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I read an interview with Australian wire music composer Alan Lamb that a stringed instrument with multiple overtones vibrating on the string can be analyzed by
by _spduchamp 4y ago
I read an interview with Australian wire music composer Alan Lamb that a stringed instrument with multiple overtones vibrating on the string can be analyzed by breaking down the vibration into eigenvalues, but I've never found any reference material that explain that. I'm wondering if he was referring to FFT.
- auxym 4y agoIf you discretize the string into a bunch of tiny masses, linked together by a bunch of tiny springs, you can build a mass Matrix (diagonal) M and a Stiffness matrix K (element ij = stiffness of spring that links mass I and mass j). I can't remember the next part exactly, you can look it up in a textbook, but you multiply the matrices KMK, or similar, and the eigenvalues of this are the natural frequencies of the string. The eigenvectors represent the mode shapes, ie the displacement of each mass element. The same technique is used in Finite Element Analysis to find the modes and modeshapes of complex structures (a car frame, a bridge, etc)
- alanbernstein 4y agoComplex exponentials are the eigenfunctions of the Fourier transform. In other words, frequency component values are the eigenvalues. https://en.m.wikipedia.org/wiki/Eigenfunction#Vibrating_strings https://en.m.wikipedia.org/wiki/Eigenfunction#Vibrating_stri...
- contravariant 4y agoThat makes no sense, the Fourier transform of a complex exponential is a delta function.
- alanbernstein 4y agoHmm, you're right, that should have been obvious. Thanks for the correction.
- sfpotter 4y agoSee my other reply.