Most people tend to think of sound from a speaker as air moving. This leads to the idea that something that will block wind (like thin plastic) will also block sound. The air is moving, but there is no "flow". Instead, think of that movement as shivering - it's vibrating very slightly but not going anywhere.
As with all solids, some sound will reflect off of the thin plastic, but almost all of it will pass right through unobstructed. Think of light hitting a pool of water - some reflects and some goes through so you can see the bottom of the pool.
So a damping material like rockwool performs essentially the same as it would in its raw state, if it is sealed inside a plastic bag.
Sound is energy that travel through and acts upon mediums. Mediums are any solid, liquid or gas (like air) and they vibrate when sound passes through them.
They can also reflect the energy. If the sound is travelling through a medium (like air) and if it meets another medium of different thickness, density and mass some of it will reflect. The new medium (like a wall) will reflect some of the energy and let some pass through.
For example a thick, solid concrete wall will reflect almost all of the energy that hits it, while a thin wall made from lighter, less dense material will only reflect the higher frequencies and let most of the bass frequencies pass through. You can hear this effect easily with your stereo playing in another room.
Damping absorbs energy and converts it to heat. When sound passes through a damping material, some of it is converted to heat and used up in that way. That's how the piece of rockwool I put inside the speaker stopped the standing wave - it absorbed the excess energy from that standing wave and converted it to a very small amount of heat.
Sound is not simple. Most think of it in 2D terms, when it is fully a 4D process. It moves through 3D space with a beginning and end time. It usually starts at a single point, but then expands out in all directions from that point until all of the energy has been converted to heat. This expanding is called propagation and the sound energy is spread thinner and thinner as it happens.
Think of a balloon being inflated and how the rubber gets thinner as the balloon gets bigger. There's still the same amount of rubber there was when the balloon was not blown up, but it's now spread over a much larger area.
For sound to dissipate quickly, something has to speed up the conversion of that sound energy to heat. That's the function of damping, like that rockwool I used.

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