(Mis)Understanding How My SPL Meter Sums Spectral Amplitudes 1

[H.A. Camp]

I have found a number of forum threads that describe the process of summing a 1/3rd octave frequency spectrum into an overall sound pressure level. For example, vanstoja's response in this old thread (and the great follow-up by GregLocock and others) describes the process as simply adding the individual 1/3rd octave bins logarithmically:

dB(SUM)=10*LOG10(Summation of 10^(dB/10)for each frequency or bin)

This make sense to me and I can plug in theoretical numbers (just as vanstoja did) to convince myself... until I try the same thing with real spectral data from my B&K 2250 SPL meter. The device provides 1/3rd octave unweighted (LZeq) spectral band values, and a corresponding broadband LZeq value. However, when I logarithmically sum the spectral bands together, I don't get the broadband LZeq value.

This Cirrus Research article shows the same process, but I seem to fail with spectra from my 2250 SPL meter (sometimes off by 15 dB or more).

I don't know if it's bad form to post actual data, but here's an example:

Freq(Hz) SPL(dB)
12.5	93.86
16	96.45
20	99.53
25	99.52
31.5	99.73
40	97.38
50	97.22
63	93.74
80	90.1
100	86.78
125	85.24
160	81.53
200	75.66
250	79.73
315	77.31
400	73.95
500	72.93
630	70.49
800	69.52
1000	68.03
1250	64.56
1600	65.91
2000	65.63
2500	64.29
3150	56.5
4000	51.08
5000	47.44
6300	43.32
8000	38.83
10000	36.17
12500	31.37
16000	27.42
20000	25.75

The measured LZeq = 100.75, while the calculated LZeq = 106.95.

What (wrong) assumptions am I making about how my SPL meter works? What am I missing to compute the same broadband LZeq that the 2250 is producing?

Thank you,
- H.A. Camp

 

[Strong]

I think the equation from vanstoja is wrong. You would divide the dB-SPL value by 20 and not 10 to convert to Pascals (pressure squared) and then sum and then convert total Pa to dB-SPL. No time to try it.

Walt

 

[GregLocock]

Just looking at the 4 biggest bins at 99 dB, you'd expect 105 dB, just from them. So your LZeq is not just an RMS sum, and if you look in the documentation for Leq you will find why.






Cheers

Greg Locock


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[H.A. Camp]

Thank you, Greg and Walt, for your responses!

Hmm, I must be misunderstanding the fundamentals. My understanding of the equivalent continuous sound level, Leq (after re-reading some definitions) is that it's the average sound pressure level of the fluctuating noise being measured. In fact, the first link listed states that "...the Leq is in fact the RMS sound level with the measure­ment duration used as the averaging time."

So, Greg's comment leads me to believe that if LZeq is not just the RMS sum of the 1/3rd octave bins, then perhaps I'm failing to weight the octave bins appropriately? I guess I envisioned that, if Leq is equivalent to the total energy of the fluctuating sound over the measurement time, then the 1/3rd octave bins were similar Leq averages of the total energy, but only over their individual frequency ranges. But since the size of the frequency bins is not uniform, then perhaps I need to weight them somehow when I add them logarithmically?

...Or am I way off in left field?

 

[GregLocock]

I suspect the spectrum you have shown is not Leq, otherwise I can't see why the answer is not 106.95.

Cheers

Greg Locock


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[H.A. Camp]

That is not something I had considered -- I will go back to the original source and verify that the data is indeed what it is supposed to be.

I appreciate the consideration and effort to look at the data!

 

[Vibac]

One thing to be aware of: The meter's broadband value may come from a (broadband) RMS detector, and not the summation of the 1/3-oct bands. Sometimes the RMS detector operates on a slightly broader freq.
range, which would lead to a higher level.

 

[BrianE22]

Seems like a 4-6 db/(frequency bin) is a fairly large slope. I would think that would make the 1/3 octave readings pretty sensitive to the energy inside the bin limits and the energy leaking out past the bin limits for each bin measurement.

 

[GregLocock]

Yes that was a big deal to the purists when we were switching from analog 1/3 octave to digital. The shoulder of the analog filters meant that a 0 dB signal at the center frequency of the next band would read -20 dB in the band of interest. During the transition digital instruments often had the alternative of replicating the analog filter shape, or just giving the digital filter. I don't know if that is still the case, it is two decades since I have touched an SLM.

Here's the gory details, P9 is of interest

https://law.resource.org/pub/us/cfr/ibr/002/ansi.s1.11.2004.pdf

Cheers

Greg Locock


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