"Musicians and researchers have known about this robust effect of geometry for some time, but the underlying mechanisms have remained a mystery," said Suraj Shankar, a Harvard Junior Fellow in Physics and SEAS and co-first author of the study. It could be an S with a big curve at the top and a small curve at the bottom or visa versa. Importantly, the specific geometry of the S-curve doesn't matter. The geometry of the curved saw creates what musicians call the sweet spot and what physicists call localized vibrational modes-a confined area on the sheet which resonates without losing energy at the edges. But, if you bend the sheet into an S-shape, you can make it vibrate in a very small area, which produces a clear, long-lasting tone." The same result is observed if you curve it into a J-shape. The energy is quickly lost through the boundary where it is held, resulting in a dull sound that dissipates quickly. "When you strike a flat elastic sheet, such as a sheet of metal, the entire structure vibrates. "How the singing saw sings is based on a surprising effect," said Petur Bryde, a graduate student at SEAS and co-first author of the paper. While all musical instruments are acoustic resonators of a kind, none work quite like the singing saw. The research is published in The Proceedings of the National Academy of Sciences ( PNAS). "Our research offers a robust principle to design high-quality resonators independent of scale and material, from macroscopic musical instruments to nanoscale devices, simply through a combination of geometry and topology," said L Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics and senior author of the study. Paulson School of Engineering and Applied Sciences (SEAS) and the Department of Physics used the singing saw to demonstrate how the geometry of a curved sheet, like curved metal, could be tuned to create high-quality, long-lasting oscillations for applications in sensing, nanoelectronics, photonics and more. In a new paper, a team of researchers from the Harvard John A. As it turns out, the unique mathematical physics of the singing saw may hold the key to designing high quality resonators for a range of applications.
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