Tibetan singing bowls

We present the results of an experimental investigation of the acoustics and fluid dynamics of Tibetan singing bowls. Their acoustic behaviour is rationalized in terms of the related dynamics of standing bells and wine glasses. Striking or rubbing a fluid-filled bowl excites wall vibrations, and concomitant waves at the fluid surface. Acoustic excitation of the bowl’s natural vibrational modes allows for a controlled study in which the evolution of the surface waves with increasing forcing amplitude is detailed. Particular attention is given to rationalizing the observed criteria for the onset of edge-induced Faraday waves and droplet generation via surface fracture. Our study indicates that drops may be levitated on the fluid surface, induced to bounce on or skip across the vibrating fluid surface.

[1]  T. Charnley,et al.  Chladni's law and the modern English church bell , 1985 .

[2]  J. Miles,et al.  Standing radial cross-waves , 1991, Journal of Fluid Mechanics.

[3]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[4]  J. M. Bush,et al.  The fluid trampoline: droplets bouncing on a soap film , 2008, Journal of Fluid Mechanics.

[5]  Yves Couder,et al.  Single-particle diffraction and interference at a macroscopic scale. , 2006, Physical review letters.

[6]  Y. Couder,et al.  Wave propelled ratchets and drifting rafts , 2008 .

[7]  Andrew J. Bernoff,et al.  An experimental study of micron-scale droplet aerosols produced via ultrasonic atomization , 2004 .

[8]  J. Mahony.  Cross-waves. Part 1. Theory , 1972, Journal of Fluid Mechanics.

[9]  E. Fort,et al.  Unpredictable tunneling of a classical wave-particle association. , 2009, Physical review letters.

[10]  Michael Faraday,et al.  XVII. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces , 1831, Philosophical Transactions of the Royal Society of London.

[11]  S. Douady.  Experimental study of the Faraday instability , 1990, Journal of Fluid Mechanics.

[12]  Yves Couder,et al.  Information stored in Faraday waves: the origin of a path memory , 2011, Journal of Fluid Mechanics.

[13]  John W. M. Bush,et al.  Quantum mechanics writ large , 2010, Proceedings of the National Academy of Sciences.

[14]  Kuan-Wen Chen,et al.  Variations on a theme by a singing wineglass , 2005 .

[15]  E. Hopfinger,et al.  Evolution and breaking of parametrically forced capillary waves in a circular cylinder , 2009, Journal of Fluid Mechanics.

[16]  Yih-Yuh Chen.  Why does water change the pitch of a singing wineglass the way it does , 2005 .

[17]  Diane M. Henderson,et al.  PARAMETRICALLY FORCED SURFACE WAVES , 1990 .

[19]  E. Fort,et al.  The self-organization of capillary wave sources , 2005 .

[20]  J. Viñals,et al.  Amplitude equation and pattern selection in Faraday waves. , 1997, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  L. Tuckerman,et al.  Parametric instability of the interface between two fluids , 1994, Journal of Fluid Mechanics.

[22]  J. Miles.  Parametrically excited, standing cross-waves , 1988, Journal of Fluid Mechanics.

[23]  Peilong Chen,et al.  Pattern Selection in Faraday Waves , 1997, patt-sol/9702002.

[24]  A. P. French.  In Vino Veritas: A study of wineglass acoustics , 1983 .

[25]  Thomas Brooke Benjamin,et al.  The stability of the plane free surface of a liquid in vertical periodic motion , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[26]  Jerry P. Gollub,et al.  Patterns and spatiotemporal chaos in parametrically forced surface waves: A systematic survey at lar , 1996 .

[27]  N. Vandewalle,et al.  Resonant and rolling droplet , 2008, 0806.4811.

[28]  A. Akay.  Acoustics of friction. , 2002, The Journal of the Acoustical Society of America.

[29]  Neville H. Fletcher,et al.  Vibrational modes of partly filled wine glasses , 2006 .

[30]  T. Rossing.  Acoustics of the glass harmonica , 1991 .

[31]  Thomas D. Rossing,et al.  Wine glasses, bell modes, and Lord Rayleigh , 1990 .

[32]  Lord Rayleigh F.R.S..  VII. On the crispations of fluid resting upon a vibrating support , 1883 .

[33]  W. G. Pritchard,et al.  Cross-waves. Part 2. Experiments , 1972, Journal of Fluid Mechanics.

[34]  N. Vandewalle,et al.  Dynamics of a bouncing droplet onto a vertically vibrated interface. , 2008, Physical review letters.

[35]  H. Saunders,et al.  Fundamentals of Acoustics (3rd Ed.) , 1983 .

[36]  John William Strutt,et al.  Scientific Papers: On the Crispations of Fluid resting upon a Vibrating Support , 2009 .

[37]  John Lamb.  Fundamentals of Acoustics (3rd edn) , 1982 .

[38]  Jose Antunes,et al.  The dynamics of Tibetan singing bowls , 2006 .

[39]  E. Fort,et al.  From bouncing to floating: noncoalescence of drops on a fluid bath. , 2005, Physical review letters.

[40]  W. S. Edwards,et al.  Patterns and quasi-patterns in the Faraday experiment , 1994, Journal of Fluid Mechanics.

[41]  L. Rayleigh,et al.  The theory of sound , 1894 .

[42]  D. Y. Hsieh.  Theory of water waves in an elastic vessel , 2000 .

[43]  J. Moukhtar,et al.  Path-memory induced quantization of classical orbits , 2010, Proceedings of the National Academy of Sciences.

[44]  Moti Fridman,et al.  Coupling between two singing wineglasses , 2009 .

[45]  C. Garrett.  On cross-waves , 1970, Journal of Fluid Mechanics.

[46]  Daniel P. Lathrop,et al.  Viscous effects in droplet-ejecting capillary waves , 1997 .

[47]  A storm in a wineglass , 2007 .