• WANTED: Happy members who like to discuss audio and other topics related to our interest. Desire to learn and share knowledge of science required. There are many reviews of audio hardware and expert members to help answer your questions. Click here to have your audio equipment measured for free!

How to best explain dB to non-audio experts?

cochlea

Active Member
Forum Donor
Joined
Dec 27, 2020
Messages
157
Likes
387
If 0dB is total silence, how can something be twice as loud?
 

MRC01

Major Contributor
Joined
Feb 5, 2019
Messages
3,424
Likes
4,030
Location
Pacific Northwest
0 dB is not total silence. It is a reference point of loudness or amplitude. Total silence is not possible, since air molecules are always moving and bumping into each other. There is always some non-zero level of thermal activity or noise, no matter how small. That's not only true of air, but also of analog electronics like resistors.
 

danadam

Addicted to Fun and Learning
Joined
Jan 20, 2017
Messages
957
Likes
1,497
If 0dB is total silence, how can something be twice as loud?
dB without any suffix is a measure of change and 0 dB means zero change.

dB with a suffix is a level and 0 dB with suffix is a reference level. For example 0 dB SPL is a sound pressure of 20 μPa, which is considered (roughly) a threshold of human hearing. 10 dB SPL would be a level increased (a change) by 10 dB relative to 0 dB SPL, so it would be 63.2 μPa.

If you wanted to be very pedantic, then sure, you could say that if you didn't hear anything at 0 dB SPL but you hear something at 10 dB SPL then it is an infinite increase in loudness :)
 
Last edited:

digitalfrost

Major Contributor
Joined
Jul 22, 2018
Messages
1,521
Likes
3,086
Location
Palatinate, Germany
If 0dB is total silence, how can something be twice as loud?
dB is always relative to something. So the 0 is like a made up number. Also, you're thinking of multiplication I assume so if something was twice as loud you'd go 0*2 = 0 ???

That's not how decibels work. A muliplication of ratios is an addition in decibels (this what makes them so great).

FactorAndDecibel01.gif

So 10dB would be twice the perceived loudness, you are not multiplying with 0, you are adding 10 to it.
 
Last edited:

Blumlein 88

Grand Contributor
Forum Donor
Joined
Feb 23, 2016
Messages
20,524
Likes
37,057
And since you can have less than 0 db SPL (because this isn't total silence), you would hardly think such a number represents less than nothing. It represents a ratio as always.
 

danadam

Addicted to Fun and Learning
Joined
Jan 20, 2017
Messages
957
Likes
1,497
A somewhat interesting fact, which maybe is not obvious to everyone, is that 0 dB XYZ reference level cannot be set to 0 XYZ, because then, from the dB definition: 20*log10(p/p0) you would have to divide by 0 (p0 is the reference level).
 

Spkrdctr

Major Contributor
Joined
Apr 22, 2021
Messages
2,212
Likes
2,934
Math? This thread has really strayed from the original question. This thread "should" have no math in it at all. If it does, the person using the math can't explain the issue to Mom. So you lose all your points the first time you bring up math. Like in a political argument, the first person to say the word "Hitler" is disqualified as an idiot. Where did the KISS principle go? Not that I'm trying to stir the pot or anything.........:)
 

MRC01

Major Contributor
Joined
Feb 5, 2019
Messages
3,424
Likes
4,030
Location
Pacific Northwest
Math? This thread has really strayed from the original question. This thread "should" have no math in it at all. If it does, the person using the math can't explain the issue to Mom. ...
When I explained this to my Mom, I told her a dB is a ratio from comparing 2 values. If A is 26% bigger than B, that is 1 dB (power). If A is 12% bigger than B, that's about 1 dBV.
 

Spkrdctr

Major Contributor
Joined
Apr 22, 2021
Messages
2,212
Likes
2,934
When I explained this to my Mom, I told her a dB is a ratio from comparing 2 values. If A is 26% bigger than B, that is 1 dB (power). If A is 12% bigger than B, that's about 1 dBV.

Then she said, "wait, you changed what you are talking about. One thing is db the other is dbv. which is it"?
 

MRC01

Major Contributor
Joined
Feb 5, 2019
Messages
3,424
Likes
4,030
Location
Pacific Northwest
:facepalm: Nope, she didn't say that.
She did say, "So there are two different sizes of dB?" I said, "Yes, there are 2 different dB units and you use one or the other depending on what you're measuring."
 

