Sound and Noise Distance

[nuke11]

I was looking for a chart or formula that would help figure out how loud something would be over a distance, so I had a look around on the internet and found this that should help in the game.

In the world of TMP loud sounds will be uncommon in most areas of the country so any noise will be unusual. So the following formulas can be used to tell how loud a noise will be at a certain distance or used to figure out how loud it was at the source (might not be that useful but interesting). Variables to also consider atmospheric conditions and the environment around the observer. High frequencies are absorbed faster than low frequencies by water vapor and dust in the air. All sound is measured in decibels (dB).

If you know or have an educated guess of the sound level from source you can use the following;

Sound source - (20log(distance in m's) + 11) = sound level at observer dB (outdoors)

If you know the sound level and distance of source from the observed level from source:

(20log(distance from source) + 11) + level heard = sound level at the source

Example: you are 1060 m from a road, you hear a sound level of 20 dB where you are.

(20log(1060) + 11) + 20 = 91.5 dB (at roadway)


There are a number of websites that list common sound levels for everyday objects and sounds.

I'll work on an spreadsheet that helps calculate sound levels at different distances.

[nuke11]

Lets put this into some context. From this website http://www.freehearingtest.com/hia_gunfirenoise.shtml we see that a typical .223 Remington or 5.56mm gunshot will be 155.5 dB. A person with good hearing can hear a sound as low as 10 dB and a whisper or wrist watching ticking will be around 20 dB.

A PC fires a shot from their M16 and you want to find out if a group of bad guys will hear the gunshot where they are.

The bad guys are 2325m away. 155.5 - (20log(2325)+11) = dB at there location. 155.5 - (67+11) = 77.5dB. They are going to hear it.

A typical suppressor lowers the sound level by -28dB to -35dB so this will help out.

[rob]

I too am interested in the distance sound travels. Had to wing it last night from an explosion and from sporadic gun shots. The setting is a rural, low mountain/high hill area that is mostly forested. The distance involved was about 8-10km as the crow flies. Thanks.

[RandyT0001]

According to the equation one can hear at a 30dB level, a whisper, the report of a 5.56mm cartridge from about 530km (323 miles)

(log^-1)((155.5-30-11)/20)=530884meters
inverse log of 5.725 (what number has a log of 5.725?)

Truck traffic, 90dB, can be heard as a whisper from about 282 meters (924 ft)
Chainsaw, 100dB, can be heard as a whisper from about 891 meters (2923 ft or little more that half a mile)

I think wind conditions, speed and direction will affect the distance sound is percieved.

After Nuke11 made the original post I did look up sound ranging on wikipedia which was perfected in WW2 (at a tech level the Republic has :D)

[rob]

Thanks for the mathematics RandyT0001. While it is above this old brain, it still will come in handy since one of the players is a math wiz, I'll let him do the math for me! Thanks again.

[nuke11]

The formula I posted is a very simplistic one at best.

For 150dB it would be 30dB at about 11.3 km taking into account no environmental effects or terrain / obstacles to absorb the sound.

Flat plain, gun fired straight at you and sound spreads out evenly, but of course it does not.

1/6*4/3*3.14=0.697. 0.697*X^3=Y{m3} X=1 when dB=150.

11.3km you'd have 1,005,699,209,000m3 which is 120dB difference, so the sound would be around 30dB, just above a whisper.

Source : http://www.thehighroad.org/archive/index.php/t-226357.html

[nuke11]

An interesting website that will help give estimates of sound reduction per Km based on atmospheric conditions. You will need to know the sound frequency thou.

http://www.csgnetwork.com/atmossndabsorbcalc.html

[nuke11]

And for those that want to figure out how far aware you can hear an explosion;

180dB - 1 POUND T.N.T. AT 15 FEET

[mmartin798]

There are other factors to consider if you want to dig deep enough. Lets say you have birds singing nearby (44dB). A firefight breaks out at the 11.3km, using the distance referenced above (30dB). If we add the two sounds together, we get 44.169 dB (The math is non-trivial, see here for a calculator http://www.sengpielaudio.com/calculator-spl.htm)

This change in sound is well below the 3dB threshold for hearing a change. So the bird will completely hide the firefight. The 1 pound of TNT might be heard.