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Magical Singing Saw Physics Mystery Solved

Back before the internet or television – even before radio, people loved making and listening to music. Without expensive store bought instruments, music got made from what was at hand, things like bottles, spoons, even a basic ordinary cross cut saw. You would be amazed at the intense jam which can come out of a flathead shovel. Young researchers took a hard look at the physics behind singing saws and figured out a breakthrough way to make super-sensitive sensor equipment.

A proper bend in the saw

Thanks to cheap, flexible, early 19th century steel, the inexpensive ripsaw quickly became a favorite improvised instrument in Appalachian folk music. The key to making one sing with eerie, ethereal sound, when bowed like a cello, is the shape of the curve the musician bends into the saw blade.

After hitting it’s peak in the early 20th century, the art-form died out, until recently resurrected on social media. YouTube, it seems, has become the new Vaudeville.

Over at Harvard’s John A. Paulson School of Engineering and Applied Sciences, their Department of Physics discovered that singing saw topology holds “the key to designing high quality resonators for a range of applications.

They recently published a paper demonstrating “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.

Another interesting aspect is the unique mathematical singing saw physics has a “fractal” nature.

According to senior author, L Mahadevan, “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.” The paper came out in The Proceedings of the National Academy of Sciences.

Acoustic resonators

The scientists explain that all musical instruments are “acoustic resonators” of one type or another but none of them work the same as a bent sheet of steel. “The singing saw sings is based on a surprising effect,” Petur Bryde points out.

When you strike a flat elastic sheet, such as a sheet of metal, the entire structure vibrates.” Not for long, though. “The energy is quickly lost through the boundary where it is held, resulting in a dull sound that dissipates quickly.

If you bend a simple single “J” shaped curve, you get the same result. To make the magic happen requires a compound “S” curve. 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 geometry of the curved saw is what forms the “sweet spot.” At Harvard they call it “localized vibrational modes.” No matter what you call it, you create a “confined area on the sheet which resonates without losing energy at the edges.

Shankar, Bryde and Mahadevan were working with an analogy to very different class of physical systems — topological insulators – when they “found a mathematical argument that explains how and why this robust effect exists with any shape within this class, so that the details of the shape are unimportant, and the only fact that matters is that there is a reversal of curvature along the saw.

In quantum physics applications, “topological insulators are materials that conduct electricity in their surface or edge but not in the middle and no matter how you cut these materials, they will always conduct on their edges.” They ended up demonstrating “that they could tune the localization of the mode by changing the shape of the S-curve, which is important in applications such as sensing, where you need a resonator that is tuned to very specific frequencies.

What do you think?

Written by Staff Editor

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