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? he'd buy me a fairing should please me, And then for a kiss, oh! he vowed he would tease me, He promised he'd bring me a bunch of blue ribbons, To tie up my bonny brown hair. </poem> Cohen's "Folk Music" gives a different version of the lyrics: <poem> O dear, what can the matter be? O dear, what can the matter be? O dear, what can the matter be? Johnny's so long at the fair. He promised he'd bring me a bunch of blue ribbons. He promised he'd bring me a bunch of blue ribbons. He promised he'd bring