Physicists call the pattern of a Japanese woven basket, where triangles and hexagons alternate, a kagome lattice. In this lattice, the nodes split into three groups, and a wave traveling through it lingers differently on each group. Until now, this was hard to see in real materials, because electronic methods don't reveal the phase of a wave. So scientists built an acoustic model of the lattice out of plastic, printed on a 3D printer, with cells measuring 28 millimeters.

One by one, they placed a speaker at each node, emitting sound at frequencies from 100 to 12000 hertz, while a microphone on a robotic arm listened to how the sound spread to neighboring nodes. In this way, the scientists measured how the wave distributed itself among the three groups of nodes. It turned out that at one frequency, 10.9 kHz (a high-pitched whistle), the wave freezes on two neighboring rings, and adjacent nodes oscillate out of phase. This means that waves from neighboring nodes cancel each other out, and that is what produces the flat band. At other frequencies, 5.5 and 8.0 kHz, the distribution among the groups turned out to be different: at the lower frequency, two groups light up, while at the higher one, only one does.

This acoustic snapshot of an invisible pattern showed for the first time exactly how a wave binds to groups of nodes in a kagome lattice. Previously this was unknown, because in electronic materials the phase cannot be measured. Now physicists have a reference standard against which they can compare data from complex materials, where such binding may determine superconductivity. The method could also help create acoustic devices with a desired distribution of sound. But as for applications today, no direct devices based on this work are in sight yet: its main value lies in providing a way to test theories about how waves behave in such lattices.