Definition of decibel

[Ghostbird]

§ Success Criterion 1.4.7 Low or No Background Audio has a part that says:

20 dB

The background sounds are at least 20 decibels lower than the foreground speech content, with the exception of occasional > sounds that last for only one or two seconds.

NOTE

Per the definition of "decibel," background sound that meets this requirement will be approximately four times quieter than the foreground speech content.

This confused me. As far as I know, the Bel is a base 10 logarithmic scale, and 20 decibel would therefore equal 2 bel or a factor of 10² or one-hundred. Which is much more in line with my understanding of a 20 decibel sound difference.

Hint: Think of the difference between a band with five musicians (all equally loud), where one plays a completely different song than the other four. Versus the same situation with a orchestra of 101 musicians where still one plays the wrong song. In the second case, the one musician that's off, can be considered low background noise. In the first case it's a terrible nuisance.

Is this an error in the NOTE section of the document?

[patrickhlauke]

Indeed, well spotted. 20dB indeed shakes out to something being 100 times louder/quieter, which now makes me wonder if it's the 20dB or the note that are wrong as well... (i mean the 20dB is normative, so even if that was not the correct/intended value, then it's now far too late and far too complicated to retrospectively change in errata, so only the note that explains it would be more flexible/open to change)

[JediLin]

I think that the signal-to-noise ratio here is based on Sound Pressure Level difference. SPL (dB) is calculated by 20×log(P/P0) where P0 is the reference pressure (by definition 20 micro pascals). So the 20 dB SNR means 20×log(P1/P0) - 20×log(P2/P0) = 20, therefore P1 should be 10 times P2. Not 4 times anyway.

Extra note: I would like to recommend the "Back to Basics: Speech Audiometry" article. Killion and colleagues (2004) suggest that a person with severe SNR loss would require more than 15 decibel signal-to-noise ratio to obtain 50% speech understanding. (QuickSIN test uses 25 dB SNR at max.)

[Ghostbird]

Ah, relative SPL difference would lead to a factor 10 loudness indeed.

[JAWS-test]

"four times" is from the linked article in the understanding: https://ds.gpii.net/content/about-decibels-db

Perception of Loudness (20dB = 4x). Interestingly, our perception of loudness is not the same as sound pressure level. Although the actual formulae is somewhat complex, as a rough rule of thumb, an increase of 10db SPL is perceived to be approximately twice as loud. Thus a 20 Db gain would seem to be about 4 times as loud. And a 40 Db gain would seem to be about 16 times as loud.

[Ghostbird]

Thanks for the answers. I think the 20dB is correct, based on my personal "gut feeling", and @JediLin's citation. However, it's interesting that the note may be right when it comes to perception of loudness. As this is a psychoacoustic matter, it's probably based on research on a large amount of people. I've worked in audio engineering, so it's possible that my personal perception has been calibrated away from the "default" towards the absolute decibel factor used by audio equipment.

Maybe the note could be updated to read:

Per the definition of "decibel," background sound that meets this requirement will be perceived approximately four times quieter than the foreground speech content.

[Ghostbird]

No wait, the part that states per the definition of "decibel" still makes no sense. Because it's not the definition of decibel that leads to this conclusion.

It should be something like:

According to psychoacoustics, a background sound that meets this requirement will be perceived approximately four times quieter than the foreground speech content.

[patrickhlauke]

so the note is just badly handwaving things / not clarifying what it actually means. I'd suggest proposing a change to the definition's note in a PR

[GreggVan]

I suggest we use DBA going forward to avoid confusion

[JediLin]

I think dB A is primary used to measure an environment. For example, to quantify noise exposure.
dB SPL is used to measure device output, dB HL to measure human hearing threshold, and dB SL to indicate perceived sound pressure level of particular ear.

For SNR, just dB.