There will be differing opinions on this subject so I'll present my assumptions. I used the A-weighted Sound Pressure Level method to measure and calculate. The SPL scale is useful to determine how the human ear perceives sound. A-weighting aligns well with sounds under 45dB. I used that because while neighbors are outside to enjoy a quiet evening, ambient noise is likely around below that level so that's the relevant area. And my city uses this scale despite that fact their limit is really in the B-weighting range. It's clear they did not have a qualified consultant help them to write the ordinance.
My local code limits noise to 55dBA but they are unclear how, or where they measure. Since they didn't specify, I'm guessing they will measure at my property line. This leaves me vulnerable to fines based on the opinion of whomever shows up to measure. I measured one of my S9s to be 73dBA at 1 foot.
Sound energy, like all unfocused energy, dissipates spherically in all directions equally. When this is measured linearly, like from yours to your neighbors house, the sound energy is reduced by the inverse proportion law, 1/r, where r is the radius of the sphere. So if you measure the SPL from 1 foot away, it allows us calculate the SPL by knowing how many feet away your neighbors ears will be. When threatened with sound complaints, it's good to know your city's ordinances.
Each time you double the number of miners, the SPL level increases by 3dB. Each time you double the distance it decreases by 6dB. So to use the chart, the quantity of miners is in the left column and the distance in feet is in the top row. These numbers increase logarithmically to match sound energy characteristics.
If you start by knowing your sound level tolerance and the distance to whatever you need to limit the noise to, just go down the distance column to find the dBA level tolerable to see how many miners can be installed. Some interpolation may be required but you can easily get an idea of the sound level. Once the sound level diminishes down to ambient, the miner noise is "lost in the noise", literally.
55 dBA Limit
73 dBA at 1 foot
Code:
Qty 1 2 4 8 16 32 64 128 256 512 1024 Feet
1 73 67 61 55 49 43 37 31 25 19 13
2 76 70 64 58 52 46 40 34 28 22 16
4 79 73 67 61 55 49 43 37 31 25 19
8 82 76 70 64 58 52 46 40 34 28 22
16 85 79 73 67 61 55 49 43 37 31 25
32 88 82 76 70 64 58 52 46 40 34 28
64 91 85 79 73 67 61 55 49 43 37 31
128 94 88 82 76 70 64 58 52 46 40 34
256 97 91 85 79 73 67 61 55 49 43 37
512 100 94 88 82 76 70 64 58 52 46 40
1024 103 97 91 85 79 73 67 61 55 49 43
This simple chart is useful but could be misleading. Be sure to consider anything would could reflect some of the sound energy toward the adversary instead of dissipating as assumed. Of course you could reflect sound energy away from the offended neighbor too.
Also note if you have an existing farm, you can measure the noise level to establish a baseline. If you double the miners you should see a 3dB increase. If you have a noise problem, you can reduce the level 3dB by halving the miners to satisfy the limit.
(Moderator's note: This post was edited by frodocooper to format the chart as a code blob.)