Solutions of the dispersion relation, Eq. (31), for the acoustic wave case. Left and right panels present the real and imaginary parts of the dimensionless wave frequency ω, respectively, as functions of the dimensionless wavenumber k. The axes are scaled in nondimensional units E and F, defined in Eq. (32) for better visualization. Four solutions are marked with different colors and line styles: solid red for solution 1, orange dashed for solution 2, blue dot-dashed for solution 3, and green dotted for solution 4. We note that solutions 1 and 4 have the same imaginary parts and are superposed in the right-hand panel. Solutions 2 and 3 have the same real part equal to zero for large α/k and are also superimposed on top of one another. The values of k for which we compare the analytical and numerical solution using the values of ω, corresponding to solution 4 (green dots), are marked in the panels: orange circle (k = 618 m⁻¹), pink triangle (k = 6.18 m⁻¹), cyan diamond (k = 2.06 m⁻¹), and black “X” (k = 6.18 × 10⁻⁶ m⁻¹).