Tibetan singing bowls are known for their soothing harmonic tones, ideal for meditation. But they can also produce "chatter," a kind of knocking sound. A group of Florida undergraduates think they have figured out why this happens.
Singing bowls are usually made from bronze metal alloys, containing cooper, zin, zinc, silver, nickel, gold, and other common metals. They're played by striking the rim with a special padded mallet called a puja (usually wrapped in leather), or gently rubbing the mallet around the bowl's rim.
The effect is the same as the gentle tones produced by rubbing a moistened finger around the rim of a wine glass. It's due to a phenomenon called resonant frequency: when any sound starts vibrating in phase with an object's natural frequency. in the case of a wine glass or a bowl, you get those soothing harmonic tones. The singing bowls have relatively small resonant frequencies, so it's easier to produce the tones than with a wine glass.
These unusual acoustic properties have long interested researchers, largely because it's a good way to study liquid interactions with solid materials -- something of keen interest to engineers designing, for example, bridges and buildings that can withstand high-force winds. (The infamous collapse of the Tacoma Narrows Bridge (a.k.a. "Galloping Gertie") in 1940 is a classic example of the power of resonances.)
Back in 2011, MIT researchers studied how Tibetan singing bowls filled with water could resonate strongly enough to propel droplets off the water's surface. Those resonances slightly change the shape of the bowl, and the energy from that shape-shifting generates so-called "Faraday waves" in the water within. Eventually the resonant effects become so strong that you get breaking waves and fizzy droplets. Check it out in the video below:
The phenomenon of "chatter" in Himalayan singing bowls is a little different. "As the puja moves around the rim of the bowl, it switches very quickly between stocking to and skipping on the metal, which is called 'slip-stick motion,'" co-author Chloe Keefer, an undergraduate at Rollins College in Florida, said in a press release. Similar motion shows up in other instruments, including violins and cellos, but little research has been done on the phenomenon in singing bowls.
Keefer and her fellow undergrads -- part of a special program at RollinsCollege focusing on original undergraduate research on the physics of musical instruments -- set out to correct that oversight. They used a laser Doppler vibrometer to measure the surface vibrations without making contact with the bowl, focusing on several points on the inner rim, combined with a high-topped visualisation technique capable of taking pictures at 10,000 frames per second to image of those vibrations.
They were looking specifically for the location of a point of zero vibration, known as a "node," on the bowl. It wasn't where they thought it would be.
"People would expect the puja to lie on the node of the bowl's vibratory motion, but in fact, it doesn't," said Keefer. Instead, their analysis showed that it falls within a couple of millimetres of the puja. When someone moves the puja along the bowl's rim to play it, the node is following just behind it. Increase the speed of the puma's rotation, and you increase the amplitude (strength, or loudness) of the vibrations of the rim.
And once that vibrational amplitude gets large enough, it knocks the puja off the bowl, a bit like the jumping water droplets produced in the 2011 experiments. Voila! You get chatter.
Their study is not entirely academic. The measurements might one day prove useful for better understanding of the mechanics of how your car brakes squeal, with an eye towards reducing such unwanted sounds.
In the meantime, the Rollins undergraduates will continue their investigations into the physic of piano string, clarinet reeds, brass wind instruments, and singing bowls.
Faraday, Michael. (1831) "On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces," Philosophical Transactions of the Royal Society (London) 121: 299-318. [appendix]
Keefer, Chloe, and Moore, Thomas R. (2015) "The etiology of chatter in the Himalayan singing bowl," Paper 4aMU7, 170th Meeting of the Acoustical Society of America.
Terwagne, Denis, and Bush, John W.M. (2011) "Tibetan singing bowls," Nonlinearity 24: R51.
Top image: Rin gong in Kyoto, Japan. Credit: Michael Maggs/Wikimedia Commons. Bottom images: C. Keefer and S. Collin/Rollins.