# Am I understanding basic audio science right?

#### sergeauckland

##### Major Contributor
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The arithmetic doesn't require it, it's done for convenience.
In other words, we could have a single definition of a dB, say 20 * log(R). That would be simpler and mathematically consistent, eliminating any confusion about which formula to use since there's only 1. But that would mean a 6 dB change in voltage (say increasing volume) leads to a 12 dB change in power delivered to the speaker. By defining a power dB to be different from a voltage dB, 10*log(R) and 20*log(R) respectively, a 6 dB change in voltage leads to a 6 B change in power, simply because a power dB is "bigger".
Having 1 formula or 2, the math works either way. Using 2 different formulas and definitions for a dB is done by convention, presumably for convenience.
It's a consequence of power being proportional to Voltage squared. P=V^2/R Ditto with dBs related to current. Power is proportional to current squared. P=I^2R

S.

#### MRC01

##### Major Contributor
It's a consequence of power being proportional to Voltage squared. P=V^2/R Ditto with dBs related to current. Power is proportional to current squared. P=I^2R
S.
Exactly. If you change voltage by a certain ratio R, power changes by the square of that ratio or R^2.
This fact of nature doesn't require us to have 2 different sized units for measuring ratios (e.g. dB). We do that by convention.

#### somebodyelse

##### Major Contributor
1. Is it worth paying for 24 bit audio files with 48khz or higher, as opposed to CD quality tracks with 16 bit at 44khz?
The technical side of this has been covered already. What hasn't is the underlying assumption that the CD quality version is just a downsample of the high res version - this isn't necessarily true. They may be different mixes, or have different dynamic range, and it's not necessarily the 'hi def' version that's better. Also some 'hi def' versions have been found to be upsamples of the CD quality version. I don't know if anyone's been tracking this in the same way as the 4k movies.

#### andreasmaaan

##### Major Contributor
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That's with IEMs, maybe with speakers the range would be bigger?
The range will almost certainly be much smaller with speakers. IEMs block out a large amount of ambient noise, which lowers the ambient noisefloor (typically by 10-30dB), allowing you to hear lower-pressure sounds than you would in the room.

A poll was run a few months (or years?) back of members. IIRC the typical range was 70-80dB with speakers.

#### mhardy6647

##### Major Contributor
The arithmetic doesn't require it, it's done for convenience.
In other words, we could have a single definition of a dB, say 20 * log(R). That would be simpler and mathematically consistent, eliminating any confusion about which formula to use since there's only 1. But that would mean a 6 dB change in voltage (say increasing volume) leads to a 12 dB change in power delivered to the speaker. By defining a power dB to be different from a voltage dB, 10*log(R) and 20*log(R) respectively, a 6 dB change in voltage leads to a 6 B change in power, simply because a power dB is "bigger".
Having 1 formula or 2, the math works either way. Using 2 different formulas and definitions for a dB is done by convention, presumably for convenience.
Point taken.

#### MRC01

##### Major Contributor
The technical side of this has been covered already. What hasn't is the underlying assumption that the CD quality version is just a downsample of the high res version - this isn't necessarily true. They may be different mixes, or have different dynamic range, and it's not necessarily the 'hi def' version that's better. Also some 'hi def' versions have been found to be upsamples of the CD quality version. I don't know if anyone's been tracking this in the same way as the 4k movies.
Indeed, and there lies the irony. Looking at the HDTracks home page, just about every "high res" download either comes from a decades old analog recording, or it comes from a heavily compressed modern recording. In either case, "high res" is pointless. No doubt they eq or remaster to ensure it sounds different from the CD, but in most cases that actually makes it worse. With a few notable exceptions, if you have the original CD, it sounds better and actually has more dynamic range than the latest "high res" download.

The question whether 44-16 is perceptually transparent, is quite different from the question whether it's sufficient to encode various kinds of music. Even if the answer to the first is "no", the answer to the second could still be "yes".

