Brillouin spectroscopy is used to determine the effects of polymer concentration, crosslinking density, and polymerization on the longitudinal storage and loss moduli of polyacrylamide hydrogels. The model established by Chiarelli et al. is implemented to calculate the speed of sound in the free water [Chiarelli et al., The Journal of the Acoustical Society of America, 2010, 127(3), 1197-1207]. The polymer concentration has the greatest effect on the moduli of the polymer matrix. We determined that the crosslink density has no measurable effect on the logitudinal storage or loss modulus of polyacrylamide hydrogels when measurements are made at GHz frequencies, in contrast to measurements made at kHz frequencies as documented by other studies. However, the moduli are independent of monomer concentration if the acrylamide is not polymerized. We show at the GHz frequency that the incorporation of acrylamide polymer chains affects the mechanical properties of the free water. The speed of sound in the free water is reduced by the introduction of polymerized acrylamide. The long polymer chains and their interactions with the bounded water disrupt the bonding organization of the unbound water, causing a reduction of the average hydrogen bond strength between free water molecules. This results in a decreased speed of sound in the free water and an increase in the longitudinal storage modulus of the hydrogel.