Back To Plastic indeed! Some contractors insist that putting up plain sheets of plastic as in the plastic tablecloths you put on your table will help reduce sound transfer through walls. They mean putting the plastic onto the studs and dry walling over it. While we wouldn’t want to rely on that when doing soundproofing for a customer you still may want to consider doing it for yourself in a situation where you do not have more than $10 dollars extra!
The real plastic that may actually give you some sort of sound control would be Mass Loaded Vinyl this heavy vinyl will actually add mass to your walls creating a sound barrier which is one of the principles of sound control. It can come as heavy as two pound mass loaded vinyl which weighs two pounds per square foot. I would only use something that heavy on floors.