The scientific “unit” we call the decibel

https://lcamtuf.substack.com/p/decibels-are-ridiculous

by Ariarule • 1 year ago

644 460 1 year ago

lcamtuf.substack.com

smat• 1 year ago

Great post, the fusion of scale with unit is a mess.

When using it as a factor, for example when describing attenuation or amplification it is fine and can be used similar to percent. Though the author is right - it would be even more elegant to use scientific notation like 1e-4 in this case.

For using it as a unit it would really help to have a common notation for the reference quantity (e.g. 1mW).

But I guess there is no way to change it now that they are established since decades in the way the author describes.

rocqua7• 1 year ago

Scientific notation would be worse, because you can't add them to get the combined gain. That's where dB's really shine.

rebolek2• 1 year ago

While the author is technically right, I must argue that in the area of sound work, decibels make sense. Zero is base level, -3db is half loudness, +3dB is double. There may be a better way to describe loudness, but decibel is good enough.

readthenotes1• 1 year ago

So on my amplifier, 0db is the loudest and -50db, where I usually listen is what?

-47db is definitely not twice as loud as -50db, of course.

hgo• 1 year ago

I'm not confident in what I'm saying here, so please correct me if I'm wrong as I'd like to learn:

Human hearing isn't linear in terms of loudness. So a 3db increase in loudness sounds like "an increase", but the pressure is actually double. Hence, it makes sense to use db to describe loudness even in the context of perceived loudness to human-hearing.

This is similar to brightness. In photography, "stops" are used to measure brightness. One stop brighter is technically twice the light, but to the human eye, it just looks "somewhat brighter", as human brightness appreciation is logarithmic, just like "stops" and "db".

bloppe• 1 year ago

I mean, it should be, unless your amplifier is taking its own liberties with the definition of dB.

rebolek2• 1 year ago

Again, technically, it is. But ear isn't scientific device, neither is your amplifier. What I was describing is more than an agreement than some precise measurement. 3dB is more or less double the volume but different frequencies have different responses so I really wouldn't want to have some "perfect" way of measuring loudness as it would be so needlessly complicated that it would be useless.

timewizard3• 1 year ago

Human hearing perception response is logarithmic. This is part of the reason we use the unit. Our senses naturally work in that domain.

masklinn• 1 year ago

3dB is “twice as loud” in that it’s twice (or half) as much power.

Part of the reason why the bel is used is that human perception is closer to logarithmic than linear (weber-fechner law), so a logarithmic scale is a better approximation of “loudness” than a linear one.

coldtea2• 1 year ago

-47db is double the power. Perceived double loudness would be ~ -40db

relaxing3• 1 year ago

You should have a legitimate question as to what dB’s the amp is referring to. What brand and model is it?

First, is it actually specified as dB’s? Most amps I’ve seen display volume on an arbitrary scale, no units specified.

Second, the amp has no way to know dB sound pressure, as that depends on the rest of signal chain.

So is the displayed figure referring to dBu, dB mV, something else, or something totally bunk?

djaychela• 1 year ago

As someone else alluded to, 3dB is a doubling in power, not perceived loudness. 10dB will be perceived as a doubling in loudness. This is the original unit (the Bel, rather than deciBel) which was I believe derived by testing on human subjects to measure this.

TBH I don't agree with a lot of the article - yes, dB on its own only indicates a ratio, but certainly in the field I work with this is known, and there are qualifiers (dBA, dbFS dbU) which tie the ratio to a known value so you're talking about an absolute, known quantity - even the dBa which is mentioned as if it comes out of nowhere is something which most audio engineers know about and use regularly because it's important to know the difference betweent he signal present and perception of it by the listener.

svara4• 1 year ago

For practical day to day use in very narrow context, yes.

But, what you're saying is only approximately correct (the factor is a bit less than 2) and there are many related fields, even in areas that would be relevant to the physics of sound reproduction, in which the same notation "dB" means something different.

ajuc4• 1 year ago

-3db is half loudness, +3dB is double

It isn't tho. It's close but not exactly. And there's nothing about -3 behing half that makes sense except for familiarity (and it's not even wide-spread familiarity - most people wouldn't know how much louder +3dB is).

It's just an unnecesarilly confusing definition that stuck for historic reasons.

danadam2• 1 year ago

It isn't tho. It's close but not exactly.

