An analytical treatment for the calculation of intensities of diffraction orders in a general case of superposed sound waves of frequencies in the ratio 1 :n and having any phase difference Δ is given proceeding from Raman and Nath's simplified theory for normal incidence. Because of the integral harmonic relationship between the frequencies of the sound waves superposed, a particular order may contain a number of combination lines in addition to the orders due to the individual sound waves. As such, Fues theory, which gives a single expression for the intensity of a combination line, cannot be applied to this case.
Expressions are obtained for the intensities of the diffraction orders in the two specific cases of even and odd values of n. In the case diffraction by two sound waves of frequencies in the ratio 1:2k+1 expressions for the intensities of the orders suggest symmetry in diffraction for all values of Δ. But, when the superposed frequencies are in the ratio 1:2k, the expressions suggest asymmetry in diffraction for all values of λΔ, except π/2. When Δ = π/2, the diffraction is, however, symmetric.
Using the expressions, the intensities of the diffraction orders obtained by two sound waves of frequencies in the ratio 1:3 superposed in three different phases 0, π/2, and π are calculated for the values of v1 = 1 and v3 = 1, 2, and 3.