Combining noises

[EcoMan]

An old textbook of mine says to use the power, not pressure, formula when combining noises but later that ten identical sound sources have an SPL 10 dB louder than just one source. Shouldn't it read PWL (power level of the noise), not SPL (sound pressure level)?

 

[tomirvine]

Yes, ten sources with the same Sound pressure level (SPL) will and have a combined SPL that is 10 dB greater than just one source.

Here is a Matlab script that can be used to demonstrate the calculation:

disp(' ');
disp(' add_dB.m ver 1.0 February 9, 2010');
disp(' by Tom Irvine ');
%
disp(' ');
disp(' This script assumes that the dB values represent ');
disp(' a sound pressure level or a power spectral density ');
%
clear a;
clear sum;
clear length;
clear C;
%
disp(' ');
disp(' Enter vector name of dB values ');
a=input(' ');
n=length(a);
%
C=10;
sum=0;
for(i=1:n)
sum=sum+10^(a(i)/C);
end
sum=C*log10(sum);
%
out1=sprintf('\n overall level = %8.4g dB \n',sum);
disp(out1);

Tom Irvine

http://www.vibrationdata.com

 

[SomptingGuy]

But "identical" though? Coherent sources in phase. Surely not??

- Steve

 

[MikeyP]

EcoMan, when you say "noise" do you mean "random noise"? What do you mean by "identical"?

10 identical sources could produce an SPL anywhere between 20 dB greater and -infinty dB less, depending on the type of noise and where you are in relation to the sources!

M

--
Dr Michael F Platten

 

[SomptingGuy]

I had a complaint once from an "expert" customer. The combination of two near-identical tailpipe noises was 6dB higher than each in isolation. He insisted it should be 3dB. I had to teach him the basics without being condescending. All very embarrassing.

- Steve

 

[rob768]

I'm certainly not an expert on noise, but in my textbook two identical sources combined generate 3 db extra. Where's my mistake?

 

[GregLocock]

Phase

Cheers

Greg Locock


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[rob768]

So, two sources of identical frequency and in phase add to 6 dB extra? and in counter-phase they cancel each other out? (at least that's what my woofers do at home). Does this apply only to sources with identical frequencies? for random noise, 2x source = 3 dB extra?

 

[SomptingGuy]

Yes. If the sources have the same frequency and are coherent, you need phase information to predict the combined level.

For random noise or for sources with different frequencies, the 3dB rule of thumb applies.

- Steve

 

[GregLocock]

...and when it is more complicated than that... then it is more complicated than that.

Instantaneously x1+j*y1+x2+j*y2 = xresult+j*yresult always applies. If people are trying to confuse you about that then walk away. You can derive all results for a linear system from that, tho broadband results need a bit of work.





Cheers

Greg Locock


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[MikeyP]

Forget about acoustics for a minute and just think of 2 signals.

If I have 2 uncorrelated random signals with the same rms amplitude (say 1 to make things nice and easy) and I add the two signals together, what is the rms amplitude of the combined signals?

The answer is sqrt(2). Some of the random bits of one signal happen to add together and some happen to cancel out, but on average the increase is a factor of 1.414.

Now what happens if I add 2 identical signals (say add signal 1 to itself)? Obviously the signal is doubled so the rms is doubled

If those signals were sound pressures, then adding the 2 uncorrelated signals would mean an increase of 3dB in sound pressure level (add 20 log 1.414), but adding the 2 identical signals would mean an increase of 6dB (add 20 log 2).

M


--
Dr Michael F Platten

 

[Rob45]

That is a nice simple explanation, Dr. P!

 

[hydtools]

Here is information for combining sound power levels and combining sound pressure levels:

http://www.engineeringtoolbox.com/adding-decibel-d_63.html

Ted

 

[SomptingGuy]

... and the misunderstanding continues. Nowhere in that link did the author mention coherent signals, which are very common in some fields.

- Steve

 

[hydtools]

I believe the op is asking about combining incoherent sounds. Not tonal coherent sounds. I believe the question about combining 10 identical sounds refers to combining 10 incoherent sound levels of equal levels. The link would be correct for that.

Your are correct that coherent sounds are handled differently when combining levels.

Ted

 

[EcoMan]

Thank you all. The book doesn't talk about coherence, frequency, or phase--just identical machines in a theoretically free field. hydtools, that's a good link. It shows that SPLs, not ony PWLs, can be combined and gives the formula (but not one for adding unequal SPLs).

 

[MikeyP]

"identical machines in a theoretically free field"

For example geared electric motors running at the same speed? Or maybe a number of turbines sitting next to each other in a power station? Or perhaps a pair of loudspeakers connected to a hifi system?

M

--
Dr Michael F Platten

 

[spshone]

10dB comes form 10 log (10) --- base 10 log

3+3 = 6dB
3+3+3+3 = 9dB etc

i.e. it assumes 10 incoherent sources all with the same LW and directivity.

If you double the pressure on a single output then add 6dB.
If you double the sound power on a single output then add 3dB.

If you add sources together IN A FREE-FIELD, consider their realtive phases. Coherent - include phase, incoherent - don't worry.

Guess what, you need a better textbook consider Beranek or Fahy.

 

[Strong]

Sound pressure levels from multiple sources are summed on a Power (10LOG base-10) basis. Two equal amplitude sources produce 3 dB increase over one source. 10 equal amplitude sources produce 10 dB higher than one. This works for most time-averaged sounds. Two tones with same frequency that are in-phase would add pressures on 20LOG base-10 basis; which is very rare in practice. With two equal tones the pressure is 2x or 6 dB higher. I have been doing this since the Slide Rule days, and then the HP scientific calulator days, and now the MW Excel days. I use Beranek, Harris, and several other books.

Walt

 

[GregLocock]

"With two equal tones the pressure is 2x or 6 dB higher."
No, not necessarily. Or even, not very often.

Cheers

Greg Locock


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