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Drums That Sound Alike

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Author:Ivars Peterson (MathLand)
Description: Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normal-mode vibrations. He outlines the progress made on Mark Kac's original question of whether knowledge of a drum's normal-mode vibrations is sufficient for unambiguously inferring its geometric shape, including Carolyn S. Gordon and David L. Webb's proof that two "soundalike" drums have different geometric shapes but equal areas and perimeters and identical spectra; and Toby Driscoll's computations of the standing wave patterns and frequencies for the same pair of shapes that physicist S. Sridhar and his colleagues tested experimentally.

Levels: High School (9-12), College
Languages: English
Resource Types: Problems/Puzzles, Articles
Math Topics: Fourier Analysis/Wavelets, Triangles and Other Polygons, Music

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