How to best explain dB to non-audio experts?

[Chrispy]

Since it's still pretty common to explain that 50% of a volume dial is only so meaningful, especially when comparing to a dB based volume scale....but I think of how many just didn't pay that much attention to math to understand linear vs logarithmic.....

 

[HammerSandwich]

Lets say you have a DAC where the jitter is at -130dB or lower. How you would explain to somebody who is not familiar with audio...?

Remember that regular people simply don't grok BIG numbers. The most important thing is to keep it dead simple. And you'll want a visual aid.

1. Go to the convenience store.
2. Buy Twinkies.
3. Read label to note that a single Twinkie is ~40g. Or trust Wikipedia, as I just did.
4. Remember the visual aid? Refer to Ghostbusters:
   
5. Give your friend a Twinkie.
6. Explain: "Remember that decibels are ratios. You'd need almost 7000 of these Twinkies to make 600 pounds. That means this one's at about -80dB versus Egon's. To get a ratio that's 130dB bigger than the Twinkie you're now holding, you'd need 465 Ghostbuster Twinkies, each the size of a 32-passenger bus. Placed bumper-to-bumper, those Twinkies would be more than 3 miles long."
7. 

For reference:
600lbs = 272kg
40g / 272000g = 1 / 6800
20*log(1/6800) = -76.7dB
10^(130db/20) = 3.2M = 6800 * 465
Of course, 600lbs is WAY too low for a 35' Twinkie. If they'd used an accurate number in the movie, no one would have believed it! In rough terms, Egon's is ~100x longer, so a volume/mass ratio of a million to one. That's a 40-ton snack.

Final overthinking this: by volume, 3.2M:1 is ~150x in length. IOW, the 35' bus is reasonably close.

 

[pjug]

Thing is you cannot use examples where our perception is linear, like twinkies. With light and sound we perceive something like log scale. So 130dB is [shout out to @Thomas savage ] going from a dark bar out into bright sunlight, before your pupils adjust. So blinding or deafening but we have incredible range with sound and light.

 

[Koeitje]

Thing is you cannot use examples where our perception is linear, like twinkies. With light and sound we perceive something like log scale. So 130dB is [shout out to @Thomas savage ] going from a dark bar out into bright sunlight, before your pupils adjust. So blinding or deafening but we have incredible range with sound and light.

I think you can focus on example of things happening at the same time.

 

[JSmith]

That's a 40-ton snack.

That's one big Twinkie man... Stay Puft is made of marshmallow.





JSmith

 

[pjug]

I think you can focus on example of things happening at the same time.

I did like the twinkie one. Haven't had one of those in a while, let alone enough to count in dBs.

 

[sergeauckland]

Where I worked once, we worked out our annual pay rises in dB....

S.

 

[MrPeabody]

It is difficult to say whether it is useful to bring exponential growth and decay into an explanation of decibels. To explain decibels adequately, it is necessary to discuss logarithms and logarithmic scaling. The only good way to make sense of logarithms is by first discussing the exponential function, since the logarithm function only becomes intuitive when understood as the inverse of the exponential function. The question thus becomes whether, in order to adequately explain the exponential function (not y = e^x, but rather y = 2^x or y = 10^x), it is desirable to discuss exponential growth and decay. My sense is that in order to demonstrate the behavior of y = 10^x (or y = 2^x), where the independent variable 'x' is the exponent to which some constant is raised, it is probably not necessary to discuss exponential growth and decay. Nevertheless, for anyone who deems this useful and is looking for some good examples:

Exponential growth:
1. Rabbits, mice and cats increasing in population. Most everyone is familiar with how unchecked population growth leads to a doubling in population at fixed time intervals, i.e., the population doubles every three months, or every six weeks, etc.
2. Compound interest. Most everyone has an intuitive understanding of the benefit of compounded interest over time, when the rate is fixed.
3. Many people are familiar with a story about how some king was duped by a clever man who asked for his reward (for something he had done for the king) to be only a single kernel of wheat (or rice) for the first square on a chess board, then two grains the next day for the next square, then four grains the 3rd day, then eight grains the 4th day, etc., doubling the number of grains each day and continuing through 64 days. This is an excellent way to illustrate exponential growth. Note, though, when this example is used, you'll likely not be able to keep from explaining the shortcut for calculating the sum (2^65 -1). This shortcut for calculating the sum isn't an essential aspect of exponential growth, and if you discuss it, it will obfuscate or diminish the essential facts about exponential growth.
4. Then they tell two friends, then they tell two friends, etc.

Exponential decay:
1. Zeno's paradox (the one everyone knows, among the several that were preserved by Plato). If individual steps are taken at constant time intervals, and each step is only half as great as the preceding steps, then distance as a function of time will exhibit exponential decay.
2. Half-life of anything that decays exponentially, but this is best understand from the standpoint of elimination of a drug from the body, i.e., at fixed time increments, the amount remaining in the blood is half the amount that remained at the end of the prior time increment. This is easy to comprehend and is an excellent way to illustrate exponential decay.

