A.Fernando Pages Ruiz, a building contractor in Lincoln, Neb., and the author of Building an Affordable House, responds: Unfortunately, you cannot build a soundproof enclosure of any kind that would also provide adequate ventilation for the AC unit. Noise travels through air, so by definition a soundproof enclosure would have to be airtight.
The solution to your neighbor's AC noise output lies at your own bedroom window. First, check that your window seals tightly. You'd be amazed how much sound you can block with good weather stripping. Remove the casing around your window and seal the area around the jambs with caulking or expanding foam sealant. If that doesn't help, consider...
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