What if we used dB for everything? A small dose of humor / perspective.

[kemmler3D]

Decibels have been in use for measuring the strength of signals since the very early days. I looked it up and apparently they were first employed to measure attenuation in telegraph wires. They're useful because they are a tidy way to compare values across very wide ranges of absolute values, due to being based on logarithms.

However, I think we've all maybe noticed at one time or another that we get fixated on changes in performance measured in decibels that isn't very consequential, (e.g. going from 92 to 102 SINAD) or perhaps we fail to appreciate just how amazing the difference between (say) 65 and 92dB SINAD really is... or how good 65dB SINAD actually is in the first place.

Logarithms are very handy for dealing with the big swings we see in audio, but they're not quite intuitive the way counting on our fingers is.

So it occurred to me to compare some real-world, more tangible things using our trusty equation dB = 20 * log(A/B). To make it a bit more interesting I did some (mostly) to-scale illustrations. I think they came out kind of amusing. You'll notice that once the difference in size gets beyond 50dB or so, the smaller item starts getting hard to see.

I think this also brings home just how amazing our ears' dynamic range is. The ratio of heights of a normal person and the statue of liberty is only 35dB... we can hear that! Once you get past 110dB or so, it's clear that the smaller value is truly meaningless.

PS: I am not sure if, according to convention, I've used the correct formula for all of these comparisons. They're all just computed with the equation above using the values in the graphic.

PPS if people get a kick out of these it's not too hard to make more.

 

[Blumlein 88]

Decibels have been in use for measuring the strength of signals since the very early days. I looked it up and apparently they were first employed to measure attenuation in telegraph wires. They're useful because they are a tidy way to compare values across very wide ranges of absolute values, due to being based on logarithms.

However, I think we've all maybe noticed at one time or another that we get fixated on changes in performance measured in decibels that isn't very consequential, (e.g. going from 92 to 102 SINAD) or perhaps we fail to appreciate just how amazing the difference between (say) 65 and 92dB SINAD really is... or how good 65dB SINAD actually is in the first place.

Logarithms are very handy for dealing with the big swings we see in audio, but they're not quite intuitive the way counting on our fingers is.

So it occurred to me to compare some real-world, more tangible things using our trusty equation dB = 20 * log(A/B). To make it a bit more interesting I did some (mostly) to-scale illustrations. I think they came out kind of amusing. You'll notice that once the difference in size gets beyond 50dB or so, the smaller item starts getting hard to see.

I think this also brings home just how amazing our ears' dynamic range is. The ratio of heights of a normal person and the statue of liberty is only 35dB... we can hear that! Once you get past 110dB or so, it's clear that the smaller value is truly meaningless.

PS: I am not sure if, according to convention, I've used the correct formula for all of these comparisons. They're all just computed with the equation above using the values in the graphic.

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PPS if people get a kick out of these it's not too hard to make more.

You mean Warren Buffet is 20 bits (not $2.50, not those bits) better off than me? Surely in the modern (re digital) world you need to convert all your comparisons to bits of difference?

 

[kemmler3D]

Bonus:

The very biggest "real world" comparison I could come up with is the size of an atom vs. the size of the universe. This was not something I could figure out how to visualize in an interesting way, but someone has done the video so I don't have to. The ratio is about 719 decibels, FWIW.

 

[nerdstrike]

I am very fond of the idea of a state of the art DAC "resolving" individual bacteria in an elephant recording, while intentionally misunderstanding size versus sound amplitude.

 

[sergeauckland]

Years ago we laughingly worked out our annual pay rises in dB...

S.

 

[MCH]

Cool examples.
And this is why we shouldn't use dB and other similar dimensionless units outside of the niches where they might be useful. They might be practical but they are just not intuitive.
I like this paper, the guy explains it well in section 3, even if the context is different.

 

[Deleted member 48726]

Only on ASR..

 

[AnalogSteph]

Good to know I'm not the only nerd doing this. I guess it just happens naturally when you've been dealing with dBs a lot for years.

BTW, a blue whale would add another 13ish dB over the elephant. A few headphone amps manage a dynamic range like that.

 

[kemmler3D]

I guess it just happens naturally when you've been dealing with dBs a lot for years.

I think at some point I started to wonder... what is the absolute difference we're talking about when something is >100dB ? I think a change of 2-20dB is something most people can have an intuitive sense of. I think I have a good grip on that. "A little louder, vs. way louder".

But changes of (say) 40dB or more start to get murky... so putting it in terms of physical objects or absolute amounts is helpful for me to understand just how big a swing we are talking about.

