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Sound, Distance and Hearing... physics help with decibels needed

Negalith

New member
For the home brew system I am working on, I wanted to work in a mechanic for the likelihood of being able to perceive various sounds over distance. I figured starting the the decibel volume of various sounds would be a good start and then figuring out how decibel lower over distance... all good so far.. but there is a physics problem that is screwing me over and I could use some info from somebody. here is my problem... 1 it's very easy to find lists on the internet of how loud things are in decibels. 2) the physics formula of dropping 6 db for ever doubling of distance is pretty easy to make sense of..... but... its the initial sample area I don't know where to stat with.

Lets say my handy on line reference tells me that a gunshot is 170 db... but 170 db at what distance . the standard equation drops 6 db every doubling of distance from the initial reference point. If for example we were to imagine that the pistol was 170 db measured at 1/1000 for an inch from the gun. doubling that very small initial area would result in a very small sound at distance of only a few ft away. were that 170 db measured at a 1000 ft, we could easily expect a gunshot to be heard clearly many many miles away.

Is there a standard assumption of how far away most decibel measurements are taken at?
 

Knaight

Registered User
Validated User
It's not as standardized as you'd like - but, what helps here is that a lot of these decibel measurements are averages in an area. This lets you make approximations where the characteristic length corresponding to the area can be used as a starting "distance". Some charts will also give specific distances, which gets you some of the rest of the way. For instance, there's this:

which is pulled from corporate numbers for a noise management company.

For the jet, chainsaw, disco, truck, vacuum cleaner, and speech we have distances given. We also have that for the road, but that's a very distributed noise system, though 5m is not a bad approximation there. The rest are ambient noises, added over a lot of point sources. You could use area to scale these outward, like if you had that quiet library in an otherwise silent void. It would depend on the size of the library, but that's pretty much to be expected.

The gunshot is probably a meterish, give or take.
 

Cloud Divider

Registered User
Validated User
Noise measurements are usually not at the actual noise source (muzzle of gun, for instance). I'll have to look at some of the test specifications, but as a rough order magnitude estimate, figure the baseline distance is somewhere between 1-10 meters for most things.

So a handgun, assuming 170dB at one meter, drops to 164 at 2m, 158 at 4m...and still 116dB at 512m. It probably doesn't get quiet enough to blend into background outdoor noise until 60dB, which is 6 more doublings, or 32km. Which is probably off by a bit, but not as much as you'd think. You can easily hear small arms fire several miles away under good conditions. So easily 2mi/5km. The pistol peak dB seems high, but I honestly haven't looked.

The jet plane, 140dB at 50m, would be 170dB at 1m-ish, working the math the opposite direction. The plane is audible outdoors (70dB) out to roughly 50km (again, off by a doubling or two). You can easily hear a passing jetliner at 30-50k feet plus some horizontal distance (10-20km).

It's by no means a perfect abstraction, but the above figures feel pretty reasonable to me (as order-of-magnitude estimates). Being off by 2-4x isn't bad at all, considering.
 

Max

A dapper chap without a doubt
RPGnet Member
Validated User
The end result is heavily modified by circumstances, though. Different environments and acoustic conditions can muffle sounds or make them carry for miles and miles and miles and miles...
 

Cloud Divider

Registered User
Validated User
The end result is heavily modified by circumstances, though. Different environments and acoustic conditions can muffle sounds or make them carry for miles and miles and miles and miles...
Absolutely. Sound modeling and propagation is really complicated. Ground terrain, ground cover (trees, vegetation, rocks, water), sound-reflective objects (buildings, plus atmospheric effects like inversions), temperature, pressure, humidity, air density and on and on. I need to see if I can find a copy of the paper that documented the process NASA uses to estimate sound and blast hazard zones for space launches. Really interesting reading.

All of that is probably waaaay too much effort for an RPG, especially if you're computing it live. But scaling the doublings one way or the other based on a SWAG might be more than adequate. Gunfight in dense forest covered in fog? Sound probably won't carry as far. Gunfire inside an abandoned mall? You'll probably hear it everywhere...but you probably will have a hard time figuring out where it's coming from (lots of high reflective surfaces).

You might actually have an easier time categorizing noise sources as broad categories (insanely loud, like jet planes, artillery fire, big explosions, at 150dB; very quiet, like a whisper or an arrow whizzing by at 40dB), and then giving table columns that provide distances where you'd hear it. Better (or worse) hearing capability, or better/worse propagation conditions just shift you up and down the "detection distance" table. That actually might be a reasonably playable solution with the veneer of scientific accuracy behind it.
 
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