论文标题
班卓琴断裂角度调制作为参数振荡
Banjo Break Angle Tension Modulation as Parametric Oscillation
论文作者
论文摘要
班卓琴的浮动桥的运动，以及该桥上的琴弦的断裂角度，会产生弦张张调制，这是弦运动振幅中的第一阶。本说明完善了先前关于对字符串和桥梁运动频率的影响的建议。对于给定模式的字符串和桥梁，产生的张力调制会产生一种新的，以原始张力和差异为特征的新的运动。严格来说，与字符串频率相比，这仅在调制速度较慢的情况下对应于规范的“频率调制”。更一般的结果恰恰是雷利（Rayleigh）首先分析的所谓“参数振荡”的一个例子。张力调制对班卓琴音色的质量影响仍然如前所述。只有确切的数学和物理才能需要这种纠正。
The motion of the floating bridge of the banjo, in conjunction with the break angle of the strings over that bridge, produces string tension modulation that is first order in the amplitude of the string motion. This note refines a previous suggestion regarding the impact on the frequencies of the strings' and bridge's motion. For a given mode frequency pair of string and bridge, the resulting tension modulation produces a new, additional motion characterized by the sum and difference of the original ones. Strictly speaking, this corresponds to canonical "frequency modulation" only in the limit of modulation slow compared to the string frequency. The more general result is precisely an example of what is known as "parametric oscillation," first analyzed by Rayleigh. The qualitative impact of tension modulation on banjo timbre remains as suggested previously. It is only the precise math and physics that warrants this correction.