It isn't tho :-). It's not close to double loudness. It's double power, which is 1.41 higher sound pressure, which is only slightly louder.

kazinator8• 1 year ago

But, no! -3dB is half power, not half loudness. -3dB down is just slightly less loud.

globular-toast• 1 year ago

Exactly. There's no way +3dB is perceptibly twice as loud. That's easy to test for yourself. +10dB is roughly twice as loud.

Sharlin2• 1 year ago

-3db is half loudness

Sure, perfect sense.

verzali3• 1 year ago

10*log10(0.5) = -3

That's the math of it.

rocqua7• 1 year ago

That's great, but only if 'Base level' is clear to everyone involved. Besides the base level, you also need to define what exactly you are measuring. Including the frequency weighting.

This makes a spec sheet that says "this machine produces X dB of sound" effectively useless.

davrosthedalek14• 1 year ago

Any reasonable spec sheet would not say that. I say reasonable, because in the audio world, people pay extra money for oxygen-free copper cables.

ziofill• 1 year ago

The nice thing about dBs is that they are logarithms: successive applications of gain/attenuation are easily computed by just adding up the dBs. (but yes, I agree that there should be more consistency in their definition)

xnx• 1 year ago

Weird that the author makes no mention of Sones: https://en.wikipedia.org/wiki/Sone

itchingsphynx• 1 year ago

Nor phons!

“The phon is a logarithmic unit of loudness level for tones and complex sounds.”

https://en.wikipedia.org/wiki/Phon

svara4• 1 year ago

A pet peeve I share! An expanded version of this article should become the article on decibels on Wikipedia.

I've read that article many times over my life and for the first couple times came back thinking I was too dim to understand.

Transparently leading it with "Here's something ridiculously overcomplicated that makes no sense whatsoever..." wouldn't fit Wikipedia's serious voice but actually be pedagogically very helpful.

esperent• 1 year ago

There's often a Criticism of... section in Wikipedia pages.

Maybe this blog post could work as a source, although it would be better to find something more established.

timewizard3• 1 year ago

That said, I don’t know how to pronounce “3e5”

"Three to the exponent of five." Or "Three Exponent Five." Or "Three Exp Five."

Seeing this, some madman decided that 1 bel should always describe a 10× increase in power, even if it’s applied to another base unit. This means that if you’re talking about watts, +1 bel is an increase of 10×; but if you’re talking about volts, it’s an increase of √10×

This is power vs. amplitude. This is the specific reason the dB is so useful in these systems.

the value is meaningless unless we know the base unit and the reference point

No you just need to know if you have a power or a root-power quantity. Which should generally be obvious.

https://en.wikipedia.org/wiki/Power,_root-power,_and_field_q...

ggm2• 1 year ago

No you just need to know if you have a power or a root-power quantity. Which should generally be obvious.

There has to be a Yogi Berra witticism about obvious things. Suffice to say fools like me work unadvisedly in spaces where this kind of axiom isn't obvious, because we're simpletons.

bigiain2• 1 year ago

> That said, I don’t know how to pronounce “3e5”
"Three to the exponent of five." Or "Three Exponent Five." Or "Three Exp Five."

Somehow, you need to distinguish between 3^5 (=243), 3 x e^5 (=~445.24), and 3 x 10^5 (=300,000).

I'd pronounce "3e5" and "three times ten to the 5" in most cases.

timewizard3• 1 year ago

3^5 (=243)

Three to the power of five.

3 x e^5

Three times the fifth power of e. Or Three times e's fifth power.

3 x 10^5 (=300,000).

Three to the exponent of five.

A calculator user once suggested "decapower." I think exponent and "EXP" are comfortable and easy to say and are ingrained to most old school calculator users. Which is also why I think "e's fifth power" can be a more natural sequence.

ggm2• 1 year ago

Do a deep dive into audio vu Meters and how they got calibrated. Without being 100% sure, it's basically a totally subjective model, where back in the 1920s the BBC and some US company decided to assert "like us" and two models persist which have been retconned into some BIPM acceptable ground truth but it basically was "test it against the one we made which works"

The hysteresis in the coil-magnet meter response turned out to be a feature, not a bug.

formerly_proven7• 1 year ago

Decibels make sense and it’s usually only laymen who use only „dB“. I’d be surprised if you’d find „-45 dB“ as the specification for a microphone. Here’s two random examples:

Sensitivity at 1 kHz into 1 kohm: 23 mV/Pa ≙ –32.5 dBV ± 1 dB

Sensitivity: -56 dBV/Pa (1.85 mV)

nothacking_• 1 year ago

Except finding '-45 dB' is frustratingly common. Have a look at this random microphone datasheet from DigiKey: https://www.sameskydevices.com/product/resource/cmm-3125at-4...

