According to the point of view that static dense granular matter is a nonlinear elastic body, we derive an analytic sound speed expression given by its elastic potential, for the case of samples with cylindrical symmetry and sound waves propagating in the directions along and perpendicular to the symmetry axis. By a detailed comparison of the expressions with experiments reported in the literature, we conclude that the acoustic method can determine all material parameters appearing in the elastic potential accurately, which provides us with an important way of studying detailed nonlinear elasticity behaviors of granular materials, if stresses, density, and their uniformity of samples are thoroughly controlled and measured.