Spkrdctr

Major Contributor
Joined
Apr 22, 2021
Messages
2,212
Likes
2,934
:facepalm: Nope, she didn't say that.
She did say, "So there are two different sizes of dB?" I said, "Yes, there are 2 different dB units and you use one or the other depending on what you're measuring."

Hmmm I wonder which size db she prefers versus your preference. Does size matter? Do electrons matter? All she wanted was to buy something on sale and you have mucked it up beyond all comprehension. You sir, are my hero! I am going to use your technique with my wife. "Honey, I need new speakers". "What's wrong with the old ones"? They have the wrong db for the movies we watch. If we get the correct db they will sound amazing"! If she asks what's a db? I will tell her it is an unfathomable idea only known to math experts and engineers, she just needs to trust me as I'm a member on ASR. So, I know what I'm talking about. That should shut her down and allow for new expensive speakers. It is finally time to get rid of the old speakers from Sears that I bought in 1985.......:) I was surprised all these years how good they sound after the surrounds rotted out in the late 90's. I just don't turn them up very much and they sound pretty good without surrounds. But it is time top replace them as the paper cones are disintegrating now. Expensive hobby!
 

MRC01

Major Contributor
Joined
Feb 5, 2019
Messages
3,424
Likes
4,030
Location
Pacific Northwest
Well, she understands that an ounce is actually two different things. It can measure weight (1/16 of a pound), or it can measure volume (30 milliliters). They're the same only when you're measuring water, and they're different for anything else. So how hard is it really to understand dB?

In short, a dB (even the power vs. voltage difference) is a simple concept that can be explained as ratios or percentages, which everyone understands. Of course, when engineers explain anything, they tend to make it sound far more complex than it really is. Likely because they understand all sorts of provisos, caveats, details, derivations that they add to the explanation, quite unnecessarily.
 

RayDunzl

Grand Contributor
Central Scrutinizer
Joined
Mar 9, 2016
Messages
13,204
Likes
16,984
Location
Riverview FL
"How to best explain dB to non-audio experts?"

10dB is like "times 10", not "plus ten".

Why?

Because.

Easy enough?
 

Blaspheme

Senior Member
Joined
Apr 14, 2021
Messages
461
Likes
515
Well, she understands that an ounce is actually two different things. It can measure weight (1/16 of a pound), or it can measure volume (30 milliliters). They're the same only when you're measuring water, and they're different for anything else. So how hard is it really to understand dB?
I guess people still running on imperial have an advantage being accustomed to needless complexity.

Don't forget to explain ounces vs fluid ounces. US vs imperial. Then teaspoons, tablespoons and cups. Which might work, if your mother is a cook. Me, I need a pint.
 
Last edited:

Blaspheme

Senior Member
Joined
Apr 14, 2021
Messages
461
Likes
515
"How to best explain dB to non-audio experts?"

10dB is like "times 10", not "plus ten".

Why?

Because.

Easy enough?
That's a good distinction, actually.
 

MaxBuck

Major Contributor
Forum Donor
Joined
May 22, 2021
Messages
1,515
Likes
2,118
Location
SoCal, Baby!
Count me better informed now, though still woefully ignorant. Heretofore I was unaware of the use of decibel in any regime other than SPL.
 

JustAnandaDourEyedDude

Addicted to Fun and Learning
Joined
Apr 29, 2020
Messages
518
Likes
819
Location
USA
As of this post, this thread is 20dB (power) longer than it needed to be.

If three positive numbers P, Q and R are such that P equals Q times R (P = Q x R), then we normally say that P is R times as large as Q.
We will use alternate names for two numbers when they are used in the alternate way of describing how much larger P is than Q that is discussed below. We will refer to the number 10 as a bel, and to a number that is approximately 1.258925412 (but which will be defined precisely below) as a decibel.

In addition to saying that P is R times as large as Q, we will in another manner of speaking of relative largeness say that P is E bels times as large as Q when Q must be multiplied by a bel E times to make the answer as large as (i.e., equal to) P:
P = Q x R = Q x (bel x bel x bel x ...... x bel [E times]).

For example, P is 10 times larger than Q and is also 1 bel as large as Q if P = Q x 10 = Q x bel.
P is 100 times larger than Q and is also 2 bels as large as Q if P = Q x 100 = Q x bel x bel.
P is 1000 times larger than Q and is also 3 bels as large as Q if P = Q x 1000 = Q x bel x bel x bel. etc.

