# Fan Noise Comparison

Setup 1:
3 x 30dBA Fans
2 x 32dBA Fans

Setup 2:
5 x 24dBA Fans
2 x 27dBA Fans

Which setup is louder and by how much?
###### Who is Participating?

Commented:
First, I must disagree with tmj883 on the "wave cancellation and wave convergence" issue.  The noise generated by fans is generally of the broad spectrum type (i.e. similar to white noise) and such noise is, by definition NOT subject to cancellation or other wave effects.

I agree with the statement that the dB (decibel) scale is NOT linear.  In fact, it is a LOGARITHMIC scale based on log10.  So a 3dB increase represents a 2X increase in perceived volume.  For example 73 dB sounds twice as loud as 70dB to the human ear.  A 20 dB increase represents a sound intensity that is 10X greater.

With that in mind, let's look at your question:

1) 3 x 30dB does NOT produce 90dB of sound level.  It doesn't work that way, if it did, we'd all be deaf!  Sound specified in dB (or dBA - basically the same) cannot be added like this.  Remember you high-school algebra class and logarithms.  What happens when you ADD LOGs?  You are MULTIPLYING the base numbers.  So by addding 30 + 30 + 30 dB we are attempting to multiply sound pressure and there is no multiplication involved here.

We need to "un-dB" these numbers, add them together, and then "re-dB" them to get the resultant sound level.

The formula for Sound Pressure Level (SPL) is:

SPL = 20 log10(P)  ; where P is sound POWER

If we want the P, given an SPL in dBA, we use:

P = 10^(SPL/20)

In this example, SPL = 30 so P = 10^(30/20) = 31.62
For the other SPLs we have:

SPL     P
32 -> 39.81
24 -> 15.85
27 -> 22.39
30 -> 31.62

OK, now to calculate:

Example 1:

3 x 30dBA Fans
2 x 32dBA Fans

(3 x 31.62) + (2 x 39.81) = 174.48
That, expressed in dBA is 20log10(174.48) = 44.83 dB

Example 2:

5 x 24dBA Fans
2 x 27dBA Fans

(5 x 15.85) + (2 x 22.39) = 124.03
that, expressed in dBA is 20log10(124.03) = 41.87 dB

So in your scenario, example 1 is going to be TWICE as loud as example 2.
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Commented:
Setup 1 has the greatest intensity while Setup 2 has the greater volume...go figure? T
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Commented:
Seriously, it cannot be predicted due to the effects of wave cancellation and wave convergence. This is even further complicated if the different sound sources have varied frequencies. Some sound wave will cancel each other and produce no sound...others will converge and be amplified instead of canceled. With varied frequencies, cancellation and convergence can produce periodic(occuring at a new frequency) fluctuations in amplitude. Hope this helps...T
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Commented:
Practical approach:
Sound Level Meter
digital...\$us89
analog....\$us59
www.action-electronics.com
T
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Commented:
The problem is that decibels are not a neat linear scale.  The 30db fan isn't 20% louder than the 24db fan.   I'm sure someone on this forum can do the math involved to give an exact number value as to which setup is louder, but I forget the formula.
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Commented:
BTW, one word of caution.  The dBA specification is a RELATIVE term where the P in the calculation is actually a ratio of the sound power vs. a reference power.  Be SURE that all the fan SPL dBA numbers are expressed using the SAME REFERENCE POWER.  If all fans are from the same vendor this should not be an issue but double check the specs.  Some companies play "specsmanship" games with stuff like this....
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Author Commented:
example 1 is using high-preformance ThermalTake fans
example 2 is using low speed Panaflo fans

would this value be twice as much?
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Commented:
>>would this value be twice as much?

???

What part of the analysis don't you understand?

I thought I was clear.
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Commented:
It is obvious that jhance does not know the definition of "white noise" but I'll give him a hint: It was defined in my previous statement. ALL sound is subject to cancellation and convergenge. White noise is used to describe the effects of cancellation, it is not some mystical things that is not subject to the laws of physics. If this problem where as simple as he would like you to believe, Dr. Bose would be looking for a job. First of all, his formula barely applies if the column of air is static, but it is not...it is a moving air column thus dynamic, complicating calculations even more so due to the doppler effect and turbulent vs laminar flow issues. For someone with little physics background and an extermely limited scope of knowledge, his answer may be appealing, but it is greatly oversimplified. T
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Commented:
You're overcomplicating this.

