Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Bar Vibrational Modes

巴 振动模式

The elastic property involved in the vibration of bars is usually stated in terms of Young's modulus.

杆的振动所涉及的弹性性质通常用杨氏模量来表示。
Clamped bar details
夹持棒详情
Free bar details
自由杆细节
Index

Percussion instruments

Musical instruments

Reference
Hall
Ch. 9
索引 打击乐器 音乐乐器 参考 Hall 第9章
 
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Clamped Bar Modes

固定端杆的模态

The frequency f1 depends upon the density and elasticity of the material from which the bars are made. The amplitudes for the f2 and f3 modes would actually be much smaller than the fundamental. These mode frequencies appear with a tuning fork since it can be considered to be two clamped bars.

频率 f₁ 依赖于制成音叉材料的密度和弹性。f₂ 和 f₃ 模式振幅实际上会比基频小很多。这些模态频率出现在音叉中,因为可以将其视为两个夹紧的棒。

Free bar modes
自由杆模式
Comparison
比较
Index

Percussion instruments

Musical instruments

Reference
Hutchins
索引 拍击乐器 音乐乐器 参考 Hutchins
 
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Free Bar Modes

自由巴模式

The frequency f1 depends upon the density and elasticity of the material from which the bars are made. The amplitudes for the f2 and f3 modes would actually be much smaller than the fundamental.

Clamped bar modes
固定棒模态
Comparison
比较
Example: Glockenspiel
钟摆
频率 f₁ 依赖于制成棒材的材料的密度和弹性。f₂ 和 f₃ 模式的振幅实际上会远小于基频。
Index

Percussion instruments

Musical instruments
索引 打击乐器 音乐乐器
 
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R Nave
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