I bought a new TV several months ago and even on the lowest setting it still projects the sound into my upstairs neighbors apt. The speakers are on the back of the TV and aimed right at the wall about 6" from the speaker. I decided to try and do something about this today and thought I would get some suggestions first.
Maybe get some smallish external speakers and hook them up to the TV. You can move these around to find an arrangement that gives you suitable audio but doesn’t fill the whole room with sound that bleeds out to other apartments.
The sound might be traveling up the wall if it’s hollow behind there. Get some cheap foam rubber and use it to damp the wall behind the speaker. (As big as you can stand to make it, but certainly cover from stud to stud and from the floor to the top of the TV.)
https://www.atsacoustics.com/foam-wedge-acoustic-panels-12charcoalblue.html
If you really want to spend some money to make it look nice, they will do custom panels with whatever artwork you supply.
ETA: My Dad had a similar problem, but it turned out what he needed was hearing aids. If you find yourself saying “What?” a lot in conversations, do the world a kindness and get your hearing checked. 
I bought theseto use as external monitors not for sound isolation, but because the sound from my built in TV speakers fire out the back of the TV and the sound was weak and poor. These Mackies are self-powered, not large, not terribly expensive and sound GREAT.
I wonder if my TV speakers will turn off automatically when I plug in external speakers?
Add an inexpensive “sound bar” for easy, better, forward-firing sound. Rear speakers sound okay only at high volumes, which go right through the wall.
Put 1 inch insulation foam board behind the active speakers. Cover it with cloth for appearance.
Mount the sound bar with sound isolating mounts, so that they don’t resonate through the wall again.
Apartment life is so much fun… 
Depends on your TV, but probably. Either when you plug in the speakers or there may well be an option in your TV’s setup menus to turn off the onboard speakers. That’s what my TV has.
Post your TV’s model number and I’ll check for you.
You could also, if you care to go this route, use wireless headphones so there’s no ambient sound at all.
That sounds workable.
If you live alone, this is a fantastic solution that I cannot recommend highly enough.
My latest TV has Bluetooth. I bought two pairs of headphones. They last three hours each, and charge in about 1.5 hours. When one is discharged, I can switch to the other one with no issues.
It’s great! No ambient sound, and I can move around the apartment while still listening to the TV.
I went with the sound bar, the guy at the store told me I had a common complaint with rear speaker TV sets, the soundbar seems to solve it.
Aces. I am about to buy one (STBX keeps the TV, I am taking the amp and speakers, so I offered to install a simpler sound bar system) so I was looking at their capabilities and such. Good ones have isolated mounts so that the sound isn’t transmitted back into the wall, or mount on the TV to further limit transmission.
If there are still issues, I’d put a big surround of 1-inch foam board, covered in tasteful cloth, behind the speaker bar and as much of the TV as you can - so that it sticks out maybe six inches on all sides, and a foot past the speakers. That should damp out the last local vibrations getting to the wall.
Headphones a good suggestion, too, for later-night watching. Roku’s remote has built-in bluetooth(y) audio, which I think is a wizard feature.
The Roku remote headphone feature uses Wifi Direct, not Bluetooth, but thanks for the props. I wrote the original implementation of the headphone software.
In my experience, soundproofing with jury rigged foam contraptions is only marginally effective. I once tried to deaden the sound of a shop vac by enclosing it in a plywood box with foam all around the interior walls. The diminution in sound was barely noticable.
Ah, salud, maestro. I do the Roku happy dance at all of my “cut the cord” sessions, pointing to the headphone feature as an example of how Roku stays ahead of the engineering and feature curve.
That’s because nearly all the noise comes from the exhaust and is of frequencies that simple foam baffling won’t much attenuate. But putting foam on a wall to deaden transmission from a nearby source has some effectiveness. I’ve done it in bedroom-wall situations where stereo speakers tended to resonate through the wall, and had some success. (Along with getting the kids to turn the damn thing down…)
I hope this is not too much of a hijack but I’ve always wondered how much sound gets transmitted between my house and my neighbor’s (attached rowhouses with a shared wall). I think the shared wall is cinderblock with a layer of concrete and plaster on top. It seems to mute the neighbors’ shouting matches pretty well, but my baby son sometimes cries quite loudly and I’m curious to know how this sounds on the other side.
Anyone have any ideas how much sound gets through this type of wall?
Cinderblock with topping is just about as soundproof as you can get without special decoupled construction.
(A truly sound-resistant bedroom wall, for example, is built on 6" headers and footers and offsets the studs to each side so that each wall is independent of the other - the inner wall is attached to one set of studs, and the outer wall attached to another set, and neither set touches the other wall to transmit sound. That plus some foam or batten insulation and 5/8" drywall (or even dual-1/2" on one side) can make a wall nearly soundproof for residential conditions.)
Turn the TV around so the speakers aren’t pointing at the wall. There’s probably some kind of drawback to that approach though.
Oh, silly me, of course you wouldn’t be able to see the TV. So turn it around and put a mirror on the wall behind it.
Just turn it up until you can’t hear the neighbor complaining. Problem solved.