Determination of the Elastic Constant of the Top Plate of a Cello in the Interaction with the Bridge
Abstract
This paper aims to determine the equivalent static elastic constant of a cello’s top plate in the interaction with the bridge. Experimental results detailing this constant are presented based on measuring the deformation and forces caused by a system of calibrated springs in similar conditions to that obtained when these forces are produced by the action of the strings. Subsequent tests are conducted following an intervention by a luthier to adjust the sound post, with the aim of assessing the impact on the elastic constants.Keywords:
elasticity, organology, cello bridge, musical acoustics, boundary conditions, interferometryReferences
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4. Elie B., Gautier F., David B. (2013), Analysis of bridge mobility of violins, [in:] Proceedings of the Stockholm Music Acoustics Conference 2013, pp. 54–59, https://hal.science/hal-01060528. (access: 3.06.2024).
5. Jansson E., Molin N., Saldner H. (1994), On eigenmodes of the violin – Electronic holography and admittance measurements, The Journal of the Acoustical Society of America, 95(2): 1100–1105, https://doi.org/10.1121/1.408470.
6. Jansson E.V. (2004), Violin frequency response – Bridge mobility and bridge feet distance, Applied Acoustics, 65(12): 1197–1205, https://doi.org/10.1016/j.apacoust.2004.04.007.
7. Kabała A., Niewczyk B., Gapiński B. (2018), Violin bridge vibration – FEM, Vibrations in Physical Systems, 29: 2018021, https://vibsys.put.poznan.pl/_journal/2018-29/articles/vibsys_2018021.pdf. (access: 3.06.2024).
8. Lodetti L., Gonzalez S., Antonacci F., Sarti A. (2023), Stiffening cello bridges with design, Applied Sciences, 13(2): 928, https://doi.org/10.3390/app13020928.
9. Malvermi R. et al. (2021), Feature-based representation for violin bridge admittances, arXiv, https://doi.org/10.48550/arXiv.2103.14895.
10. Minnaert M., Vlam C.C. (1937), The vibrations of the violin bridge, Physica, 4(5): 361–372, https://doi.org/10.1016/S0031-8914(37)80138-X.
11. Reinicke W., Cremer L. (1970), Application of holographic interferometry to vibrations of the bodies of string instruments, The Journal of the Acoustical Society of America, 47(4B): 131–132, https://doi.org/10.1121/1.1912237.
12. Vakhtin A.B., Kane D.J., Wood W.R., Peterson K.A. (2003), Common-path interferometer for frequency-domain optical coherence tomography, Applied Optics, 42(34): 6953–6958, https://doi.org/10.1364/AO.42.006953.
13. Woodhouse J. (2005), On the “bridge hill” of the violin, Acta Acustica united with Acustica, 91(1): 155–165.
14. Woodhouse J. (2014), The acoustics of the violin: A review, Reports on Progress in Physics, 77(11): 115901, https://doi.org/10.1088/0034-4885/77/11/115901.
