We present solutions for effective dynamic elastic and diffraction properties of composites with random structures composed from compound n-phase inclusions. These solutions are obtained on the basis of analysis of corresponding averaging wave equations of generalized method of self-consistency. The model of the averaging problem includes a diffraction of longitudinal and transversal waves by isolated n-phase compound inclusion that is surrounded by a transient layer having non-homogeneous elastic properties. We present the results of numerical calculations for components of the tensor of dynamic effective elastic properties and sections of dispersion for the case of uni-directional fiber composite having hollow fibers in the plane of isotropy under various values of the circular frequency. Considering a composite on the macro-level, we obtain non-monotonous relationship between the sections of dispersion and coefficients of waves damping, on the one hand, and radii of inner and outer surfaces of fibers, on the other hand.