They do state the test conditions "at 94 dB SPL, 1 kHz", but don't specify the units attacked to the actually measurement. It's given as a ratio to an unspecified quantity.

formerly_proven7• 1 year ago

Thanks, it's a good example for this bad practice. Especially because this could reasonably be both dBu and dBV, so it's actually ambiguous. (On the other hand with that tolerance the difference between the two is not that significant)

hock_ads_ad_hoc• 1 year ago

The author seems confused. Decibels aren’t units. They’re a way to express a ratio between a reference value and some other value.

They’re used where they are useful.

coolcase2• 1 year ago

They are units too. When you have regulations relating to sound they will say how many dB the limit is.

formerly_proven7• 1 year ago

I've never seen dB being used like that in anything remotely official.

neepi• 1 year ago

No. dB is not a unit. If it's quoted as a unit, then the person using it doesn't know what they are doing. dBx where x is some reference value is a unit and that means dB relative to the reference unit. So dBm/dBv etc are units. dB is not.

Mathematically, dB is the ratio between two unit values and for example if you divide metres by metres you cancel the units.

jononor2• 1 year ago

No they will specify something like dB SPL, A-weighted with Fast time integration. Sometimes referred to as dB(A) SPL. And measured with a particular method, which specifies things like distance from sources, environmental conditions, etc.

rocqua7• 1 year ago

dBs are so often used as units. That's 80% of the complaint in the article.

The fact that dBs aren't units, but are used like units, is the point being made.

atoav3• 1 year ago

But dB is not a unit, it is a multiplier. dB on its own is unitless and if we say "X is reduced by 6 dB" you know that the value of X is half of what it was before (×0.5) if something is amplified by 6 dB it is double of what it was before (×2.0)¹

Note that the unit only starts to play a role when you reference your dB value to some absolute maximum, e.g.:

  dBV which is referenced to 1V RMS
  
  dBu which is referenced to 0.775V RMS (1mW into a typical audio system impedance of 600 Ohms)  
  
  dBFS which is referenced to a digital audio maximum level (0dBFS) beyond which your numeric range would clip (meaning all practical values will be negative) 
  
  dBSPL which is refrenced to the Sound Pressure Level that is at the lower edge of hearing (0 dBSPL), this is what people mean when they say the engine of a starting airplane is 120dB loud

Now dB is extremely useful in all fields where your values span extremely big ranges, like in audio engineering, where the ratio between high and low values can easily have a ratio of 1:10 Millions. So unless you want people to count zeroes behind the comma, dB is the way to go.

When we think about the connection between analog and digital audio dB is useful because despite you having volts on the one side and bits on the other side a 6dB change on one side translates to a 6dB change on the other, the reference has just changed. If we had no dB we would have to do conversions constantly.

Going from multiplier x to dB: 20×log₁₀(x)

Going from dB to multiplier x: 10^(x/20)

If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)

But you can see, dB is just a way to describe a unreferenced size change in a uniform way or to describe a referenced ratio. And then it would be good to know what that reference is. So if someone says a thing has 40dB you they forgot to tell you the unit.

¹ this is true for the amplitude of a signal and differs when we talk about the power of a signal, where 3dB is a doubling/halving.

rocqua7• 1 year ago

But dB is not a unit, it is a multiplier. dB on its own is unitless.

The point of the article is exactly that this should be the case. But it ends up not being the case. Mostly because people use dB with reference to some assumed baseline. But also because a 20db change could be a 10x change conpared to baseline, or a 100x change compared to baseline, depending on what unit you are measuring in.

mikewarot3• 1 year ago

20 dB is always the same, actually. If you multiply voltage (and thus current as well) by 10:1 (20 db) the power is multiplied by 100:1 (also 20 dB)

atoav3• 1 year ago

Yes but my conclusion would not be that Decibels are ridiculous, but that "People don't understand Decibels".

Decibels are okay. They are useful. They work. The problem is that people use referenced decibel values without adding anything that would allow us to understand which reference was used.

Maybe one could have come up with a better numeric way of doing the same thing (I am missing a proposal for this in the blog post), but then you'd have the XKCD-yet-another-standard problem. Everything uses dB for ages now, so dB it is or you need to convert between one and another all the time.

