The Departure of the Overtones of a Vibrating String from a True Harmonic Series
The Departure of the Overtones of a Vibrating String from a True Harmonic Series
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振动弦的泛音与真实泛音级数的偏离
DOI：
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发表时间：
1938
期刊：
影响因子：
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通讯作者：
R. Shankland
中科院分区：
文献类型：
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作者：
R. Shankland
由导线振动幅度引起的张力变化引起的频率变化用摄动法处理。根据拉曼研究，桥在末端节点上引入的约束以及由于钢丝刚度引起的弯矩也包括在处理中。泛音一般不会形成真正的谐波级数。一般来说，刚度和振幅的综合影响使泛音相对于基音变得尖锐。设计了一种新型单弦，用阴极射线示波器测量不同长度、直径和材料的弦的振幅对频率的影响。绝对频率由闸流管标度为16的电路与里斯勒标准时钟连接确定。电维持的振动本质上是自由振动，与钢琴线的振动相对应。这些乐器的精确谐波级数的偏离程度…
The changes in frequency caused by variations in tension due to the amplitude of vibration of a wire are treated by the method of perturbations. The constraints introduced by the bridges at the end nodes as studied by Raman, and on the bending moments due to the stiffness of the wire are included in the treatment. The overtones do not, in general, form a true harmonic series. In general, the combined influence of stiffness and amplitude sharpens the overtones with respect to the fundamental. A new type of monochord has been designed with which a cathode ray oscillograph is used to determine the effect of amplitude on frequency of strings of various lengths, diameters and materials. The absolute frequency is determined with a thyratron scale‐of‐sixteen circuit in connection with a Riesler standard clock. The electrically maintained vibrations are essentially free vibrations corresponding to the vibrations of piano wires. The degree of departure to be expected from an exact harmonic series for these instrum...