## Two identical sources (50dB +50dB = 53dB or 56dB)???

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### Two identical sources (50dB +50dB = 53dB or 56dB)???

Hi

Doubling the acoustic pressure results in a 6dB increase. If you measure SOURCE 1 with a sound level meter, you get say 54dB SPL. Then, if you measure 2 identical Sources (both like SOURCE1) you get 60dB SPL. Both sources located at the same place and with a fixed measuring position.

Then why in the acoustic world (noise control, etc) when we add sources, when we add dBs, we use 54dB + 54dB = 57dB (3dB increase rather than 6dB). DIRECT SOUND(70dB) + FIRST THEORETICAL REFLECTION(70dB) = 73dB ???
MEASURING VERY CLOSE TO A RIGID WALL

I understand that this comes from having 10log (intensity) rather than 20log (pressure). But in real life our ears respond to pressure changes (hence SPLs), am I right?

Sound level metres measure SPL, loudspeakers come with SPL specs.. Then why on earth when we add two identical sources we use +3dB instead of +6dB (which would be the pressure summation).

Any opinions?

Thanks

Sergio
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

sergioTOOL

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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

I'll go deeper into your question afterwards, with graphs I made (lost one).

What you're talking about is the typical confusion between environmental acousticians calculating energetically, and electro-acousticians thinking in sinuses and phase relationships.
Both are right, but approach the same question from another angle.

Hence doubling sound can as well increase pressure with 3 dB as with 6 dB, and to expand it even further, between -infinite dB and + 6 dB.

divinely-inspired
Eric.Desart
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

sergioTool,

To decipher this problem, you need to know two things about your sources:

a. Are they correlated or uncorrelated? f.e. two sine waves with identical phase shifts would be considered correlated sources. Two cellists playing together are uncorrelated sources. These two types of sources sum differently. For correlated sources you can translate to linear quantities (such as acoustic pressures), then add together and convert to a log quantity (such as SPL) - for two identical pressures this would yield a +6dB increase.
Uncorrelated sources add statistically, so two pressures would result in a 10*log(2) increase, which is comparable to +3dB.

b. What quantity are you calculating? Pressure, intensity and power are represented on different scales; so two correlated powers (acoustic or electric) would add up to +3dB and two correlated pressures (or voltages) add up to +6dB. This can be easily proven mathematically, as power is essentially the square of pressure/voltage with respect to some impedance. Intensity is a little trickier, as essentially for non-plane waves it is a vector quantity, so you can expect all sorts of scenarios.

A loudspeaker near a rigid wall is considered a source radiating into half-space, so you have doubling of its power (i.e. it can now do more 'work'), therefore a +3dB increase. Analysing this situation as a discrete reflection sum is just the wrong way to go about it.

The important thing to remember here, is that a 'decibel' is just a 'prefix' denoting we are on some sort of log scale and does not imply anything about the discussed metric itself. So if somebody says that we have +3dB, you should always ask yourself "+3dB in what?" the same way that if someone would say we have a '100 more units' you would ask yourself 'what units are we talking about?'.

Hope this helps,

If you want a more thorough explanation, I strongly suggest looking at Chapters 1&2 of Jamie Angus's book "Acoustics and Psychoacoustics".

Cheers,
Jon.
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Since Jon toke over I'm not needed anymore I assume.

I will add more explanation later in the ACOUSTIC FAQ. The main thing here is the phase relationship.
Some things can be read here also: viewtopic.php?f=6&t=3300.

Just a temporary idea: (I don't have an English version yet, for now the Dutch text will be probably more annoying than helpful)
This is an animation: hence a bit patience, the animation stops temporarily at strategic points to read these texts or have a better look).

divinely-inspired
Eric.Desart
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Great animation, Eric!
By all means feel free to take over; your explanations are far more thorough than mine...
Didn't mean to step on your toes earlier, so sorry if I did.

Cheers,

Jon.
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Coherent sound is the acoustical equivalent of a laser, Sergio.

Walking around outside with a SLM you won't measure much coherent sound.
So most of the time it's safe to say two sources of identical level add 3 dB.

when measuring speakers you sometimes use the grouind plane measurement method (to virtually make the measurement environment bigger and eliminate reflections); you put the speaker on a rigid flat floor and the mic also.
This gives a 3 dB 'boost' for the speaker (as Jon explained) and a 3 dB 'boost' for the mic. (Boost in the sense of 2 pi radial radiation).

