(top) Chladni figures forming on a violin back plate. Image: J. E. McLennan/University of New South Wales. (bottom) Similar patterns forming in a liquid. Image: G. Vuillermet et al.

Chances are you’ve seen the gorgeous patterns that sound waves produce when sand is sprinkled on a vibrating metal plate. Now French physicists have produced inverse versions of these patterns using microbeads suspended in a liquid. They described their work in a recent paper in Physical Review Letters.


The original patterns are known as Chladni figures, after the late 18th century acoustics pioneer Ernst Chladni. Inspired by Robert Hooke’s experiments over a century earlier, Chladni sprinkled sand over a solid metal plate, and then ran a violin bow along the edge to make it vibrate. As if by magic, the grains of sand rearranged themselves into patterns corresponding to various frequencies. But it’s actually due to some intricate (and intriguing) physics, as Diana Cowern, a.k.a. the Physics Girl, explains with her own DIY demonstration:

Every material object has a natural resonant frequency (or set of frequencies) at which it vibrates, and the metal plate is no exception. We can’t see them, but the plate will only vibrate in certain regions, set off by lines where it won’t vibrate at all (the so-called nodal lines). Set the plate to vibrating at one of those resonant frequencies, and the sand will be pushed away from the vibrating regions and cluster along the nodal lines. As the frequency shifts, so do the locations of the vibrational nodes. That’s why you get different Chladni figures for different frequencies.

Chladni’s technique soon became a vital tool for violin makers, since the resulting patterns let them visualize just where those all-important modes of vibration fell in the back plates of the instruments. It’s still used by instrument makers today—and as a popular demonstration for physics classes.


Physicists at the University of Grenoble Alpes in France recreated Chladni’s seminal experiment, only they used polystyrene microbeads suspended in water instead of sand. And instead of a metal plate, they stretched a thin membrane of polysilicon across a circular opening (much like the skin of a drum) at the base of a standard “lap-on-a-chip” microfluidic device, injecting the microbeads in water. As the drum vibrated, a camera attached to a microscope recorded the changing positions of the beads at various frequencies.

Nothing happened at higher frequencies. The beads didn’t move, and no pattern emerged, because the membrane was so small and thin that higher frequencies just didn’t resonate. That changed when the frequencies shifted into the low ultrasound range. Then the beads started clustering into patterns. The researchers found they could switch the pattern almost instantly, just by altering the frequency.



Shift those vibrations just a little bit off the resonant frequency, and the microbeads begin to rotate in a circle, in a motion reminiscent of the farandole, a traditional French folk dance:

These are not the same patterns as Chladni figures, however. Chladni noticed that very fine particles, like those shed by his bow, didn’t get pushed to the nodes like the coarser grains of sand. They moved in the opposite direction, congregating at the so-called “antinodes.” The phenomenon is known as acoustic streaming, and as Derek Stein writes at APS Physics, it’s “the reverse of the process by which air flow generates vibrations in a musical instrument.”

That’s what makes this technique potentially useful for a variety of applications. Sound waves are already being used to mix and pump fluids in microfluidics devices. Scientists could also use them to manipulate living cells on a surface, getting them to form clusters and influence how they develop simply by changing the frequency of the sound waves. Right now, they must rely on prefabricated patterns, many of which require clean room conditions, and cannot be quickly and easily changed.


[Physical Review Letters]