Whereas the trigonometric functions in a Fourier series represent the fundamental modes of vibration in a string, the spherical harmonics represent the fundamental modes of vibration of a sphere in much the same way.
2.
Whereas the trigonometric functions in a Fourier series represent the fundamental modes of vibration in a string, the spherical harmonics represent the fundamental modes of vibration of a sphere in much the same way.
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A concrete physical application involves the problem of hearing the shape of a drum : given the fundamental modes of vibration that a drumhead is capable of producing, can one infer the shape of the drum itself?
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The mathematical formulation of this question involves the Dirichlet eigenvalues of the Laplace equation in the plane, that represent the fundamental modes of vibration in direct analogy with the integers that represent the fundamental modes of vibration of the violin string.
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The mathematical formulation of this question involves the Dirichlet eigenvalues of the Laplace equation in the plane, that represent the fundamental modes of vibration in direct analogy with the integers that represent the fundamental modes of vibration of the violin string.
6.
Okano's group experimentally correlated the shear modulus to the frequency of standing shear modes using mechanical resonance techniques in the oscillatory experiments at lower frequencies ( < 40 Hz ), the fundamental mode of vibration as well as several higher frequency partial overtones ( or harmonics ) have been observed.
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