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, What Songs of the Heart blest, There's no word, there's no thought can impart, But our rapture will be All the soul can attest, In the heavenly songs of the heart; But our rapture will be In the vision we'll see Best expressed in the songs of the heart Oh, what songs we'll employ! Oh, what welcome we'll hear! When we kneel at our dear Savior's feet. And the heart swells with joy In embraces most dear When our heavenly parents we meet! Oh, what songs we'll employ As the heart swells with joy, When our heavenly parents we meet! </poem> "Oh, What Songs of