Classical elastic wave features like pulse velocity and attenuation have been used for decades for concrete condition characterization. Relatively recently the effect of frequency has been studied showing no doubt over the dispersive behavior of the material. Despite the experimental evidence, there is no unified theory to model the material and explain this phase velocity change at frequencies below 200 kHz. Herein, the Mindlin's strain gradient elastic theory including the additional micro-stiffness and micro-inertia parameters is considered as an alternative of multiple scattering theory. Experimental results are produced from material with dictated microstructure using a specific diameter of glass beads in cement paste. Results show that Mindlin's theory provides conclusions on the microstructure of the material and is suitable for describing the observed dispersion in different length scales (from millimeters in the case of mortar to several centimeters in the case of concrete).