We're not talking about room acoustics, we're talking about fan noise.  If we were interested in preparing a 3D plot of the fan noise at any point in space then things like you've mentioned might be needed.  But you'd be looking at a serious engineering analysis and need a 3D FEM for the box, the fans, the environment.  Sheesh!

I'll stand by my analysis as correct and more importantly APPROPRIATE for this problem.
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Commented:
BTW, you are incorrect about your noise and cancellation assertion.  Noise is a random process and as I said, random processes do not cancel.  Any 2nd year engineering student knows this.  If it were not so, you can reduce or eliminate noise in a system by adding in "inverse" noise and letting them cancel each other out.  As is all to obvious, it doesn't happen that way and noise, BY DEFINITION, is always ADDITIVE.

If you can demonstrate otherwise, you'll be a rich person and darned famous as well.

Of course, fan noise is NOT TRULY random and there are dominant frequencies in it related to the rotational speed of the shaft and the number of blades, etc.  But in the overall GROSS analysis of this problem, it's my opinion that it is reasonable to ignore those effects and treat the fan noise as random.

To do otherwise simply complicates this problem to the point where it cannot be solved without a very difficult analysis and the answer reached will not differ significantly from the simple (i.e. FIRST ORDER) analysis.  Does anyone really care if the first example is 44.83dB or 44.85dB??  Of course not, especially since the DIFFERENCE between the two systems being analyzed is MUCH MUCH greater than such a difference.
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Commented:
There are many companies making fortunes producing "white noise" generators that do exactly what you are saying "can't be done". This technology is used extensively in the aircraft industry to controll noise from jet engines(a large fan), in military application, in heavy industry, in large business offices, in electronics, etc.. You should get your facts straight, as your "definitions" are off the wall. T
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Commented:
You're talking out of ignorance.  Noise cancellation is a control system problem and cannot be done IN GENERAL.  In fact, it can't be done period.  What is done in noise abatement is to analyze (in real time) a noise problem, identify the most objectionable parts of it and cancel out those portions in a SPECIFIC CLOSED area.  A generalized broadband noise cancellation is impossible.

In your example, aircraft noise is NOT white noise and in the noise abatement inside an aircraft cabin the LOW FREQ noise if reduced by cancellation.  This is the same principle used in noise cancelling headphones (at a much less sophisticated level) but two things are important:

1) The spectrum of the noise cancellation is limited.
2) The noise cancellation area (actually volume, as in 3D volume) is limited.

This also involves human hearing properties (i.e. psycoacoustics) and depends on the fact that humans find certain frequencies and types of noise more objectionable than others.
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Commented:
It can't be done...now who's talking out of ignorance and proving your limited scope...it has been done, it is done. The controll of aircraft engine noise is done on the deck(outside) for both commercial and military aircraft to protect the ground crew form hearing damage and to facilitate communication. Your problem is that you simply can't tolerate someone who disagrees with you...that's an ego problem...
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Commented:
jhance's "cannot be done IN GENERAL" is clearly a reference to tmj883's claim that aircraft noise damping systems are generic white noise generators.  Instead, attach a microphone to a computer to analyze the sound and you can generate the exact counter-frequency on a speaker.  That's how those things work.  They are not random white noise generators.  That would just make EXTRA volume on top of the jet sound.  jhance may not have bothered to detail his response but tmj883 is operating on incomplete information.

True random white noise drowns out other sounds, but cancels nothing.  A sound source that's random would cancel nothing because it would almost never have the same peak/valley pattern and THAT is what does the cancellation.

Now, everyone shut up about this esoteria - I can't unsubscribe from this closed question and am sick of getting spammed!
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Author Commented:
jhance:
"Be SURE that all the fan SPL dBA numbers
are expressed using the SAME REFERENCE POWER.  If all fans are from the same vendor this should not
be an issue but double check the specs."

I just wondered if you knew if your statment held true for these specific fans. If you don't know, that's fine. I'm just clarifying.
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