Some images for inspiration... these boxes are apparently quite common in the Netherlands.
Yup, pretty much standard growing gear. Actually the carbon filter and the "offsucker"
lol: verbatim translation usually no good - the ventilator that sucks off the air through the carbon filter, pulling fresh air inside) are standard because of snitching neighbors that might smell something. And since those make noise AND vibrate, they are put in a softbox.
Ruck is a popular (german engineering...) brand for tube ventilators, but the soft boxes work better with snail ventilators.
As for the US term, we have this weird habbit in dutch to combine words, so I'd just add a space and call it a soft box, but Google tells me that's used in photography already.
It's a ventilation silencer?
I see my previous reply above, didn't stress the sonodeck hose enough. So let me put it this way, I consider it (or similar insulated hosing) an essential part of the softbox (without it it will blow out the noise ).
I'll paste in a photo of my setup from my pc in a few min.
EDIT: last pic is outside the grow closet. As I mentioned previously I don't actually have a softbox myself. Most because I just had to invest in other stuff first, so I went with just the padding. All on ropes, but the ones with weight on it have rubber bands at the top.
Would have been optimal if there was a small piece of that hosing between the carbon filter and the ventilator (which is an awesome thing by itself, thermostat, only goes as hard and as noisy as it needs to).
People who grow in tents here, or small closets, often place the softbox outside the tent/closet (which especially in DIY cases gives a lot of options).