These audio alerts are for the flight deck crew, and given that the door isn't designed to be soundproof, it does happen that passengers in the forward rows might hear audio output from the flight deck fixed volume speakers.
I don't think it is likely to bother many people. Those that are nervous flyers are nervous flyers in any event. There are many sounds and events that might bother them, but that is the reality of flying and they have to put up with it.