Is the loudness of sound cumulative?

[PaperclipGod]

If you're sitting in a room (just a typical room at STP, not a lead-lined room on top of everest or anything :/ ) with one device producing a 40 dB noise, would turning on a second device which produces 30 dB increase the ambient/background noise that you perceive? Consider they're both the same type of noise, too... not a vacuum cleaner and a doorbell.

Just in case my unedumacated question is confusing, here's another example: What if two devices, producing the same type of noise, at the same 20 dB level, are turned on in an otherwise silent room. Would the background noise be greater than 20 dB? If so, by how much?

I'm just trying to figure out what the perceived difference in noise level might be for, say, one 40 dB case exhaust fan vs. four 20 dB fans. I know there's other sources of noise (air gaps in the case, static pressure, etc), but I'm just hoping for info on this specific, idealized sort of situation.

 

[JM Aggie08]

I'd imagine so.

 

[Crusty]

Are two speakers louder then one?

 

[Howard]

Depends on the frequency, I think. If the frequency spectrum is the same, then yes, the power will add and 3dB is a doubling of sound pressure.

 

[fuzzybabybunny]

Could you think of it in terms of power?

A 30W speaker compared to two 30W speakers. The latter are pumping out a total of 60W energy if the frequencies are all the same.

 

[her209]

Powers of 10 baby!

 

[jamesbond007]

From my car audio days and if memory serves me, every 3dB increase is doubling the sound pressure. However, it requires roughly 10dB to be a perceivable difference to the human ear.

 

[dullard]

A 20 dB sound has a 10 Pa * 10^(20dB/10dB) = 1000 Pa pressure.

Two 20 dB sounds have a 2*1000 Pa pressure. Converting this back to decibels, the sound is log (2000 Pa / 10 Pa)*10 dB = 23.01 dB.


Yes, loudness of sound is cumulative. But the artificial decibel rating given to sound isn't directly additive. You first have to convert it back to pressure, then add, then reconvert to decibels.

Doing the same math, a 30 dB + 20 dB sound is equal to 30.41 dB. You'd never notice the difference if they were the same frequency of sound.

 

[RedArmy]

Have at it: Text

 

[jteef]

Originally posted by: jamesbond007
From my car audio days and if memory serves me, every 3dB increase is doubling the sound pressure. However, it requires roughly 10dB to be a perceivable difference to the human ear.

close, 10dB is a perceived doubling(or halving) in loudness to most human ears. humans can differentiate much smaller levels.

 

[PaperclipGod]

Originally posted by: dullard
A 20 dB sound has a 10 Pa * 10^(20dB/10dB) = 1000 Pa pressure.

Two 20 dB sounds have a 2*1000 Pa pressure. Converting this back to decibels, the sound is log (2000 Pa / 10 Pa)*10 dB = 23.01 dB.


Yes, loudness of sound is cumulative. But the artificial decibel rating given to sound isn't directly additive. You first have to convert it back to pressure, then add, then reconvert to decibels.

Doing the same math, a 30 dB + 20 dB sound is equal to 30.41 dB. You'd never notice the difference if they were the same frequency of sound.

So if I've got four 40 dB fans all at the same frequency, would that work out to something like 52 dB for the cumulative noise level?

 

[Howard]

Originally posted by: jteef

Originally posted by: jamesbond007
From my car audio days and if memory serves me, every 3dB increase is doubling the sound pressure. However, it requires roughly 10dB to be a perceivable difference to the human ear.

close, 10dB is a perceived doubling(or halving) in loudness to most human ears. humans can differentiate much smaller levels.

About 1dB. Very roughly, anyway.

 

[BornStar]

Originally posted by: PaperclipGod

Originally posted by: dullard
A 20 dB sound has a 10 Pa * 10^(20dB/10dB) = 1000 Pa pressure.

Two 20 dB sounds have a 2*1000 Pa pressure. Converting this back to decibels, the sound is log (2000 Pa / 10 Pa)*10 dB = 23.01 dB.


Yes, loudness of sound is cumulative. But the artificial decibel rating given to sound isn't directly additive. You first have to convert it back to pressure, then add, then reconvert to decibels.

Doing the same math, a 30 dB + 20 dB sound is equal to 30.41 dB. You'd never notice the difference if they were the same frequency of sound.

So if I've got four 40 dB fans all at the same frequency, would that work out to something like 52 dB for the cumulative noise level?

Close, it would be 46dB. You're doubling twice which is 2x3dB.

 

[Evadman]

they are cumulative. 50 db speaker + 50 db speaker = 53 db combined.

 

[PaperclipGod]

Ahh... got it. Thanks.

 

[Brownshoe]

I've been doing similar "research" to figure this out...specifically b/c I'd like to build a very quiet system and I'm wondering how the fans add up. Some of the answers above don't appear to be accurate, so I'll post what I've found and what I think.

The following site/links were particularly helpful:
http://www.phys.unsw.edu.au/jw/dB.html (background on the math)
http://www.sengpielaudio.com/calculator-soundlevel.htm (simple conversion)
http://www.phys.unsw.edu.au/jw/musFAQ.html#add (Commentary on adding a second source, versus doubling the power of one source)
http://www.phys.unsw.edu.au/jw/musFAQ.html#extraviolin (commentary specifically on the topic of adding multiple sources of the same sound)

All in, I'm still a little unclear on the math. According to this last "violin" example, "adding the second violin adds 3 dB to the sound level produced by the first, the third adds 2 dB to the level produced by the front desk, the fourth adds 1 dB, and so on, and adding the 15th violin gives you an extra 0.3 dB." So, adding 4 of the same 40 dB fans would be the equivalent of adding like 6.5 dB...

However, I'm not sure how this text gets here if the equation it references is that the change in levels is "= 10 log(1+1/n)." With this equation, I'd show the change by adding a second (making "n" 2) =1.76, making n = "3" results in 1.25, and making "n" 4 = 0.97...or a cumulative 3.98 over the original 40 by adding the fourth 40 db fan.

 

[Harvey]

they are cumulative. 50 db speaker + 50 db speaker = 53 db combined.

That is correct for non-correllated sound sources. That is, non-identical sounds. For two identical sounds that are in phase with each other, the sum would be 6 db as a voltage or 3 dB for sound pressure (power).

 

[Rubycon]

In theory yes. Of course not just frequency and timbre change this but location and environment! Room gain, cancellation, etc. play a huge part on actual sound pressure level at the measurement point.

With mechanical sources like fans that are electronically driven and not exactly synchronized an off beat noise often sets up producing a throbbing noise that can be bothersome to some. Add in the amplification of whatever it's attached to and perceived loudness can increase 10dB or more!