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How to best explain dB to non-audio experts?

MRC01

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The take-away is simple: use 20*log(R) for most of the specs that Amir publishes for DACs & preamps (SINAD, THD, IMD, etc.). Every factor of 10 is 20 dB, e.g. -40 dB is 1% or 100:1.
Exception: when measuring power output use 10*log(R).
This is important to note cuz some people might look up the standard dB formula, see 10*log(R) and use this for the DAC/preamp specs which would be incorrect.
 

MRC01

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Speaking of bases, I've always thought we should express the frequency axis in log base 2, since that matches our perception. However, using log base 10 doesn't distort it much, it's still way better than linear.
 

DonH56

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As audiophiles we should use log base pi because...

It's irrational! :)
 
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Koeitje

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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.
Nail, head.

Plus I feel like I wouldn't need to explain how logarithmic scale works even if I would like to explain how good -130dB is. I think a couple of good real world examples of differences of a 130dB (or whatever the number is) can help explain what kind of scale we are talking about, that's what I am looking for I guess.
 

tmtomh

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Nail, head.

Plus I feel like I wouldn't need to explain how logarithmic scale works even if I would like to explain how good -130dB is. I think a couple of good real world examples of differences of a 130dB (or whatever the number is) can help explain what kind of scale we are talking about, that's what I am looking for I guess.

Your point about real-world examples is an interesting - and somewhat challenging - one, because so many of the real-world examples I can think of are about dB above ambient noise, rather than dB below max volume.

That said, how about this: -130dB means the noise level of the DAC compared to maximum volume is the same as the difference between total silence (0dB) and standing next to a jackhammer (130dB).

Or, think of the loudest concert you ever attended. Comparing that to total silence, this DAC is perceptually 10-20 times quieter than that.
 

Spkrdctr

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After reading most of these posts and thinking about Twinkies and the Sta-Puf man, I have come to a conclusion. To explain this to your mom, you have to ask non-engineers and non-geeks. You have to make it so simple a 5 year old can understand it. As a near 5 year old in mental ability, I would put it this way. Mom, the difference between a -100 vs a -130 distortion level is extremely small and you will never notice it in real life music listening. Your mom might then say, "Well, just buy the one on sale then". Your mom would be correct and you are feeling bad about that because you are into audio as a never ending hobby that can cost a large amount of money. Remember, just because things are measurable does not mean they are audible to a music listener. In todays' world, audio equipment is quite good and has come a long way. Buy the best you can easily afford and enjoy it! Mom will be happy too. :)

I can tell all of you will say, "By Golly he did it. He used his innate ability as an idiot to explain this to Mom".
Even an idiot is useful every few years! :)
 

Cbdb2

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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

Thats a power meter not a voltage meter. On a voltage meter 10db is 10x the voltage. How many more volts is 10dBV than 0dBV?
 

MRC01

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For 10 dBV, 20*log(R) = 10, so R = 10^(10/20) = sqrt(10) = 3.16. So 10 dBV is 3.16 times more voltage than 0 dBV.

Example 1: suppose someone analyzes an analog audio waveform (which has Volts on Y axis, time on X axis) and says, "The signal is 10 dB louder at time T1, than it is at time T2". This means the voltage at T1 is 3.16 times higher than at T2.

Example 2: suppose someone analyzes a digital audio waveform (same as above, Volts on Y axis, time on X axis) and says, "How much quieter would this signal be if we right-shifted every sample?". Right-shifting is the same as dividing by 2, or cutting the voltage in half. The dBV would be 20*log(1/2) = -6 dB, or 6 dB quieter.
 

stevenswall

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Aren't we talking about this in the context of normal people?

My conversations usually go: "1dB is the smallest increase the average human can hear in a silent room. 3dB is the smallest change humans hear when there is some background noise. If you want something to sound twice as loud, it needs to be 10dB higher, but keep in mind it's exponential so if something is using 10 watts, then it will take 100 watts to go twice as loud."

