If you've ever lived in an apartment with someone living just above you, you probably know how much a soundproof ceiling would have increased your comfort in that situation. If you are living in an apartment now, you might approach your apartment manager about having access to the upstairs unit so that you can soundproof its floor.
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In doing so, however, you'll not only be faced with the physically challenging job of putting up the soundproofing materials; you'll be reducing the height of the room.
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You can simplify your job by deciding to install acoustical ceiling tiles, which will do a moderately good job of preventing noise from bleeding down from above, but for a really soundproof ceiling, you really need to add a new layer to your existing one.
You would do this by putting in resilient bars, which are designed to keep your original ceiling separated from the new one. You would first install the resilient bars, and then place your soundproofing materials like rock or mineral wool, and mass-loaded vinyl into them, before adding the drywall which will be the surface of your new ceiling.
While this will be a lengthy and difficult job, it really is the best way you have of creating a soundproof ceiling that can give you the peace and quiet you deserve.