With speakers you have to take in account that when you add a speaker parallel to an amplifier, you double the speaker surface, which gives you a 3 dB boost, and you decrease the impedance with a factor 2, giving you another 3 dB boost. (Boost in the sense of more radiating surface and less resistance so the current flows more easely)
This is what some speaker guys confuses.
Last edited by bert stoltenborg on Fri Aug 27, 2010 4:04 pm, edited 2 times in total.
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Jon,

Eric went to bed extremely late, so you can relax until noon when he'll get at your heels again.

If you view life with the knowledge that there are no problems, only opportunities, you are a marketing manager.......this is my personal philosophy
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Unless its a tube amp in which case you should be using a different output transformer tap for the lower impedance pair-of-speakers & amp power is unchanged. Correct?

But what about the case of adding the second speaker in series versus parallel in which case impedance is cut in half? Even with a solid state amp you got twice the speaker working half as hard - no change. Correct?
SRF
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

exactemento!
If you view life with the knowledge that there are no problems, only opportunities, you are a marketing manager.......this is my personal philosophy
bert stoltenborg

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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Shit, my GF tells me it should be: EXACTEMENTE!
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

If a man speaks out loud while standing in a forest - and there is no woman around to hear him - is he still wrong?
SRF
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

I am male but even I didn't hear that question from Scott.
seb

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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

bert stoltenborg wrote:when measuring speakers you sometimes use the grouind plane measurement method (to virtually make the measurement environment bigger and eliminate reflections); you put the speaker on a rigid flat floor and the mic also.
This gives a 3 dB boost for the speaker (as Jon explained) and a 3 dB boost for the mic.

That's not a matter of 3 dB boost for this and 3 dB boost for that totaling 6 dB.
That's just a matter of minimizing the pathlength difference between direct and reflected wave causing the direct and reflected wave to remain in phase (except for the highs where this always, even if minor, pathlength difference becomes gradually more significant versus wavelength), hence a phase shift of 0 (or very little) degrees resulting in 6 dB level increase (as per my animation shown above).

divinely-inspired
Eric.Desart
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Scott R. Foster wrote:If a man speaks out loud while standing in a forest - and there is no woman around to hear him - is he still wrong?

I think the real question is, if a man is being yelled at by two sisters, is it 3dB or 6dB louder than if it's just one sister.
What if the sisters are identical twins?
Bob

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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Bob wrote:
Scott R. Foster wrote:If a man speaks out loud while standing in a forest - and there is no woman around to hear him - is he still wrong?

I think the real question is, if a man is being yelled at by two sisters, is it 3dB or 6dB louder than if it's just one sister.
What if the sisters are identical twins?

..and I thought the twin sister thing was yet another north american male obsession, didn't know u guys were in it for pure scientific phasing.
gee, sorry.
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Ido

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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Thanks a lot!
sergioTOOL

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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

Bob wrote:
Scott R. Foster wrote:If a man speaks out loud while standing in a forest - and there is no woman around to hear him - is he still wrong?

I think the real question is, if a man is being yelled at by two sisters, is it 3dB or 6dB louder than if it's just one sister.
What if the sisters are identical twins?

Two sisters is 9dB, twin sisters is 12dB, ask my son his sisters are yelling all the time. The 3 dB boost is from sisters trying to be louder then the other, twins just try 3dB harder on top of normal sisters.

Dan Nelson
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### Re: Two identical sources (50dB +50dB = 53dB or 56dB)???

drnelson wrote:
Bob wrote:
Scott R. Foster wrote:If a man speaks out loud while standing in a forest - and there is no woman around to hear him - is he still wrong?

I think the real question is, if a man is being yelled at by two sisters, is it 3dB or 6dB louder than if it's just one sister.
What if the sisters are identical twins?

Two sisters is 9dB, twin sisters is 12dB, ask my son his sisters are yelling all the time. The 3 dB boost is from sisters trying to be louder then the other, twins just try 3dB harder on top of normal sisters.

Dan Nelson

more than 2 children in one space should have acoustic absorption, regardless of ratios.
go Dan !!
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Ido

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