As an audio engineer I have no issue with dB as a unit. It is much better than using raw amplitude numbers.

roelschroeven• 1 year ago

If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)

This is the part I don't get. This is the part where "dB is just a multiplier" falls short. It's there to "so that the related power and root-power levels change by the same value in linear systems" (that's how Wikipedia formulates it). Why is that even something you would want? Isn't it much more logical, intuitive, consistent and useful to reflect the fact of power being proportional to the square of the signal in it having double the dB value?

thrdbndndn2• 1 year ago

this is in the same tradition that prompted us to name the “wat” in honor of James Watt.

The unit is Watt, not Wat.

ahofmann• 1 year ago

I'm sorry, that you missed the hilarious joke!

For reference: https://www.destroyallsoftware.com/talks/wat

thrdbndndn2• 1 year ago

Ahh, I get the joke now. Good one :)

As for the reason, if I have to guess, is because "decibel" looks better than "decibell".

(Keep in mind decibel was actually renamed from the previous unit called "Transmission Unit" and was meant to be used as the main unit even at the beginning. "bel" was simply derived/implied from it, not the other way around).

kazinator8• 1 year ago

Whoosh ...

reichstein• 1 year ago

Your irony detector may need calibration.

Or mine does.

kristjank• 1 year ago

This seems exceedingly ignorant of the work decibels do in telecommunications, RF and fibre engineering. The voltage vs power relationship is something that exists and is a core memory of beginner blunders in the field, but it boils down to a simple 10 vs 20 division operation. Besides that, the decibel simplifies a lot of multiplying very small and very big numbers to summing of two-digit numbers that you can do in your head, and still preserve a big degree of accuracy.

Whining about it makes me really doubt that the OP has any practical experience about the things they're talking about.

atoav3• 1 year ago

As someone who teaches this concept to.. art students I have to say that this complaint sounds a lot like the typical misconceptions and confusions a beginner would have.

Yes, dB is a weird and unintuitive concept and it takes a moment to understand it, but it is also extremely useful once you get it. The fact that people don't write out the reference values does not help either, people will bounce out that audio mix at -20dB when in fact they mean -20dBFS which is referenced to the digital maximum (Full Scale) value. Above 0dBFS you clip the waveform.

People leaving out the reference part is the mean reason for the confusion IMO.

im3w1l• 1 year ago

So one thing I always wondered about with audio mixing is that clipping should be random? Like if the sine waves somehow all line up the momentary amplitude could be much greater than the typical amplitude.

And this would mean that there isn't a fixed volume above which you get clipping and below which you don't get clipping. Playing tricks with phases could prevent/cause clipping.

Is -20 db then simply a rule of thumb for preventing occasional clipping?

rocqua7• 1 year ago

Decibels in gain, those are fine. Though they use a silly base. dBm makes a decent amount of sense, given the RF background. The fact that decibels work differently for voltage and power is very weird, but understandable in isolation.

But audio decibels are horribly underspecified. And any other use of a decibel as a dimensionful unit is horrible. I think the RF people know, and that's why they use dBm. Any system that uses decibels as dimensional units needs to make their baseline clear.

I recently saw a fan advertising a low decibel noise "at 3 meters". And it's nice that they advertise (part of) the baseline, but it sweeps a ~10db difference in pressure under the rug, comparee to the standard 1m reference.

mikewarot3• 1 year ago

Decibels aren't units... they are ratios. The ratio could be gain, or loss, or compared to the noise floor, or the signal of interest, or a standard unit, such as Watts, milliWatts, or microVolts into 50 ohms.

The fact that decibels work differently for voltage and power is very weird, but understandable in isolation.

If you have a given load, increasing the voltage by a ratio of 10:1 (20 dB) is exactly the same as increasing the power by a ratio of 100:1 (20 dB) (because increasing the voltage ALSO increases the current, and the power is the product of the two)

holowoodman• 1 year ago

Decibels are completely ridiculous. They are only useful if you are a cable monkey just adding and subtracting amplification/dampening factors. As soon as you need to do any kind of non-trivial conversion or computation, dB* is more of a hindrance to understanding and simplicity, because you will always need to look up in some strange table of dB weirdness. Integrate over a spectral power density in dB/Hz? You better convert that to real metric first... Need to solder in a capacitor/resistor/coil as a filter? Better convert to real metric first, because only some pre-made filters are specified in dB (and there are quite a few weird conventions, so you better convert to real metric and check first...).

lifthrasiir5• 1 year ago

I do see needs for something like decibels. It is a useful way to communicate an inherently logarithmic quantity. The real and IMHO only mistake is that it was described as a typical unit, while it should have been a unit constructor and specially treated in the SI unlike others. (Not in the SI, but the [milli]meter in mmHg etc. and `p` in pH---really p[H+] [1]---are other popular examples of unit constructor.)

