The Sarasvati Veena is an Indian stringed musical instrument with a curved bridge having a parabolic equation. We study the effect of such a bridge on the timbre of the instrument. We model the interaction of the vibrating string with the bridge as frictionless impact. So we implemented an energy-conserving method where string–bridge interaction is modelled with a penalty approach. We solve the resulting Hamilton’s equations numerically. Simulations are performed with different values of bridge parameters, namely slope and curvature. The numerical model is validated by comparison with experimental analysis. We isolate the contribution of the bridge by mounting it on the sonometer in place of one of its knife-edges and a mechanism is provided on the sonometer to change the bridge slope. We mounted the sonometer on foam to minimize the effect of other structural parameters. The typical Veena timbre shows sustain of most harmonics and the revival of higher harmonics with time. These features are attributed to the shape of the metallic layer at the top of the Veena bridge, its slope and curvature. Our model also shows these features, which are further corroborated by the experiment.

Sarasvati Veena 是一种印度弦乐器，其曲桥具有抛物线方程。我们研究了这种琴桥对乐器音色的影响。我们将振动弦与桥的相互作用建模为无摩擦冲击。因此，我们实施了一种节能方法，其中使用惩罚方法对弦桥相互作用进行建模。我们用数值方法求解得到的哈密顿方程。使用不同的桥梁参数值（即坡度和曲率）进行模拟。通过与实验分析的比较验证了数值模型。我们通过将桥安装在声波计上代替它的一个刀刃来隔离桥的贡献，并且在声波计上提供了一种机制来改变桥的坡度。我们将声波计安装在泡沫上，以尽量减少其他结构参数的影响。典型的 Veena 音色显示出大多数泛音的延音和高泛音随时间的恢复。这些特征归因于 Veena 桥顶部金属层的形状、坡度和曲率。我们的模型也显示了这些特征，实验进一步证实了这些特征。