How does dB noise work?

[bbarnes]

Please don't give me a really technical answer, because I want to understand this.

How come 2 50dB fans don't sound twice as loud as one?

I read in someones post that it would only be like a 3dB increase or so...

TIA.

Edit: (I won't be on any longer tonight, so don't expect a reply from me until tomorrow about mid-day.)

 

[blahblah99]

50dB is on the log scale...so you can't add them up in the usual sense... 50dB corresponds to about 10^(50/20) = 315 noise units.

if you have two fans, thats 2*315 = 630 noise units... 10^2.8 = ~630. 2.8*20 = ~56 dB

So the MAXIMUM noise increase is 6dB, although in reality it is less than that.

In short, you can't just add numbers represent on the decibel scale because its not linear. You need to convert it to its linear representation, add it, and convert it back to decibel scale.

 

[bizmark]

To be a little more explicit:

The decibel scale is logarithmic. It takes a linear scale of something that can be easily measured (a pressure, I think -- in units of Watts/meter^2) and converts it into a logged value.

The way that logs work is exemplified the following. The log (base 10, to be specific) of 10 is 1. The log of 100 is 2. So even though the values of 100 and 10 are very different and certainly not on the scale of 2 versus 1, you can see the relationship between them fairly easily. It's because 10^1 is 10 and 10^2 is 100. Similarly, the log of 1000 is 3. So if you compare the log of 100 versus the log of 200, you get 2 versus 2.3. Doubling a value will always give around 0.3 log-units difference when you're taking the log base 10. Log of 5000 is 3.7, log of 10,000 is 4. That's why doubling the real sound output of something (say you double the power of an amp from 50W to 100W) will increase its dB level by 3dB.

The basic reason why logs are commonly used is to make things more understandable to humans, who like to work in small, easily-compared numbers. If I told you that sound A was 300 loud and sound B was 7 million loud, then you'd think that sound A would be essentially a non-sound because it's so much smaller than 7 million. But if I told you that sound A was 25 and sound B was 68, then you could understand a little bit better. It's actually sort of a tribute to the fine-ness of our measuring devices (in the case of sound, our ears) that we can use logs in an understandable way at all. The fact that we can perceive sounds that differ in magnitude by 10^12 =1,000,000,000,000 times is quite remarkable.

 

[Agent004]

wbwither explained very nicely on the physical (calculation) part of it. Let me just to add some more info

As stated by wbwither, it's really relates to how our ears respond to sound(intensity), more specifically, changes in sound (intensity)

For example, supposely a speaker pumps out 5 db noise, at 50w. Then you turn the power up to 100w, then the noise will be 10db, since the change in the intensity is 100%. ie, your ear can tell there is a massive different

Or you have a speaker pumps out 40 db at 400w, then you turn it up to 450w, the change in power is only 12.5%, so it will not double in db (noise ) level. Probably it will be at 41 db(you hardly can tell the different)


I assumed some pretty heavy linear relationship, and rough example to demonstrate my point

 

[highwire]

blahblah managed to confuse himself with some dandy arithmetic.

Two equal and independent noise sources will have TWICE the noise power.

But, it will not sound TWICE as loud. That is because our ears do not perceive sound levels in a linear fashion. For something to sound twice as loud requires an increase of ~ 5 to 7 db or ~ 3 to 5 times more power. It is a psycho-acoustical thing with our hearing senses that compresses sound level differences and makes the differences seem less than they are.

Some db basics:

The decibel is a logarithmic POWER RATIO. Sometimes it is used as an absolute level by comparing to a standard level. In acoustics, 0 db is the very small standard sound pressure that the measured device is being compared to.

60 db = a power ratio of 1 million
30 db = a power ratio of 1 thousand
20 db = a power ratio of 1 hundred
10 db = a power ratio of 10
3 db ~= a power ratio of 2
1 db ~= a power ratio of 1.26 ( or 26% increase)

So, if you tricked out your little rice burner and the horse power increased from 100 hp to 126 hp, you just increased your engine power by 1 db.

 

[bbarnes]

These posts helped some.

So about how many dB would this sound like?

25dB + 25dB + 27dB + 20dB + 20dB + 20dB + 30dB (Glad it wouldn't be 167dB)

 

[bizmark]

<< 25dB + 25dB + 27dB + 20dB + 20dB + 20dB + 30dB >>



33.9dB.

Decibels are one-tenth of a Bel. So 25 dB is 2.5Bel. A Bel is a pure base-10 logarithm of the actual sound intensity. You can't add logarithms, but you can add the actual intensities. So the calculation is like this:

(10^2.5)+(10^2.5)+(10^2.7)+(10^2)+(10^2)+(10^2)+(10^3)=

316+316+501+100+100+100+1000=2433 (all numbers rounded...)

Then take log (base 10) of 2433 to get 3.39Bel, times 10 to get 33.9dB.

 

[jteef]

I am wondering how these ratings are achieved. are they SPL's or power measurements? Sound measurements are usually done in terms of SPL which is 20*log(prms/pref) where prms is the rms value of air pressure in pascals and pref is the standardized threshold of hearing which is 2x10^-5 pascals.

additionally, the environment surrounding the noise sources has a very big impact on how loud the sound is. Is there a standard for measuring noise that differs from everything else in audio?

more fans wouldn't necessarily be louder either. depending on your position relative to each fan and their respective output at certain times, you could just as easily have destructive interference which would make two fans quieter than one.

jt

 

[Sahakiel]

Just like to point out something else.
Sounds are waves and therefore have constructive and destructive interference.
Have fun with this one.

 

[bbarnes]

I think I am starting to understand this more and more now...

Anyways, the new fan setup will definitely less noise than the other one, which included all those same fans with 2 of the 20dB fans being 52.5dB ones.

 

[highwire]

If you are dealing with multiple independent NOISE sources, the noise POWER ( not expressed as sound PRESSURE ) of each source is simply added for total sound power. All of the instantaneous constructive / destructive interference will resolve to the noise patterns being simply the sum of the power patterns of each. So again, a 3 db increase at points equidistant from the two equal noise sources.

If there is PHASE COHERENCE of the sources, directional lobes and moir&eacute; patterns ( standing waves ) may be expected. An example would be two speakers driven with the same audio voltages. In this case, some places might measure twice the sound PRESSURE; that's four times the sound POWER or 6 db.

Since the DECible is based on POWER and is
ten - 10 log (power measured)/(compared some to other power ),
or 10 log P2/P1.

If you are using VOLTAGE or PRESSURE measurements,
it's twenty - 20 log V2/V1.

This is because if VOLTAGE increases, the CURRENT will increase likewise. So you actually have two simultaneous factors increasing, only one of which is stated explicitly.

The factor for sound PRESSURE measurement not implicitly stated is the DISTANCE a molecule moves due to pressure. Again, two simultaneous factors, only one of which is explicitly applied in the formula.

So, to get it back to the POWER terms the the decibel always describes, the results need to be doubled on the log scale from 10 log to 20 log. Thus 20 log ( voltage or pressure ratio )

 

[Mday]

hhehehee

reminds me of lecture heheee