Okay, Andrew, here’s your justifications:
Trust me, my professional field of specialization is acoustics, electroacoustics, and psychoacoustics. Please excuse me if I get touchy in this area, but I didn’t study it for 10+ years, publish, and become a professor without some god-damned effort.
First, I think you meant that our hearing drops off above 15kHz, not 5kHz. Human hearing can extend into 20+ kHz in young people / children, however pressbycusis due to exposure to loud noise and resulting ear damage causes this high frequency loss.
The most sensitive range of hearing in humans is 4kHz to 6kHz. So, we actually hear 5kHz as 2x as loud as any other frequency. See the equal loudness contour –
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=imgres&cd=&cad=rja&uact=8&ved=0ahUKEwji_4_Q4_vRAhWIKCYKHfA_BBMQjRwIBw&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FEqual-loudness_contour&psig=AFQjCNGr5v1ur1mNKKOoZsS8J5upSPxmRQ&ust=1486481064897910
This is the critical band for speech ineligibility. Humans evolved to have high sensitivity in this region to communicate. It is also critical band for masking phenomena, and intra-aural localization.
If we’re talking about material only, we need to find the attenuation in sabins. A sabin is the amount of energy converted to heat across a barrier of dissimilar material of a given boundary area. Because sabine’s equation requires knowledge of air volume, absorptive surface area, and time (RT60), we can’t just get a convenient percentage value or any sort of useful sound proofy-ness indicator that makes sense in multiple situations.
But, yes, sound absorption is related to a material property (absorption coefficient). The misconception is that the absorption coefficient is a percentage of the sound absorbed by a material. For instance, the absorption coefficient of 2.5" of R8 fiberglass batt is about .92 at 1kHz . This does NOT mean that 92% of the sound is absorbed. It simply means that .92 is factored into sabine’s equation.
That means that in one 32ft roll, we’ve got about 13.8 sabins of absorption.
For fancy, 10cm thick acoustic foam it would be 14.85 sabins
What does this tell us? It ONLY tells us that acoustic foam works better than fiberglass batt, but not by a whole lot, except that we only need 1cm of foam vs 2" of batt.
I STILL don’t know how much the sound is deadened in our case. I’d have to know volume of the space, surface areas, average sound pressure level, current absorption of surfaces, resonances, and time variables.
I’m actually trying to say is that this is not so simple, and is virtually impossible to predict. Furthermore, the absorption of any given material means very little, actually. Much less than the structure of the building we can’t change.
Finally, I’ll put it this way. In order to significantly deaden sound between the two spaces, we would also have to eliminate heat loss between the two spaces. The two are related, and I think everyone can grasp that we’re not going to make our space or even a part of it LEED certifiable any time soon.
Finally, sound is not heat. ANY air gap, whatsoever, even just an inch, that is not sealed will negate most of the work. Hence, Nancy’s point that there are gaps in the floor / ceiling. Ever single one would have to be closed with caulk before any insane amount of batting would do much.
So, my estimate would be to decouple the ceiling and shared walls with floating rubber mounts, double stud and frame (not drop ceiling). 16" air gap. Double gypsum acoustic grade board. Packed sand and rubber at floor couplings, and vinyl seal with acoustic caulk. So, the answer is so expensive that my conclusion is:
Screw it, it’s hopeless.
If you really wanted a number, we’d probably be looking at more than $70k (DIY cost) to be able to run the bandsaw at night. At the very least, the cost of make a new timber framed ceiling for our ENTIRE ceiling space, not just the area under this dude’s apt., and two layers of sheetrock.
If folks want to put up insulation, I won’t stop you, but there is no significant return on investment.
Lorin
P.S. I went way too overboard here, but I think my point is made.