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? Oh Dear! What Can the Matter Be? "What Can the Matter Be?", also known as "Johnny's So Long at the Fair" is a traditional nursery rhyme that can be traced back as far as the 1770s in England. There are several variations on its lyrics. The "Oxford Dictionary of Nursery Rhymes" by Iona and Peter Opie traces this song back to an earlier folk ballad, recorded between 1770 and 1780, whose lyrics are: <poem> O what can the matter be And what can the matter be O what can the matter be Johnny bydes lang at the fair He'll buy