The question asks what can be done if you want to use a punching bag in an apartment. What would that look like?
The problem with using a punching bag in an apartment is that you'll create a lot of loud pounding noises and vibrations. Even if your neighbors are not trying to sleep and it's the middle of the day, it will feel to them like it's an intrusion into their lives. It will feel like you're doing something to them. They're going to be irate.
So I'm sorry, if you have an apartment, you just can't use a heavy punching bag there. Find a gym that has them. Boxing gyms sometimes have an "open gym" policy at certain times of the day or week, where you pay only something like $5 to $10 to use all the facilities. Look into that first.
That said, if you really wanted to use a punching bag of some sort in an apartment, what kind of punching bag could you use to minimize noise and vibration?
The answer is a speed bag attached by bungee cords. These kind of bags are only meant for focus, timing, and combinations. It's not meant for power. The more you put power into it, the more likely it will be that it causes noise and vibration. You can experiment with different types of bungee. The more tension they have, the more power you can use. So you're looking for a pretty loose setup that lets the bag swing more easily. That way you won't be tempted to do power punches.
How you mount it is up to you. You'll find some of them are designed to be used on door frames. But that means you won't be able to do some types of training, due to the reduced angle of attack. Probably the best as far as anti-vibration and freedom of movement is concerned is to get a bag stand that's specifically for speed bags. If you can't find one, it's easy enough to make one if you're handy. Then to dampen noise transfer to the floor, you'll want to put thick foam under the bag stand. Make sure you have carpeting on your floor, also, because that will help dampen noise as well.
Hope that helps.
