# Is there a list of root-power quantities? Or a rule of thumb?

• I
• ngn
ngn
TL;DR Summary
How to know if a quantity is a root-power quantity (field quantity). Is there a list somewhere? Or a helpful rule of thumb?
Hello, I am working with calculating decibels, and there is one equation when using quantities of power and another equation when using root-power quantities (which essentially just converts them to a power ratio and places them into the first equation). I know that common quantities of power are things like "power", "intensity", "energy density", and I know that common root-power quantities are things like "amplitude", "pressure", "voltage". And I know that root-power quantities are those that are proportional to the square root of power.

But I am wondering if there is a simple way to know or intuit if a quantity is a root-power quantity or not. If there is only a finite number of known root-power quantities, then is there a list I can find somewhere? Or are most quantities (other than direct measures of power) root-power quantities? This may seem like a basic question, but if you try to search online, you often find only the definition of a root-power quantity, and maybe a few examples, but no comprehensive list or comprehensive generalized definition of a root-power quantity that you can apply as a rule of thumb when encountering a quantity that is not one of the few examples listed.

Is there a rule of thumb that I can apply? I'd assume that some measures aren't root-power quantities, and I'd assume that some measures are proportional to the cube root of power and therefore the decibel equations wouldn't work (or you would have to use 30 x log(ratio)). So, what should I do if I encounter a new quantity that I want to convert to decibels?

For example, I generally intuit that amplitude is a root-power quantity based on the fact that when I push on a spring, I not only have to apply more power to move the spring a further distance in a given time period but I also have to apply more and more force to move the spring the harder I push, so work/power must go up exponentially (squared) as I push. Therefore, I have a sense that power is amplitude squared.

But what about a person's height? Here I don't think height is a root-power quantity. But could it be on some level? For example, doesn't it require more power to grow taller in a given amount of time and aren't limitations on height somewhat related to limitations on energy, and if I grow taller, would I require an exponential increase in energy to do so, which is why we don't currently have dinosaurs running around? This is a silly example, but I'm wondering if there is some intuitive way (rule of thumb) to decide on the correct equation to use when calculating decibels and whether some measures (e.g., height) just aren't able to be converted to power and used for decibel calculations.

Thank you!

If it is energy flow = power, use; dB = 10 * Log10( ratio ).
If voltage or current, use; dB = 20 * Log10( ratio ).
With anything else, stay consistent.

Sorry about the TLTR. "Anything else, stay consistent" exactly applies to my question. What about a quantity that isn't clear? In my silly example above, I used an organisms height as an example. Of course, you wouldn't use decibels for that but if you wanted to, is it possible? Is height a root-power quantity on some level?

ngn said:
Is height a root-power quantity on some level?
What advantage is there in using dB for height?
Height3 is more relevant than the Log( height ).

Use dB only when you have magnitude variation over several decades.

DrClaude
I think a logarithmic scale is usually used if you want to have a magnitude related to our senses. That's why also in astronomy they give the brightness of objects in "magnitudes", because it's in a sense a measure of visibility. The same for dB for the "loudness" of sounds etc.

sophiecentaur and DrClaude
Baluncore said:
If it is energy flow = power, use; dB = 10 * Log10( ratio ).
If voltage or current, use; dB = 20 * Log10( ratio ).
With anything else, stay consistent.
The Bel is basically a ratio of Powers and people must realise this at all times or they can get into difficulties with nonsense answers. It's far easier, in most cases, to measure Volts but to 'convert' from measured Volts to actual Power, you need to use P = V2/R where R is the resistance of the load that's being supplied.
In the RF Engineering world, it's practice to use a standard impedance for cables, inputs and outputs so your 20 factor works fine. 10 dB of gain means ten times the power and you will measure √10 increase in volts with the same load resistance. But what happens with a transformer? You may get three times the output volts but (obvs) no more power. (You will notice that Power Engineers seldom (never?) use dB.)

ngn said:
TL;DR Summary: How to know if a quantity is a root-power quantity (field quantity). Is there a list somewhere? Or a helpful rule of thumb?

