If you are hearing a resident complain about noises from other residents, one of the first things you should do is ask the person complaining if they have spoken to the louder resident on their own. Sadly, many people view you as someone who will deal with all of their problems related to the apartment regardless of whether or not it is something you can control. If they have not spoken to the person in question, suggest that as the first course of action. After all, the person who is disrupting your other resident may not realize anyone else can hear them.
Another thing to think about is whether or not there are multiple complaints leveraged against the same resident. If there are multiple people telling you that someone in the complex or building is too loud, then there is probably more to the issue than simple animosity. You always run the risk of there being some sort of feud when two people are complaining about one another, but this becomes less likely the more people are complaining about the same person. Maybe head over and spend some time in the area to see if the person is a little too loud. If so, then you may want to approach them.
Although noise complaints are notoriously difficult to deal with, you do have a couple of different methods that you can try. Naturally you don't want to consider asking the resident to leave, so try to find some form of mediation or an agreement between your residents that will allow all parties to leave content with the solution. This may be certain times that the noise is allowed or that the resident in question uses earphones for loud music. Whatever the end solution, know that noise complaints are just part of the territory.