[1] To be clear, I'm aware that pH and p[H+] are technically different. But that's orthogonal here.

MegaDeKay2• 1 year ago

I'd say the engineers I knew building satellites at companies like SS/L and Boeing deserved a better title than than "cable monkeys".

mwbajor• 1 year ago

They're just ratios....

svara4• 1 year ago

makes me really doubt that the OP has any practical experience about the things they're talking about.

Maybe not, but you can get used to many odd things given enough experience.

I totally share the authors view. I don't usually have trouble grasping the definition of a unit, but dBs are just hilariously overloaded.

The same symbol can literally mean one of two dimensionless numbers, or one of who knows how many physical units.

That's not normal, something as basic as units is usually very cleanly defined in physics.

Someone in this comment section said it's not a problem because there's usually going to be a suffix that is unambiguous. If that were actually the case, you wouldn't see these types of complaints.

rusk6• 1 year ago

dB for sound in particular aligns with human experience. The (10 -) 1-10 on a volume knob typically aligns with a logarithmic scale because we hear differences in loudness at an order of magnitude.

A linear volume knob would be frustratingly useless as you would have to crank it many many many times the higher up you want to go. Presumably hundreds of times. A traditional pot couldn’t do that of course but maybe you could satisfy your curiosity with a rotary encoder?

TheOtherHobbes• 1 year ago

This like arguing that aspect ratios are stupid and wrong because sometimes they apply to a screen which is really big and sometimes it's really small and sometimes they apply to a physical print or a photo or a billboard or a vintage TV and sometimes it's a jpg or a PNG.

Aspect ratio is a ratio. It can be a ratio between pixel counts, or between print dimensions, or physical display dimensions.

All of which are useful in their own way, none of which are directly comparable, all of which are understandable in context.

dB is the same. It's a ratio split into convenient steps - more convenient than Bels would be - that compares two quantities. The quantities can be measured in different units. The units are implied by the context.

The only mild confusion is the relationship between voltage and power ratios. But that's a minor wrinkle, not a showstopping intellectual challenge.

NobodyNada• 1 year ago

Consider the signal chain of a live audio system, from a singer to a PA.

The singer produces sound pressure waves into a mic. These pressure waves are measured in dB SPL, and the microphone's specifications will tell you its sensitivity, maximum sound pressure level, frequency response, on- and off-axis response, and so on. An engineer can look at all these specs to choose a mic based on the environment, how much background noise there is and where it's coming from, the quality and character of the singer's voice, etc.

The microphone will produce a voltage, which is measured in dBV or dBu. This voltage travels to a preamplifier, which boosts the signal to a nominal level by applying a gain (in dB, with no units since it's just a dimensionless ratio between input level and output level) and converts it to a digital signal -- measured in dBFS ("decibels full-scale", signal level relative to the maximum level that can fit in the bit-width of the digital signal).

Note that all the different signals going into the preamps have wildly different voltage levels -- a kick drum produces much more sound energy than a singer. And the ratio between SPL and voltage is not fixed; different mics have different sensitivities, and an active guitar amp will generate a signal many orders of magnitude stronger than a passive microphone. For some instruments like synthesizers, "SPL" isn't even a concept that makes sense because the sound is produced entirely electronically, rather than by capturing a mechanical wave. So, the preamps are configured to normalize all the incoming signals to one nominal level for processing.

After the preamp, the signal goes through a digital signal processing chain. Most of these processing steps will affect the level of the signal, and the amount is measured in dB (without units, since this is a dimensionless ratio between input level and output level. Remember, we're dealing with a fully digital waveform, so there is not even a physical measure of "loudness" or "signal strength" that can apply to the signal at this point.)

The signals from all the different sound sources are mixed together, and the mixer's per-channel volume faders are marked in decibels -- usually from +10 to -infinity, with 0 corresponding to "unity gain" (which means the output signal should have the same intensity as the input signal). Again, no units because we aren't measuring a physical quantity, just how much the mixer should change the intensity of the signal.

