar shape, it is certified that there exists a simple relationship between the vibration modes of these two tuning forks. By using this relationship, unknown vibration modes of the one can be obtained easily, if the modes of the other are known. In the tuning fork, having uniform material and section, the resonant frequencies are given by n_j(k)=m^2_j(k)^-2√<EI/Sp,> where E, p , I, S and l are Young's modulus, the density of the material, the moment of inertia, the area of the section, and the total length of the tuning fork, respectively. k means the ratio of the bottom side length of the U-shape to the parallel side length, and the proportional constants m^2, are shown in a table, with the various values of k. On the asymmetrical tuning forks of which two parallel sides have a slight difference in length, the vibration modes are calculated. The changes of the resonant frequeny and the nodal point are shown in connection with the change of the difference of the parallel sides. The results of the above theoretical analysis are compared with the experimental one, and it is ascertained that both are in good coincidence.