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Tibetan Singing Bowls

Article (PDF Available) inNonlinearity 24(8) · June 2011with648 Reads
DOI: 10.1088/0951-7715/24/8/R01 · Source: arXiv
Abstract
We present the results of an experimental investigation of the acoustics and fluid dynamics of Tibetan singing bowls. Their acoustic behavior 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.
The Tibetan Singing Bowl
D. Terwagneand J.W.M. Bush
GRASP, D´epartement de Physique,
Universit´e de Li`ege, B-4000 Li`ege, Belgium
Department of Mathematics,
Massachusetts Institute of Technology, 02139 Cambridge, USA
October 18, 2010
Abstract
The Tibetan singing bowl is a type of standing bell. Originating
from Himalayan fire cults as early as the 5th century BC, they have
since been used in religious ceremonies, for shamanic journeying, exor-
cism, meditation and shakra adjustment. A singing bowl is played by
striking or rubbing its rim with a wooden or leather-wrapped mallet.
The sides and rim of the bowl then vibrate to produce a rich sound.
When the bowl is filled with water, this excitation can cause crispa-
tion of the water surface that can be followed by more complicated
surface wave patterns and ultimately the creation of droplets. We here
demonstrate the means by which the Tibetan singing bowl can levi-
tate droplets. This is a sample arXiv article illustrating the use of fluid
dynamics videos.
The first part of the video shows a water-filled Tibetan bowl rubbed by
a leather mallet that excites vibrations via a ”stick-slip” process. The rim
deflection indicates that the main deformation mode is the fundamental one
associated with four nodes and four anti-nodes along the rim. We proceed
by reporting the form of the flow induced by the moving rim, specifically,
the evolution of the free surface with increasing rim forcing.
The bowl is completely filled with water, and its fundamental deforma-
tion mode excited acoustically. A loudspeaker produces a sinusoidal sound
at a frequency f0= 188Hz that corresponds to the fundamental frequency
excited by rubbing the rim.
1
arXiv:1010.3193v1 [nlin.PS] 15 Oct 2010
The vibration of the water surface is forced by the horizontal oscillation
of the rim. When the amplitude of the rim oscillation is small, axisymmetric
capillary waves with frequency commensurate with the excitation frequency
appear on the liquid surface. Though almost invisible to the naked eye, they
can be readily detected by appropriate lighting of the liquid surface. In Fig.
1.a, one can see the evolution of these axial waves, as viewed from above,
with increasing forcing.
a) b) c) d)
Figure 1: Evolution of the surface waves in a water-filled bowl excited with
a frequency of f0= 188 Hz. The amplitude Aof deformation at anti-nodes
is increasing from left to right : a) A= 13 µm, b) A= 20 µm, c) A= 44 µm,
d) A= 115 µm.
When the rim deflection amplitude is further increased, circumferential
waves appear at the water’s edge (see Fig. 1.b). The amplitude of these
waves grows rapidly, and is larger than that of the axial waves; moreover,
their frequency is half that of the axial waves (the excitation frequency f0).
The circumferential waves correspond to classic edge-induced Faraday waves
[1] (see Fig. 1.b). More complicated wave modes appear at higher excitation
amplitude (see Fig. 1.c).
At sufficiently high excitation amplitude, water droplets are ejected from
the edge of the vessel (see Fig. 1.d), specifically from anti-nodes of the wall
oscillations. The ejected droplets jump, bounce, slide and roll on the water
surface until eventually coalescing.
With a more viscous fluid (e.g. silicone oil of viscosity 10 cSt) the waves
are less pronounced, and the liquid surface may be induced to oscillate up
and down at a small distance from the wall’s anti-node. When a droplet
of the same liquid is deposited on the surface, it may bounce, levitated
by the underlying wave field. The air film between the drop and the liquid
surface is squeezed and regenerated at each successive bounce, its sustenance
precluding coalescence [2, 3] and enabling droplet levitation in the Tibetan
singing bowl.
2
References
[1] M. Faraday, Philos. Trans. R. Soc. London 121, 334-337 (1831).
[2] Y. Couder, E. Fort, C.-H. Gautier and A. Boudaoud, Phys. Rev. Lett.
94, 177801 (2005).
[3] T. Gilet, D. Terwagne, N. Vandewalle and S. Dorbolo, Phys. Rev. Lett.
100, 167802 (2008).
3
Project
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June 2011
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