Never, EVER use amps, current, volts, etc, if you don't have to. A trillion volts is zero watts or a hundred trillion watts, nobody cares, that's useless information without too much context that will take things off into the weeds. Current and amps? Same thing.
 

danadam

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Aren't we talking about this in the context of normal people?
My conversations usually go: ... If you want something to sound twice as loud, it needs to be 10dB higher,
Their answer: "So in order to go to -130 dB you have to halve the loudness only 13 times? That seems still pretty loud."
;)
 
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sergeauckland

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Thats a power meter not a voltage meter. On a voltage meter 10db is 10x the voltage. How many more volts is 10dBV than 0dBV?
Rubbish! 10dB is 3.16 x the voltage and 10x the power.
10dBV is exactly 3.16v
+8dBu is as near as dammit 2V, 0dBu is 0.775v, 0dBm is also 0.775 across 600ohms.

S
 

MRC01

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Their answer: "So in order to go to -130 dB you have to halve the loudness only 13 times? That seems still pretty loud."
;)
How many times you halve it is not intuitive; it shrinks much faster than most people's intuition predicts.
That said, -130 dBV is a ratio of 3.16 Million to 1, or a ratio of 3.16e-7. That's halving it just over 21 times. Put differently, log base 2 of 3.16e-7 is -21.6.

PS: to assess how non-intuitive this is, ask someone, "If you invested $1 and it doubled every year, how long would it take to grow to $3.16 Million". Most likely they will say something longer than 21 years.

Or, ask them, "The lilies in a pond grow, every day doubling the area of the pond surface that they cover. If it takes 30 days to cover the entire pond, on which day do the lilies cover half the pond?" The obvious answer is day 29, but surprisingly few people say this.
 
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Blaspheme

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Aren't we talking about this in the context of normal people?

My conversations usually go: "1dB is the smallest increase the average human can hear in a silent room. 3dB is the smallest change humans hear when there is some background noise. If you want something to sound twice as loud, it needs to be 10dB higher, but keep in mind it's exponential so if something is using 10 watts, then it will take 100 watts to go twice as loud."

Never, EVER use amps, current, volts, etc, if you don't have to. A trillion volts is zero watts or a hundred trillion watts, nobody cares, that's useless information without too much context that will take things off into the weeds. Current and amps? Same thing.
That's so true. Lots of explanations here went off into the weeds that way. For people this thread posits explaining these things to, be sure that electrical engineering theory and practice is likely narcolepsy.
 

stevenswall

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Their answer: "So in order to go to -130 dB you have to halve the loudness only 13 times? That seems still pretty loud."
;)

I don't know that anyone is going to think halving is a small increment, especially doing that 13 times. Maybe give them an object lesson? Here is $130. Let's start halving and see what you think is still a lot.

Now you have $65.
Now you have $32.50
Now you have $16.25
$8.12... Are you understanding exponential terms like halving and doubling yet? That costs you a penny.

$4.06
$2.03
$1.02
$.51

We're only at the 8th halving out of 13, want to keep going?
 

HammerSandwich

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I don't know that anyone is going to think halving is a small increment, especially doing that 13 times. Maybe give them an object lesson?
You have a large pizza - 16" diameter. But suppose a friend shows up to share it. Then 2 of that guy's friends show up, so each person gets 1/4. When this happens 13 times, your piece of pizza is 1/8" x 1/8", and you have 8192 people sharing the whole thing.
 

MRC01

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Where is halving 13 times coming from? -130 dBV is halving 21 times. Halving 13 times is only -78 dBV.

In the pizza example I think each person's piece would be slightly bigger than 1/8" x 1/8". A 16" diameter pizza has 201 square inches of pizza. Divided equally by 8192 people is 0.0245 square inches per person. If cut into squares, that's 0.157" per side, or just under 1/6". In that case some people would get all crust, so to be more fair you'd cut it radially. The outer arc of each radial slice would span 0.006136" or about 1/163".
 

danadam

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I don't know that anyone is going to think halving is a small increment, especially doing that 13 times.
Okay, maybe I should have written "that seems still audible" instead of "that seems still pretty loud".
Maybe give them an object lesson? Here is $130. Let's start halving and see what you think is still a lot.
[...]
$.51
We're only at the 8th halving out of 13, want to keep going?
And will that teach them that $.51 becomes (or starts becoming) inaudible?
 
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