It depends on the state you live in, but it is possible. If trying to ask them nicely, calling the cops and using other (legal) means shows no improvement and if you can prove that their noise is causing you harm, then you can actually sue your neighbors.
If you can make a good case, you can have them pay you for damages and even cause them to be evicted. Getting a good case on your side is going to require you accumulate enough evidence to support it. But if you already have noisy neighbors, it shouldn’t be difficult.
All you really have to do is get recordings of the noise, at specific times, keep a log of when the noise is exceeding the limit allowed in your city/state, if possible, record conversations you have had with the neighbor that prove you tried asking them nicely to stop. If they threaten you, you can also keep a recording of that as proof.
Police reports will also give you a lot of benefits in court. If you can get police to show up at the neighbor’s house/apartment and indicate that there was a violation taking place, you can use those police reports in court as well.
That’s really all you need to do. You don’t even need a lawyer for this. There are other very helpful legal resources you can look into to get more details. Here is a VERY good article index from Nolo.com.
What about your management and/or landlord? Technically, your management and landlord are responsible for making sure you have peace within your rented home and you can always use the evidence against your neighbors, go to your management and let them know a problem is happening.
Usually the landlord will contact the neighbors and ask them to stop. This is what has been going on with me personally. Usually it helps temporarily and my neighbors will keep their noise within the limits, but it’s not a long term solution because usually noisy neighbors, especially obnoxious ones won’t obey the rules for long.
In New York City where I live, the process of evicting a tenant is not very simple and does require legal documents such as police reports be provided OR evidence that they broke another law (drugs, dangerous living conditions, criminals, ect…).
Not all landlords are the same. Some take action. Others just talk to the neighbors and that’s it and there are those who won’t even bother handling your problem. If you have a landlord that isn’t taking action, you are entitled to do it yourself.
Suing a neighbor and doing things such as calling the police should be last resorts to take. Nobody wants to have problems with their neighbors. Peaceful resolutions should always be the goal, but if that doesn’t work, laws have been put into place to help get rid of the noisy neighbor and even make them pay for causing harm to others and yes, noise is a form of harm and you have a right to live peacefully.
If you ever have a neighbor respond to that argument by bothering you more with their loud behavior, have the police give them a visit. Maybe then they’ll understand. And if that’s not good enough, once they have to pay for their behavior, that should put an end to it.