We will say that P is E bels as small as Q or that P is -E bels as large as Q if it is P (instead of Q) that must be multiplied by a bel E times in order that the answer is as large as (equal to) Q. For example, P is -3 bels as large as Q if P x bel x bel x bel = Q. Thus, it follows that if P is E bels as large as Q, then Q is -E bels as large as P.

Essentially, the answer to "how large (in bels) is P compared with Q?" is the answer to "how many times must Q be multiplied by bel (i.e.,10) so that the result is equal to P?". If P = Q, then P is 0 bels as large as Q (and of course then Q is also 0 bels as large as P), because you need no (zero) multiplications by bel to make one equal to the other.

Similarly, we will say that P is F decibels as large as Q, if Q must be multiplied by a decibel F times in order that the result is equal to P. A decibel is precisely defined by requiring that a bel is 10 decibels as large as the number one. In other words, the defining equation (in which we use the convenient abbreviation dB for decibel) is,
10 = 1 bel = 1 x (dB x dB x dB x dB x dB x dB x dB x dB x dB x dB), wherein 1 is multiplied by a decibel 10 times. This is really the same thing as saying that a decibel is the principal tenth root of a bel, but then you would be asked what an n'th root is. The decibel is a finer measure of relative largeness than the bel which is coarser.

Note that if P is E bels as large as Q, then it is also (F =) E x 10 decibels as large as Q, because of the preceding defining equation, which is why the decibel is so named. Thus, if P is 3 bels as large as Q, then P is also 30 decibels as large as Q. By pondering and using the simple rules and reasoning described above, and by practicing with actual numbers perhaps with the aid of an electronic calculator, people unfamiliar with the dB can get an intuitive feel for bel and decibel (logarithmic) measures of ratios of like quantities.

Once the person you are explaining dB to has absorbed the preceding concepts, they may come back to you at some point with a ratio P to Q that is not a whole number of bels or decibels and ask what the answer is in such a case. For example, the person may pick P = 200 and Q = 8, when P = Q x 25. This is your chance to ease them into rational exponents by pointing out that Q x bel is smaller than P, and so P is more than 1 bel as large as Q, and also Q x bel x bel is larger than P, and so P is less than 2 bels as large as Q. Next, you explain that bel x bel or 10 x 10 is written in a shorthand notation as 10^2, and 10 x 10 x 10 as 10^3, and 10 as 10^1, where 10^1 is called "10 raised to the power of 1", 10^2 is called "10 raised to the power of 2", etc. And thus 1000,000,000 is a billion (U.S.) and is also 10^9 and is also 9 bels (multiplied together). Thus the shorthand notation and the measure in bels or decibels both allow us to compactly represent giant numbers and very tiny numbers. Then show them with the y^x or 10^x function buttons on your electronic calculator that you indeed get the answer 100 when you evaluate 10^2 and the answer 1000 when you evaluate 10^3, and get the answer 10 when you evaluate 10^1 (and 1 when you evaluate 10^0). Then you explain that Q must be multiplied by 10 more than once but less than twice for the result to equal P. Next you show them by trial and error on the calculator that 10^(1.39794...) gives the answer 25. And explain that thus, in a manner of speaking, they must multiply Q by bel 1.39794... times for the result to equal P. Or P = Q x 10^(1.39794...). They can see that this is what happens on the calculator. Therefore the answer to the original question is that 200 is 25 times larger than 8, and equivalently that 200 is 1.39794... bels as large as 8. Also 300 is also 1.39794... bels as large as 12; the bels measure the ratio of P to Q, and the ratio of 200 to 8 happens to be the same as the ratio of 300 to 12. (When their understanding has advanced some more, you can show them that they can get the calculator to do the trial and error for them by finding the answer as log10(200/8) = log10 (25) = 1.39794..., as also explain the distinction between dBP and dBV).

As an aside, an explanation similar to the above can be devised for a logarithmic measure defined relative to any base (10, 2, e, ..., basically any positive non-zero number other than 1, and preferably > 1) raised to any rational exponent (such as fractions of a decibel). Real number exponents can informally be made intuitive, but a rigorous math treatment is frightfully difficult (for me). So I would steer clear of explaining real (or complex) exponents to anyone without a good background in arithmetic and elementary algebra. At the heart of the matter, exponentiation is just performing repeated multiplications while logarithms are the counting of how many multiplications are performed. And multiplication in turn is just performing repeated additions while division is the counting of how many additions are performed. And addition in its turn is just repeated counting.
 
Last edited:
Top Bottom