with, transparent fabric, is only used to control reflections of sound within the room/booth. It does nothing (or extremely little) to keep sound, particularly lower frequency content (like a snoring human being), from entering and/or leaving the room. To stop sound, you need mass. You have to keep the walls from vibrating. Recording studios typically have pretty sophisticated wall, ceiling, and floor structures designed to decouple one room from the next so that vibrations produced in the structure of one room won't be transmitted through the framing to the next room. Also, several layers of wallboard are typically used to greatly increase the mass of the walls, floors, and ceiling to keep them from vibrating. The doors can be hundreds of pounds each in weight. The foam/fiberglass products are used to control reflections and to reduce the overall reverb time within the room.

Now, for this situation where we're not really talking about big SPL numbers, a real sophisticated solution probably wouldn't be necessary. An extra layer of wallboard on one side of one wall might just be enough. There are also limp-mass (e.g., vinyl) products that could be used to quickly increase the mass of a wall. It wouldn't be recording studio worthy sound control, but it might be enough to quiet down a snoring human being. Of course, one could work on the walls in this type of manner, only to discover that the sound is flying out of the door of one room and through the door of the other room. The whole system needs to be considered. If the sound is clearly primarily transmitting through the wall, an extra layer of gypsum might do the trick.