Finally, the signal is converted back to an analog voltage (measured in dBu) and sent to a power amplifier. The power amplifier applies an adjustable gain, and outputs a signal measured in watts (dBm) for sending to the PA system. You might then walk around the room with an SPL meter to ensure the sound is at a safe level; the value you measure will depend on the frequency and directional response of the speakers, as well as how far away from the speaker you're measuring.

Throughout this process we had signals in the form of sound pressure, voltage, digital samples, and wattage, at power levels ranging from microwatts to kilowatts. Even a simple physical quantity like sound pressure for a single signal is not straightforward -- how far are you measuring it from, and are you talking about SPL before the microphone or after the speaker?

The fact that a single unit is used for all of these different purposes is a feature, not a bug. If my preamp is close to clipping and I turn it down by 3 dB, how much do I need to turn up the gain at my compressor to compensate? Easy -- 3 dB. If we used more "appropriate" physical units at each step of the signal chain, it would be impossible to determine this number quickly or in your head; and would involve taking into account even more factors I haven't mentioned (like input impedances). The fact that decibels are scaled differently depending on whether you're working with voltage or power means that 1 dB corresponds to the same change in loudness everywhere without having to remember whether it's 1 dB of voltage or power.

jeroenhd2• 1 year ago

The same can be said of any unit. "If you just learn to work with it regardless of its weirdness, it's completely normal" doesn't mean the standard isn't ridiculous.

I don't think anyone has stated that a logarithmic scale is bad. The type of logarithmic scale changing depending on the field it's being used in, and the non-standard notation (dBm being used instead of dBmW for instance), is just inconsistent for no reason.

For a unit of immense scale, I rarely see it used outside of the -100 to 100 range, though. That puts its daily use square in the middle of SIs giga/nano range. I'm sure the formulae are a bit easier by not having to include exponents, but I don't see a practical reason why dB's normal use can't have been covered by normal prefixes.

What sets the dB* aside from other American units is that this one is very close to following standard units. If it weren't for the deci- prefix and the usage of standard units like Watts and Volts ("Bell-horsepowers"), the inconsistencies in practical use would probably have been expected, making learning about the weird intricacies of each field a lot less infuriating.

em3rgent0rdr4• 1 year ago

I don't see a practical reason why dB's normal use can't have been covered by normal prefixes

Because instead of numbers going like 1, 10, 100, 1k, 10k, 100k, 1M, 10M, 100M, 1G, and so on when using prefixes, we get a much more smoother numbers of 0 dB, 10 dB, 20 dB, 30 dB, 40 dB, 50 dB, 60 dB, 70 dB, 80 dB, 90 dB. You can see the the number for the dB get bigger, while when using prefixes the numbers get bigger two times in a row and then go back to smaller. With dB you usually just see a number from 0 to around +/- 100 or so. You can plot dB nicely as an axis of a chart and then see the slope of a curve in so many dB per decade.

MegaDeKay2• 1 year ago

I don't see a practical reason why dB's normal use can't have been covered by normal prefixes

Because you can easily add dB values that are on greatly different scales in your head, especially when the values aren't exactly powers of ten. If I have 86 dBW of Effective Isotropic Radiated Power and -162 dB of free space loss to some distance, the power flux density at that distance is -76 dBW/m^2.

neuroticnews25• 1 year ago

I think the "whining" is just a stylistic choice and an excuse to talk about the things he finds worth noting. I didn't perceive the tone of the article as negative.

ajuc4• 1 year ago

You can use logarithmic scale without making it a pseudo-unit that changes the factors depending on the application.

Additionally - attacking people you don't know for ignorance because they have different opinions is very narrowminded.

baxuz• 1 year ago

You haven't addressed any of the points the author made. You only show habituation and status quo bias.

iLoveOncall• 1 year ago

Doesn't OP addres that multiple times in the article? He constantly reminds that the unit means vastly different things based on the domain, and focuses on acoustics after that, which is what every laymen would think about given the mention of decibels.

metalman• 1 year ago

sound IS funny, db does work, and for people building the things that produce or record sound. Useing db is just another unit used in engineering. Now if someone wants to get into the (very facinating), psychoacoustic side of sound, where another unit has been tried, "phons", prounounced fonz ;) , then it becomes clear that determining sound pressure levels is a tricky thing, as at the low end of perceptable sound the real world power of the actual sound is miniscule when converted into heat or mechanical power, and at the othete end a amp/speaker set up that was 100% efficient would only need 5 or 10 watts of electricity to power a stadium concert. we work with what we have, in a past lifeI got a degree in sound engineering, but barely practiced it, found myself way more into enjoying the products that have been built to be used, but am always greatfull to the people who make it possible, who on occasion are entertained by the sometimes exotic ways that I abuse the equipment, as the good ones take pride in having thought of and planed for such things, but do like confermation from the field. STC ratings anyone?

