A linear diatomic lattice of lattice constant a with masses M and m (M > m) are coupled by a force constant C. The dispersion relation is given by $${\omega ^2} = C\left( {\frac{{M + m}}{{Mm}}} \right) \pm {\left[ {{C^2}{{\left( {\frac{{m + m}}{{Mm}}} \right)}^2} - \frac{{4{C^2}}}{{Mm}}{{\sin }^2}\frac{{ka}}{2}} \right]^{\frac{1}{2}}}$$
Which one of the following statements is incorrect?

A. The atoms vibrating in transverse mode correspond to the optical branch

B. The maximum frequency of the acoustic branch depends on the mass of the Iighter atom m

C. The dispersion of frequency in the optical branch is smaller than that in the acoustic branch

D. No normal modes exist in the acoustic branch for any frequency greater than the maximum frequency at $$k = \frac{\pi }{a}$$

Answer: Option C