#### MrPeabody

##### Active Member
It is "multiply by 10" for quantities related to power. For quantities related to amplitude it is 20.
https://dspillustrations.com/pages/posts/misc/decibel-conversion-factor-10-or-factor-20.html
I have an impression something is mixed up in the above. AFAIK, SPL is "amplitude" quantity and halving/doubling happens at 6 dB, not 3 dB.
To get the nasty part out of the way, I'm not fond of the word "amplitude" being used the way you are using it. No doubt this came about as a result of the fact that amplitude is most often associated with voltage, which varies as the square root of power, thus leading to the notion or practice of classifying any quantity that varies as the square root of power as "amplitude". The word that comes to mind is "yuch."

The first excerpt you took from what I wrote was purely a mathematical statement correlating a doubling scale to a base 10 logarithmic scale. Neither power nor root-power quantities were implied. Perhaps there is another way to show why a difference of 3.01 dB implies a doubling (of power), but my way of doing it has the advantage of mathematical purity.

Here is one of the basic properties of logarithms:

log( X ^ n) = n x log( X)

Since power is proportional to the square of voltage, power ratios are obtained by squaring voltage ratios. If we are given two voltage values and want to express the implied power ratio in decibel, we would first square the voltage ratio in order to obtain the power ratio, then take the base 10 log and multiply by 10. It is appropriate to think of the multiplication by 10 as a conversion from Bel to decibel. But of course the above logarithm property reveals that this calculation is the same as taking the log base 10 of the voltage ratio and then multiplying by 20 instead of by 10.

Nearly a century ago, some engineers at Bell Labs proposed a way of expressing power losses in transmission lines using a logarithmic scale. The essential advantage of using a logarithmic scale was that accumulation of power losses could be computed via direct addition and subtraction in lieu of multiplication. They defined the "Transmission Unit" or TU as 10 x the base 10 log of the power ratio. Subsequently they changed the name from TU to "deciBel", which implicitly defined the Bel as the base 10 log of the power ratio. Even though there is no inherent mathematical reason that the deciBel should only be used in a way whereby 3 dB implies a 2:1 ratio in power, this became a de Facto rule for use of the decibel. For root-power quantities in particular, e.g., voltage and sound pressure, this means that an increment or decrement of 3 dB does not correspond to a doubling or halving of the root-power quantity itself. Ratios of root-power quantities are generally squared before taking the logarithm, thereby translating the ratio of the root-power quantity to the corresponding ratio of power. And of course this is equivalent to multiplying the base 10 log of the ratio (of the root-power quantity) by 20.

Thus, in the formula we use to convert sound pressure in Pascal to decibel (SPL), we divide the sound pressure value in Pa by the reference level (.00002 Pa), then take the common log, then multiply by 20. (The definition of Pascal is 1 Newton of force per square meter.) It is apparent that a 3 dB difference in SPL values implies that the acoustic power values (in Watts or milliWatts, etc.) are in the ratio 2:1, and that the sound pressure values for a 3 dB difference in SPL are in the ratio 1.4:1. (Even though SPL is pressure, not power.) When two SPL values (in decibels) differ by 6 dB, the two sound pressures (in Pa or in any alternative units for force per unit area) are in the ratio 2:1.

Since +/- 3 dB is a spread of 6 dB, it follows that for a speaker with sensitivity remaining within a +/- 3 dB window over some range of frequency, the ratio for sound pressure (force per unit area) at the upper and lower boundaries of the window is 2:1. The strongest sound pressure encountered in this range of frequencies will be not greater than twice the weakest sound pressure encountered in this range of frequencies. I regret that at the tail end of my prior post I muddled this so badly as to have spoiled a post that otherwise was probably half decent

#### voodooless

##### Senior Member
Forum Donor
Even more fun: our ears don't work that way either. For sound pressure you need about 10 dB of difference to perceive something as double or half as loud.

