I live in a apartment. My neighbor who live upstairs, like to drag their chair and stomp their feet when ever their relative children come to visit them.
So, what should I do to my ceiling to block the noise?
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Really really difficult. I had a house that I tried to insulate the noise from upstairs. I put on the upstairs floor two layers of 1/2 inch drywall covered with 3/4 inch ply (with no fasteners) and then carpet on top. It made perhaps 25 percent difference. If you were to hang extra layers of drywall on the ceiling, you would have to fasten it with screws and the trouble is if you drive any fasteners through your sound deadening material the sound just transmits through that "hard" point. Also if you have a recessed light or any light fixture creating a hole through your sound protection the sound projects through the hole and negates a large percentage of your protection. Bottom line, if you can't live with it....move.
Being that you are in a rental situation there is very little that you can do to attempt to modify the building structure and reduce the noise. If you cannot move to a different situation you may have to resort to wearing some ear muffs or a headset depending on whether you want quiet or to listen to your TV / Sound System.
It may be possible to condition yourself to the point of being able to ignore the noise. With time to adjust it can be amazing how much a person can block out what is around them. I work in a dense office situation with folks in adjacent cubicals all carrying on their own meetings and conversations. At first when I let it bother me I experienced distress over the situation but over time I am able to block out all of it and carry on with my own work and have my own meetings and conversations.