It is just called a window adaptor.
The problem with these type of air conditioners is they have a catch bucket for the condensation. You have to manually empoty them and if they get too full the unit stops operating till it is emptied. This can happen at inconvient times as you can guess.
These units also do not have a good track record for being reliable. They tend to retain a lot of heat and that burns them up prematurely.
They also use up a lot more electricity as they have to first cool the ambient air, distribute it, and also vent the warm air to the outside through a tube.
They are not really portable as to move it you must disassemble the window adaptor and then reinstall it in the other rooms window.
Basically they are a pain in the backside, not energy efficient, and are prone to breakdowns and control issues.
As for the window adaptor they do not come in soundproof models. all they are is a plastic sheet that expands to fit the window.
Oh did I mention that these have a bad habit of not remaining secure in the window unless you run a couple of screws through them?
Stick with the window model. You will be better off for it.
If you want to sound proof the unit or the window adaptors just gwet some one or two inch thick styrofoam or foam rubber (from an old cushion works) apply some spray on 3M general piurpose adhesive and glue it to the parts you want to soundproof.
NOTE: DO NOT COVER THE AC VENTS! It will over heat the unit and can cause it to fail, or even catch fire in some cases.
Please let me know if you have any other immediate concerns.
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