I think differences over 110dB are in the "truly inordinate" range, which is hard for my puny ape brain to grasp intuitively. Or in other words, the size of a bacterium vs. the size of an elephant is really not worth talking about. Nor is $0.01 vs. $9700. But the differences on the SINAD chart look more relevant because the differences in dB are plotted linearly... but the impact of moving from one end to the other of the blue section is nothing compared to moving from the red to blue. Etc. etc.

 

[Ken Tajalli]

I am too fat!
It seems I only need to loose less than 2dB to keep my doctor happy. go figure ...
Sounds easy, but in 30 years, I couldn't do it.

 

[DVDdoug]

Actually, our perception and our brains are naturally proportional or logarithmic... 10 miles is kind-of far to drive for groceries but if you are already driving 100 miles, 110miles is only 10% more. So although "decibels" aren't intuitive, the proportional/logarithmic concepts behind it are.

Or if you are measuring length or distance, a 1-foot error could be terrible if you are building a shelf for your living room. But if you are measuring the distance across town, a 1-foot difference or error is unnoticeable.

Or, if I weight 100 pounds more than you, that's noticeable. But if my elephant weighs 100 pounds more than yours, nobody will notice.

Or back to audio, if you are listening at 1W and you boost it to 2W that's double the power and 3dB louder. But if you are at 100W and you boost it by 1W that's an unnoticeable 0.04dB change.

 

[kemmler3D]

Actually, our perception and our brains are naturally proportional or logarithmic... 10 miles is kind-of far to drive for groceries but if you are already driving 100 miles, 110miles is only 10% more. So although "decibels" aren't intuitive, the proportional/logarithmic concepts behind it are.

Or if you are measuring length or distance, a 1-foot error could be terrible if you are building a shelf for your living room. But if you are measuring the distance across town, a 1-foot difference or error is unnoticeable.

Or, if I weight 100 pounds more than you, that's noticeable. But if my elephant weighs 100 pounds more than yours, nobody will notice.

Or back to audio, if you are listening at 1W and you boost it to 2W that's double the power and 3dB louder. But if you are at 100W and you boost it by 1W that's an unnoticeable 0.04dB change.

Yes, I agree that logarithms in general are intuitive in many important ways. I probably implied they were unintuitive in general, but what I'm really getting at is that large dB values are not intuitive for me. Before doing this exercise, I didn't really have a sense of "how big" even 50dB was in linear terms, let alone >100dB.

Your point that perception of differences seems to be logarithmic is an important one, and one that I totally agree with (because as far as I know it's very well established in the literature. ). This post is more about "So how big is 120dB anyway?" - big!

 

[pseudoid]

our trusty equation dB = 20 * log(A/B)

That word "trust" is self-serving and is not always the guiding-light.
Relative power ratios (e-6/e-3/Watts/e3/e6 (re:R)) are discussed/measured in 10*log(A/B)

 

[mhardy6647]

Not quite the same thing - but long ago, in a past life, I worked for a then small start-up in Cambridge, MA. There was an employee there who was held by other folks there to have a bit of an attitude problem. Her name was applied (actually, as I recall, by someone in my lab) to the unit definition for b!tchiness. The Kim. The problem was that the unit was too large for convenient use in most situations. Most ordinary measurements of bi!chiness in and around the company were typically reported in units of milliKims.

 

[pseudoid]

...in and around the company were typically reported in units of milliKims.

You know someone will ask what the equivalent is for the other sex.
I'll save them the ask by pre-shaming anyone in advance.
I just did!

 

[pseudoid]

These used to be measured in 20lbs brown bags.

 

[pseudoid]

Years ago we laughingly worked out our annual pay rises in dB...

LoL!
Mostly, small deltas need not be measured in dBs. It's already a 'deci-'Bel.
Uze guyz musta been working with mB (milli-Bels[?])
Defeats its raison d'être!

 

[sam_adams]

You mean Warren Buffet is 20 bits (not $2.50, not those bits) better off than me?

Like the rest of us in the 99%, you are lost in the quantization noise of the lower four bits of the economic scale . . .

 

[restorer-john]

Like the rest of us in the 99%, you are lost in the quantization noise of the lower four bits of the economic scale . . .

Or simply disposed of, as redundant data in lossy perceptual encoding algorithms.

 

[pseudoid]

Or simply disposed of, as redundant data in lossy perceptual encoding algorithms.

Everyone knows the cure for that: It will simply need just a bit (or 2) of an EQ to whack it back into doldrums.
EQ is the cure for whatever 'ails' audio; I prefer mine with the coconut scent.