jvanderbot• 1 year ago

The fact that the numbers on the scale align with intuition at a few points does not mean that the scale is a good one. dBs are jargon encoded with false rigor. No other "unit" has flexible meaning based on the background of the speaker, but jargon does.

verzali3• 1 year ago

Yeah that was my thought as well. Decibels make it much easier to do link budgets as you can just add or subtract instead of multiplying or dividing.

lxgr10• 1 year ago

That's an excellent application of Decibels (or really any other logarithmic unit). TFA's gripes are with the many not so great ones.

emilfihlman• 1 year ago

You are completely missing the point, which is that decibels are opaque and carry hidden field specific meaning that is not possible to know from the "unit".

This is not a criticism of how useful they are in calculations.

rcxdude2• 1 year ago

I work in a related field (lots of signal processing, but not necessarily RF-y or audio-y), and it's a constant source of confusion. I actively avoid using them in technical communication because they will be misinterpreted by someone, and when we have customers who use them they usually don't actually know enough context to disambiguate them.

mapt• 1 year ago

Having a logarithmic scale is a very different feature than having this one symbol to express all logarithmic scales with contextual meanings that sometimes need to be incorporated as two or three separate variations in a conversation.

Why wouldn't this work better broken out as half a dozen different units, with objective zero points and mathematical convertibility?

sanderjd17• 1 year ago

"It's weird and blunder prone but useful" is not actually a counterargument to the author, who is not arguing that it is not a useful thing.

viraptor12• 1 year ago

and is a core memory of beginner blunders in the field

Are you into creating artificial issues to make understanding things harder? If not... what's your point?

doubt that the OP has any practical experience

One quick search would save you from writing a very silly thing.

jeremyscanvic• 1 year ago

Another surprising place decibels pop up, pretty far from loudness related things, is in image comparison metrics. Peak signal-to-noise ratio is mean squared error normalized by a certain peak intensity and it is generally expressed in dB, i.e. as 10 log10(normalized mse). https://en.m.wikipedia.org/wiki/Peak_signal-to-noise_ratio

Edit: typo

rocqua7• 1 year ago

Decibels make a lot of sense for ratios in any kind of signal processing.

They are not that suited to sound, but sound is generally hard to quantify.

fouronnes3• 1 year ago

When I worked on a radar project, my fellow radar engineers (I'm software) used dB a lot. A lot of them would actually agree with the article, but historical sometimes wins even when you're aware of its shortcomings. Aren't we the same in software anyway? The email protocol, terminal escape sequences, the UX of git command line, etc... Each of those could have an "X is ridiculous" blog post (and I would enjoy every single one).

One upside of dB not touched in the article is that it changes multiplication into addition. So you can do math of gains and attenuations in your head a bit more conveniently. Why this would be useful in the age of computers is confusing, but on some radio projects both gains and losses are actually enormous exponents when expressed linearly, so I sort of see why you would switch to logs (aka decibels). Kinda like how you switch to adding logs instead of multiplying a lot of small floats for numerical computing.

lxgr10• 1 year ago

A lot of them would actually agree with the article, but historical sometimes wins

Indeed – as evidenced by some parts of the world still using non-metric units in daily life or even engineering :)

perching_aix5• 1 year ago

As a European if somebody tells me the diagonal size of a display in cm or meter, I'm simply not able to "grasp" it. I need to whip out the calculator and divide by 2.54, turning it into inches. It's just how monitors are measured in my head at this point.

deepsun• 1 year ago

Statistics once got me off-guard because that historical baggage. I thought I knew the probability theory pretty well to carry it to Statistics, but man, Statistics is a very different beast because it developed independently of Mathematics.

lifthrasiir5• 1 year ago

The only thing you should know is that any use of bel and thus decibel should ideally have the reference level suffixed (usually in parentheses or subscript), not implied. The absolute sound pressure level is dB(SPL). The human-perceived loudness level is dB(A) and similar. The RMS voltage expressed in power is dB(u) (formerly dB(v), not same as capital dB(V)). And so on. And then each different instance of dB unit is simply distinct, only connected by the fact that it represents some ratio in the logarithmic fashion. Treat any new dB unit you haven't seen as an alien.

hashhar2• 1 year ago

This is exactly it. The people who get confused by decibels are treating it a unit in it's own right when it's really just a ratio of some unit.

margalabargala3• 1 year ago

Disagree.

