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A theoretical study has been made of the vibration mode in a U shape tuning fork which consists of a semicircular yoke and two straight prongs. In such a fork, the following relation is in exist:n_j=κ(M_j/l)^2√8(E/ρ) where n_j the resonance frequency of jth order vibration mode of the tuning fork. l the total length of the median line, κ the radius of gyration of the section, E and ρ, Young's modulus and density of the material, respectively, and m_j a dimensionless constant connecting the above quantities to each other. When r, the radius of the semicircular yoke, l_1 , the length of the prong, and, k and Q are defined as follows:k=2r/(r+l_1), Q=(k/l)^2, m_j is, in general, the function of k and Q. And, it is confirmed that m_j depends only on k at the lower modes of the vibration in the ordinary tuning fork. Therefore, the numerical value of m_j is presented with the various values of k. According to wheather j is odd or even. the vibration mode is symmetric or not. When j=1, 3, the vibration mode is symmetric and the node of the vibration does not exist anywhere along the median line. The position wi[h the minimum amplitude in the yoke is indicated as the function of k in the report. When j= 2. thc vibration mode is not symmetric and the position with minimum amplitude exists in the middle point of the yoke. ln a particular casc of k≒0.38, the amplitude becomes zero in the point. Some of the above theoretica1 results are ascertained in the present experiment.
社団法人日本時計学会の論文
1968-03-20

音さの振動モード : 第2報

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