Exponential growth:

 

[Cbdb2]

That's true for a dbP, but not for a dbV. Most of the specs that Amir measures here are voltage, where every 10x change is 20 dB.
For example, if someone says SINAD is 100 dB, that's 10^5 or 100,000:1, or 0.001%.
It's not 10^10, or 0.00000001%.

This is another common confusion about dB: when to use dbV vs. dbP.

Thats wrong. A 10db increase in voltage IS 10x the voltage but 100x (20db) the power. This will confuse people.
I'm just talking about dbs, a db is a db. If you increase voltage by 10db its 10x the voltage. If you increase power by 10db its 10x the power. If you increase your bank account 10db your 10x as rich. I was trying to keep it simple like the OP suggested, and introducing dbm dub dbv dbspl etc. would be the next step.

 

[Wes]

Is that because natural logs are more analog like?

no, it's because they are organic

we just need to harvest them sustainably in worker owned communes to get the fully exponential groove from the grove

 

[sergeauckland]

Thats wrong. A 10db increase in voltage IS 10x the voltage but 100x (20db) the power. This will confuse people.
I'm just talking about dbs, a db is a db. If you increase voltage by 10db its 10x the voltage. If you increase power by 10db its 10x the power. If you increase your bank account 10db your 10x as rich. I was trying to keep it simple like the OP suggested, and introducing dbm dub dbv dbspl etc. would be the next step.

On my meters, a 10dB increase in voltage is 3.16x, which is 10x the power. 20dB is 10x voltage and 100x the power.
S

 

[Wes]

find a copy of the film Powers of Ten, and get them to watch it

- I used to force feed that film to undergraduates

 

[dc655321]

find a copy of the film Powers of Ten, and get them to watch it

- I used to force feed that film to undergraduates

That's cruel and unusual.
Was it effective?

 

[danadam]

find a copy of the film Powers of Ten, and get them to watch it

There's also an interactive tool: http://sciencenetlinks.com/tools/scale-universe-2/

 

[tmtomh]

Lets say you have a DAC where the jitter is at -130dB or lower. How you would explain to somebody who is not familiar with audio how good that is? I feel this is something that could be communicated in a better way.

I don't know why folks are getting so hung up on how to teach someone about logarithmic scales, for the audience @Koeitje is speaking to and the purpose of the question. The nature of the scale is not really important IMHO. What's important is that -130dB is really good because it means the jitter - which is a type of inaccuracy or distortion in the sound playback - is at such a low level that no human can hear it. Presumably Koeitje might want to note that there are many, many DACs with very good jitter performance, but some of them have jitter at levels that, while virtually impossible to hear, could theoretically be heard by some people in some unusual conditions. By contrast, this DAC's -130dB performance is simply inaudible, period.

The fact that -130dB is 15dB lower than the human audibility threshold on a logarithmic rather than linear scale seems to be me to be of little or no importance for the purposes of the OP's question about explaining -130dB jitter to someone who knows nothing about audio.

 

[MRC01]

Thats wrong. A 10db increase in voltage IS 10x the voltage but 100x (20db) the power. This will confuse people. ... I'm just talking about dbs, a db is a db. ...

That is incorrect. A dB for measuring voltage is different from a dB for measuring power. This is often confused.

On my meters, a 10dB increase in voltage is 3.16x, which is 10x the power. 20dB is 10x voltage and 100x the power. ...

Correct.

If there were only 1 dB unit as @Cbdb2 suggests, then a 6 dB increase in voltage would create a 12 dB increase in power. Since doubling the voltage doubles the current, which quadruples the power since P = IV. Somebody (by convention?) decided it would be simpler if a 6 dB increase in voltage caused a 6 dB increase in power. But for this to be true, a "voltage" dB would have to be smaller than a "power" dB. So by convention, that is what we have.
By definition:
for voltage: dbV = 20*log(R)
for power: dbP = 10*log(R)

 

[dc655321]

By definition:
for voltage: dbV = 20*log(R)
for power: dbP = 10*log(R)

I know you understand this, but dbV is not a thing (but dBV is!). Neither is "dbP".
The scaling factor simply changes from 10 to 20 because R = (V / Vref)^2 for voltages.

 

[DonH56]

Capital B for "Bel", as in Alexander Graham... Little d for "deci" as in one-tenth Bel. For most things a Bel is just too durn big.

dBV reference to 1 V, dBW reference to 1 W. And roughly a bazillion others...

 

[j^j=e^-pi/2]

math..... uggggg

 

[danadam]

Somebody (by convention?) decided

Looks like it is "power quantity" vs "root-power quantity" and according to wikipedia it is defined in ISO 80000-1: https://en.wikipedia.org/wiki/Power,_root-power,_and_field_quantities