How to use Fourier's theorem in a sentence
Now we may resolve these trains by Fourier's theorem into harmonics of wave-lengths X, 2X, 3A, &c., where X=2AB and the conditions as to the values of y can be shown to require that the harmonics shall all have nodes, coinciding with the nodes of the fundamental curve.
We see, then, that the conditions for the application of Fourier's theorem are equivalent to saying that all disturbances will travel along the system with the same velocity.
In many vibrating systems this does not hold, and then Fourier's theorem is no longer an appropriate resolution.
Whatever the deformation of the originally straight boundary of the axial section may be, it can be resolved by Fourier's theorem into deformations of the harmonic type.
Any periodic curve may be resolved into sine or harmonic curves by Fourier's theorem.Advertisement