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Journal of the Acoustical Society of America

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May 2012

Volume 131, Issue 5, pp. EL355-4232

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Violin bow vibrations

Colin E. Gough

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 4152-4163 (2012); (12 pages)

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The modal frequencies and bending mode shapes of a freely supported tapered violin bow are investigated by finite element analysis and direct measurement, with and without tensioned bow hair. Such computations are used with analytic models to model the admittance presented to the stretched bow hairs at the ends of the bow and to the string at the point of contact with the bow. Finite element computations are also used to demonstrate the influence of the lowest stick mode vibrations on the low frequency bouncing modes, when the hand-held bow is pressed against the string. The possible influence of the dynamic stick modes on the sound of the bowed instrument is briefly discussed.
Show PACS
43.75.De Bowed stringed instruments
43.40.At Experimental and theoretical studies of vibrating systems
43.40.Cw Vibrations of strings, rods, and beams

Effects of bending portions of the air column on the acoustical resonances of a wind instrument

Simon Félix, Jean-Pierre Dalmont, and C. J. Nederveen

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 4164-4172 (2012); (9 pages)

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The need to keep long wind musical instruments compact imposes the bending of portions of the air column. Although manufacturers and players mention its effects as being significant, the curvature is generally not included in physical models and only a few studies, in only simplified cases, attempted to evaluate its influence. The aim of the study is to quantify the influence of the curvature both theoretically and experimentally. A multimodal formulation of the wave propagation in bent ducts is used to calculate the resonances frequencies and input impedance of a duct segment with a bent portion. From these quantities an effective length is defined. Its dependence on frequency is such that, compared to an equivalent straight tube, the shift in resonance frequencies in a tube with bent sections is not always positive, as generally stated. The curvature does not always increase the resonances frequencies, but may decrease them, resulting in a complex inharmonicity. An experimental measurement of the effect of the curvature is also shown, with good agreement with theoretical predictions.
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43.75.Ef Woodwinds
43.75.Fg Brass instruments and other lip-vibrated instruments
43.20.Mv Waveguides, wave propagation in tubes and ducts
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