Spinodal decomposition both complete one cycle per second—but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.) If A(β) is the amplitude of a Fourier component of wavelength λ and wavenumber β = 2π/λ the spatial variation in composition can be expressed by the Fourier integral: in which the coefficients are defined by the inverse relationship: Substituting, we obtain on equating coefficients: This is an ordinary differential equation that has the solution: in which "A(β)" is the initial amplitude of the Fourier component of wave wavenumber β
Oh Dear! What Can the Matter Be? And nobody knew she was there. The second old lady was Abigail Splatter. She went there 'cause something was definitely the matter. But when she got there, it was only her bladder, And nobody knew she was there. </poem> One suggested precursor to the bawdy song, recorded in William's "Upper Thames" collection is the following "old morris fragment": <poem> Oh, dear, what can the matter be? Three old women tied to an apple tree! One ran away, the others stopped till Saturday. Oh, dear, what can the matter be? </poem> As with many folk songs and tall tales each verse