#### Mnyb

##### Addicted to Fun and Learning
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The technical side of this has been covered already. What hasn't is the underlying assumption that the CD quality version is just a downsample of the high res version - this isn't necessarily true. They may be different mixes, or have different dynamic range, and it's not necessarily the 'hi def' version that's better. Also some 'hi def' versions have been found to be upsamples of the CD quality version. I don't know if anyone's been tracking this in the same way as the 4k movies.
The real elephant in the room is that the actual intrinsic quality of most recordings ever made is lower than 16/44.1 anyway , we never utilized CD to to it's full extent either ,especially those old 70's rock albums or jazz from 60's you buy remastered at HD tracks Don't get me wrong some do sound god and always have , but they would sound equally good as CD. I suppose the remaster moniker has gotten so tainted that the only way to sell the 15'th remaster of DSOTM or Kind Of blue is to actually use a new medium and slap a HD sticker on it.

#### mhardy6647

##### Major Contributor
The way I look at it, the really cool part is that our auditory processing system has a dynamic range of ca. 12 orders of magnitude.

#### Mnyb

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The way I look at it, the really cool part is that our auditory processing system has a dynamic range of ca. 12 orders of magnitude.
I take my tame mosquito with me and stand behind a jet engine I'll report later if is till can hear any of them....

#### mhardy6647

##### Major Contributor
I take my tame mosquito with me and stand behind a jet engine I'll report later if is till can hear any of them....
Well -- before you do that... you can stand in a room full of people and pick out one conversation. PS Yeah, I recognize that it's not a function of dynamic range, but it's still cool. I mean, otherwise, our everyday lives would be like listenin' to a Robert Altman movie #### andreasmaaan

##### Major Contributor
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Well -- before you do that... you can stand in a room full of people and pick out one conversation. PS Yeah, I recognize that it's not a function of dynamic range, but it's still cool. I mean, otherwise, our everyday lives would be like listenin' to a Robert Altman movie It's this ILD and ITD processing that I find to be one of the most remarkable things about hearing.

#### fcracer

##### Member
The definition of a dB is different for voltage & power. 3 dB is approximately twice/half the power, 6 dB is approximately twice/half the voltage.
If that seems absurd, there's an intuitive reason for it.
I’ve been looking for a simple explanation of dB and it’s uses forever. Thanks so much for posting this link!

OP
H

#### hat28

##### Member
1a. 'dB' is like '%' or 'thousand' in that it tells you about the relative scale of the value provided, but does not tell you what the scale is measuring. (You can have ten thousand dollars or ten thousand volts, but having "ten thousand" without specifying the thing being counted is meaningless.) A Bel is a ten-fold change, so 0 Bel dollars, 1 Bel dollars, and 2 Bel dollars would be \$0, \$10, and \$100; -1 Bel dollars and -2 Bel dollars would be \$0.10 and \$0.01. A decibel is one-tenth of a Bel, so 20 dB is the same as 2 B. Straight 'Bel' is very rarely used, though, because units in dB is usually more practical.

In this context, dB are often used to describe recordings as dB full scale, or dBFS, where 0 dBFS is as loud as the samples can record, -10 dBFS is -1 Bel so 1/10th so 10% of 0 dBFS. Another use of dB is for sound pressure level, or SPL, which measures the amount of force a sound wave is carrying. 100 dB SPL has ten times as many of those force units (which isn't very complex, but let's not get into those details right now) as 90 dB SPL. Whether 10 dBFS -- going from -10 to 0 dBFS, for example -- translates into 10 dB SPL -- going from 80 to 90 dB SPL, for example -- is entirely dependent on how much amplification is used.
Right, so I had never tuned in to the fact that dBFS and SPL were so different. More things are dropping into place for me now - thank you

OP
H

#### hat28

##### Member
The Force is strong in this one! You’re doing quite well on your own. Keep it up!
Your warm words are spurring me on to learn this stuff properly now; off to get a textbook that will be structured rather than stumbling through various threads on sites - thank you!

#### watchnerd

##### Major Contributor
^^^ good point. Yup, cannot take the log of zero.
Not permitted.
Stuff blows up.
But I made zero of a log.

In my fireplace.

#### mhardy6647

##### Major Contributor
But I made zero of a log.

In my fireplace.
I'll bet you made an ash of it!    