The power and precision with which humans link language to cognition is unique to our species. By 3-4 months of age, infants have already established this link: simply listening to human language facilitates infants' success in fundamental cognitive processes. Initially, this link to cognition is also engaged by a broader set of acoustic stimuli, including non-human primate vocalizations (but not other sounds, like backwards speech). But by 6 months, non-human primate vocalizations no longer confer this cognitive advantage that persists for speech. What remains unknown is the mechanism by which these sounds influence infant cognition, and how this initially broader set of privileged sounds narrows to only human speech between 4 and 6 months. Here, we recorded 4- and 6-month-olds' EEG responses to acoustic stimuli whose behavioral effects on infant object categorization have been previously established: infant-directed speech, backwards speech, and non-human primate vocalizations. We document that by 6 months, infants' 4-9 Hz neural activity is modulated in response to infant-directed speech and non-human primate vocalizations (the two stimuli that initially support categorization), but that 4--9 Hz neural activity is not modulated at either age by backward speech (an acoustic stimulus that doesn't support categorization at either age). These results advance the prior behavioral evidence to suggest that by 6 months, speech and non-human primate vocalizations elicit distinct changes in infants' cognitive state, influencing performance on foundational cognitive tasks such as object categorization.