Psychology says people who lower their voice when someone nearby lowers theirs may automatically follow social cues
People who naturally lower their voice when someone nearby does the same may be responding to a combination of social cue detection, vocal accommodation, conversational entrainment and unconscious mimicry. A change in another person’s voice can provide a subtle social signal that the brain quickly interprets. In response, your communication style may adjust automatically, sometimes before you consciously realize that you are doing it.