But I am wondering if there is a simple way to know or intuit if a quantity is a root-power quantity or not.
The "rule of thumb" that you seem to be after is basically to understand the equations / maths involved, I'm afraid. Alternatively you can avoid dB until you actually calculate / measure the Powers and avoid getting confused by tens, twenty and thirtys.

Baluncore said:
Use dB only when you have magnitude variation over several decades.
dB can be very useful when a chain of gains and losses is involved, each step may not be many dB added or subtracted.

dBs involve logs and those of us who were taught before electronics came along used adding and subtracting logs in school (Godfrey and Siddons tables) instead of long multiplication and division or even the Slide Rule

DaveE
Remember the sliderule!!
Actually the place where log scales has the most immediate utility is filters and optical density. The OD of concatenated optical filters is additive. This follows directly from the exponential being the description for proportional growth and decay. There are of course many such systems, hence the ubiquity of logarithmic measure.
Decibels have never been my favorite unit and I much prefer the Bel. Why report some measurement as 10 decibels?? Seems patently silly to me.

hutchphd said:
Why report some measurement as 10 decibels??
Perhaps because 3dB, 6dB and 10dB are all a good bite size for everyday life. Would you want to use 0.3B or 0.6B?

We seldom use values of less than 1dB, except for 'small variations' in frequency response etc.. Imo, the dB just flourished because it was so practical and popular and the 0.1dB is the limit of accuracy that anyone needs in practice.

But basically, the dB was the choice of Engineers.

hutchphd
I do understand, but I love to tweak my audiohead friends by asking whether they mean 3 bels when they say 30 dB attenuation. You know I seem to have fewer and fewer audiohead friends.......wonder why?

hutchphd said:
but I love to tweak my audiohead friends
Always good value!! And audio heads seldom know any more than the advertising blurb. They hear ££££.

hutchphd
The neper, Np is closer to the bel.
10 dB = 1 bel = 1.1513 Np.
1 Np = 8.686 dB
https://en.wikipedia.org/wiki/Neper

Audio equipment should sound better with a natural logarithm, rather than with the rounding error of the ersatz log10(/).

Digital A-D converters operate with base 2 unit steps, which are 3.0103 dB.
A 3.0000 dB attenuator deviates from that by 0.343%. Audiophiles ignore that, as if it does not matter.

hutchphd
Baluncore said:
The neper, Np is closer to the bel.
10 dB = 1 bel = 1.1513 Np.
1 Np = 8.686 dB
https://en.wikipedia.org/wiki/Neper

Audio equipment should sound better with a natural logarithm, rather than with the rounding error of the ersatz log10(/).

Digital A-D converters operate with base 2 unit steps, which are 3.0103 dB.
A 3.0000 dB attenuator deviates from that by 0.343%. Audiophiles ignore that, as if it does not matter.
By "sound better" I think you mean that the audio level control should 'match' the subjective appreciation by equal steps. Would that really be an improvement when you consider that programme content governs its apparent loudness? Moving from speech to music and to crowd at sporting events makes several dB of difference to many people's subjective experience. Any scale on a fader would be 'wrong' half the time. Sound level meters can only do their best with a new source of sound, so assess its loudness. As long as they agree amongst themselves, you can't expect more.

What goes on in audio coding is just numbers, unless there is some non-linearity involved for data reduction. Companding (or any other name applied) will not be tied to any number base; it just performs well or badly according to the group who invent it (and commercial pressure, of course).

sophiecentaur said:
Companding (or any other name applied) will not be tied to any number base;...
I think you will find an audiophile will prefers natural to artificial, if they can tell the difference, or if somebody else might find out what they are using.

Baluncore said:
I think you will find an audiophile will prefers natural to artificial,
Vegan audio?

Baluncore

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