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Tibetan Singing Bowls

July 14, 2011

For those who have overdosed on pop music, international music comes as a refreshing change. This was true even in the 1960s, when Ravi Shankar introduced Indian music as an antidote to the British Invasion. There's something in international music for everyone, from banging on hollow logs to unusual vocals in languages involving dental clicks.

Near the end of his life, physics Nobelist, Richard Feynman, had a fascination with Tannu Tuva, a very small nation near Mongolia. This is documented in a book by his friend, Ralph Leighton,[1] and a BBC documentary that's available on YouTube.[2] Feynman and Leighton tried various tactics to secure visas to Tuva from the Soviet government that controlled the region, but Feynman succumbed to cancer a few days before permission to visit was secured.

Feynman and Leighton devised one interesting excuse to visit a Mongolian region bordering on Tuva. In the hopes of a stealthy passage over the Mongolian border into Tuva, they submitted a request to attend a throat-singing conference. Throat singing is a method that allows the human voice to simultaneously produce tones at more than one pitch. It sounds quite strange to western ears. Alas, the conference was canceled.

Musical acoustics is a very interesting field. I would enjoy reading the music articles when I received copies of the Journal of the Acoustical Society on the company routing list. Music interests many scientists, as the violin-playing Einstein will attest. An electrical engineer with whom I coauthored several papers published a paper on the acoustics of the tuba.[3] I published a computer music circuit.[4]

One interesting musical instrument that can be built in nearly every home is the glass harp. A glass harp is just an array of water glasses, typically tuned by the quantity of water that each glass contains. The performer rubs a wet finger along the rim to excite acoustical resonance. American polymath Benjamin Franklin designed and built a mechanical version, called a Glass harmonica, in which the glasses are rotated on an axle.

In affirmation of the adage that there's nothing new under the sun, the Asian version of this musical instrument, the singing bowl, has been around for millennia. These are made from copper, bronze or brass, rather than glass, Just as for the glass harp, tones in singing bowls are excited by rubbing the rim, typically with a leather-tipped wooden rod. A photograph of a small bowl appears below, and there are several sound clips of singing bowls at this web site.

Singing Bowl

A singing bowl with its excitation rod.

(Photo by Miguel Andrade, via Wikimedia Commons).)

An unusual phenomenon associated with such singing bowls was investigated by two physicists, one of whom is at the Department of Physics at the Université de Liège (Liège, Belgium); the other is at the MIT Department of Mathematics. Their findings were just published in the journal, Nonlinearity.[5-12]

This phenomenon is the unusual motion of the water contained in the bowls when excited by the acoustical waves. Upon proper excitation, water droplets appear to be levitated above the water surface. They also bounce and skip across the water surface and be ejected from the bowl.

The motivation for this study came from an unlikely source. One of the authors, John Bush, demonstrated this Faraday instability behavior that causes bouncing droplets on an episode of Time Warp on the Discovery Channel. In response to this demonstration, Bush received an email from a woman named Rosie Warburton who reported that this phenomenon happens in Tibetan bowls.[7]

Said Bush, "It was this email that inspired the study." The research showed that the Faraday instability in these bowls was "odd by any standards, even to specialists in fluid dynamics such as ourselves".[7]

Faraday waves arise because the acoustical excitation is bounded by the edge of the bowl. The unusual aspect of the bowls is that they change shape in response to the excitation, and this affects the water waves.[7] At a certain amplitude, the water becomes unstable, resulting in chaotic waves, as can be seen in the figure.[11] The chaotic motion causes droplets to break free from the surface and fly out of the bowl.[8]

Excitation of water in a Tibetan bowl.

Evolution of surface waves on the water surface of a Tibetan bowl excited at 188 Hz. The amplitude of the antinodes increases from 13 μm to 115 μm in this series. (Via arXiv Preprint Server, Ref. 11)

The Tibetan bowl experiments involved excitation of water-filled bowls by a loudspeaker, and the bowl deformation was measured by an accelerometer.[5] High speed video elucidated the movements on the water surface.[8] Not surprisingly, a mathematical model of the process shows that the low Young's modulus of the metal, as compared with glass, is responsible for the dramatic effect.[5]

Of course, every scientific study must have an application. At the very least, it serves to keep the funding agencies happy. It's noted that droplet generation is important for many things, from perfume dispensers to fuel injectors.[7]


  1. Ralph Leighton, "Tuva or Bust! Richard Feynman's Last Journey," W. W. Norton & Company, May 15, 2000, 260 pages (via Amazon).
  2. Feynman: 'The Quest for Tannu Tuva,', BBC TV 'Horizon' (1988); also shown as 'Last Journey of a Genius,' on PBS Nova.
  3. D.D. Stancil, "Use of a Spectral Model in Developing Concepts of Tuba Timbre," Brass Bulletin, vol. 19 (1977), p. 33ff.
  4. D.M. Gualtieri, "MIDI Output Interface to a Parallel Printer Port," Computer Music Journal, vol. 10, no. 3 (1986), pp. 79-82.
  5. Denis Terwagne and John W M Bush, "Tibetan singing bowls," Nonlinearity, vol. 24 (2011), pp. R51–R66 (doi: 10.1088/0951-7715/24/8/R01).
  6. Videos associated with Ref. 5, including this video of droplets ejected from breaking Faraday waves.
  7. Jason Palmer, "Tibetan singing bowls give up their chaotic secrets," BBC News, July 1, 2011.
  8. Sophie Bushwick, "Forget Diet Coke and Mentos: Singing Bowls Excite Droplet Fountains," Scientific American Blog, July 1, 2011.
  9. Elizabeth Weise, "The fluid mechanics of Tibetan singing bowls," USA Today, June 30, 2011.
  10. Geoff Brumfiel, "Cool Videos: How Tibetan singing bowls make drops dance," Nature Blog, July 1, 2011.
  11. Denis Terwagne, John W.M. Bush, "The Tibetan Singing Bowl," arXiv Preprint Server, October 15, 2010.
  12. Denis Terwagne, John W. M. Bush, "The Tibetan singing bowl: acoustics and fluid dynamics," arXiv Preprint Server, June 29, 2011.
  13. Richard Feynman page on the Friends of Tuva web site.                               

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