Hmmm @adamaero not sure that's true in all cases - take heating a steel bar to red-hot conditions. The fact that it is emitting infrared (and now visible light) means that some portion of the input energy is lost as light. So heating the bar using 1kJ of energy then dunking it in water will result in a lower water temp rise, than heating the water directly with 1kJ of energy.
I'm thinking about soundproofing the insides of a closet (spans the wall) where a shower is on the other side. Looked into it a bit and saw that quote. Wondered
The single noise question was a tangent. It seems a shower generates low and high frequency sound. I wonder if a shower mat would reduce the (I'm guessing) higher frequency noise...
$200 mass loaded vinyl (or drywall instead) $185 Thinsulate (or drywall instead) + maybe fiberglass insulation to fill the wall (not sure if it's empty)
Bathroom tiles have excellent acoustics. The magic solution might be to hang up a bunch of towels and maybe a shower curtain in the bathroom. A rug on the floor etc.