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Numerical and Experimental Study of the Effect of the Bridge of Sarasvati Veena on its Timbre

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Abstract

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.

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Notes

  1. Detailed discussion is presented in the appendix (sec. A).

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Acknowledgements

This study is part of a larger project to completely characterize the acoustic properties of the Sarasvati Veena in terms of its structural parameters. This work was partly supported by a grant from the DST-SERB Project Number EMR/2016/002338.

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Authors and Affiliations

  1. Department of Mechanical Engineering, BITS Pilani K K Birla Goa Campus, Sancoale, Goa, 403726, India

    Chandrashekhar Chauhan & Pravin Singru

  2. Department of Physics, BITS Pilani K K Birla Goa Campus, Sancoale, Goa, 403726, India

    Radhika Vathsan

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  1. Chandrashekhar Chauhan
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  2. Pravin Singru
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  3. Radhika Vathsan
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Correspondence to Chandrashekhar Chauhan.

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Appendices

Appendix

A Location of the Microphone

During the numerical simulation, the spectrum of the point on the string is studied. This point approximately lies on the vertical line passing through the point P (Fig. 3). We wish to capture the effect of all the points on the bridge which come in contact with the vibrating string. So, we select this point on the discretized string, the first point along the length (in the x direction, Fig. 3) which is not subjected to impact with the bridge. Further, a Piezotronics microphone (PCB378C01) with a sensitivity of 2.19 mV/Pa was placed at the same location on the sonometer with a bridge and experimental analysis was performed in the semi-anechoic chamber. The measured sound pressure signal of the plucked string vibrating against the Veena bridge was processed by the SPIDER-81 data acquisition system with the help of EDM software to generate the FFT. Experimental analysis was also conducted at other locations along the length to understand the importance of the microphone location. We present FFTs recorded at three different locations along the length of the string: x = 0.026 m (appx. at the end of the bridge ), x = 0.073 m (half of the plucking distance, \(x_p\)) and x = 0.145 m (plucking distance, \(x_p\)). All the three FFTs correspond to bridge slope \(B_2\) and curvature \(A_2\).

We see Fig. 12a has qualitatively better information about the energy content in the harmonics beyond 1400 Hz (8f) as compared to Fig. 12b, c. This shows that the microphone placed close to the bridge gives better information about the effect of the bridge, so the choice of the microphone location is justified.

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Chauhan, C., Singru, P. & Vathsan, R. Numerical and Experimental Study of the Effect of the Bridge of Sarasvati Veena on its Timbre. Acoust Aust 51, 53–66 (2023). https://doi.org/10.1007/s40857-022-00280-7

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