The people who get confused by decibels, are exposed to other people treating it like it's a unit in its own right.

I agree that what the parent described, should be done. If it was what was done, this article wouldn't exist.

agos• 1 year ago

people are often confused by decibels because the necessary disambiguation is more often than not absent (see: spec sheets of some kind of appliance talking about noise)

jancsika• 1 year ago

The human-perceived loudness level is dB(A) and similar.

But db(A) doesn't really measure that for anything but sounds that could cause hearing damage, or test tones. You've essentially taken a newcomer's problem of underspecification and carried it into the given domain.

I feel like it'd be better to say dB(A) measures flaunkis, which is defined by the human frequency response. Then the newcomer's next question will be something like, "how do I use flaunkis to compute the loudness of a music recording?" And that's the right question to ask, because the answer is: it's complicated. :)

davrosthedalek14• 1 year ago

That is of course not true. dB without reference is perfectly fine to use for gain and attenuation. dBm or any of the variants would be flat out wrong.

mitthrowaway2• 1 year ago

Even then, you'll get different results if it's 10 dB of voltage gain or 10 dB of power gain. You need to know what the actual units are.

nyeah6• 1 year ago

...unless we're talking about a unitless ratio, like "this has 10dB less power than that". Which happens a lot.

lifthrasiir5• 1 year ago

But we used to use the same unit for the absolute measure and the relative measure, like degrees Celcius/Fahrenheit. (Okay, % vs. %p is different but is probably an exception.) I see no particular reason to avoid suffixes in such situations.

yuvadam• 1 year ago

Decibels aren't actually that ridiculous if you just accept them as plain logarithmic ratios, between your signal and the noise floor or some other signal. (Or between anything else, really.)

3dB is roughly double, 10dB is 10x, but only sounds about twice as loud because our ears are weird.

kazinator8• 1 year ago

This means that if you’re talking about watts, +1 bel is an increase of 10×; but if you’re talking about volts, it’s an increase of √10×. This is nuts: it’s akin to saying that the milli- prefix should have different meanings depending on whether we’re talking about meters or liters.

Well no, because even if you are focusing on a signal measured in volts, the bel continues to be related to power and not voltage. As soon as you mention bels or decibels, you're talking about the power aspect of the signal.

If volume were measured in meters, which were understood to be the length of one edge of a cube whose volume is being given, then one millimeter (1/1000th of distance) would have to be interpreted as one billionth (1/1,000,000,000) of the volume.

When you use voltage to convey the amplitude of a signal, it's like giving an area in meters, where it is understood that 100x more meters is 10,000x the area.

There could exist a logarithmic scale in which +3 units represents a doubling of voltage. We just wouldn't be able to call those units decibels.

dj3l4l3• 1 year ago

The Bel is a unitless quantity. Yes, by convention, in certain fields, it applies to the logarithm of the ratio of powers. But in other fields (for example, quantifying a change in the degree of evidence for a hypothesis, as in Bayesian probability theory) it is applied to a ratio of different quantities (in the Bayesian case, a ratio of probabilities). There is no reason why dB can't be used for any unit, and its meaning is incomplete until the denominator of the ratio within the logarithm is known.

This is the gripe that is being conveyed in this article. Mathematically, the Bel is unitless. It is only by additional context that one can understand the value of the denominator in the logarithm.

paipa2• 1 year ago

The denominator isn't the issue. The context-dependent base of the logarithm is, which makes 1 Bel = 10x for some things and 1 Bel = 3.16x for others.

I've never heard of decibels used in probability theory. Did they adopt it with the same baked-in bastardizations? Please tell me +10dB(stdev) = +10dB(variance) isn't a thing.

kazinator8• 1 year ago

Mathematically, the Bel is unitless because it is a function applied to a ratio of measurements. Whatever units those measurements have disappear due to the cancelation.

If that measurement is linked to another one in a nonlinear way, that nonlinearity doesn't disappear: the fact that if the unitless fraction in which certain units canceled out is 2, then the corresponding unitless fraction obtained via different units is 4.

Just because the units disappeared in a fraction doesn't mean they are not relevant.

leoedin• 1 year ago

I worked in RF (radar) for a while and the dB/dBm is an incredibly useful tool there. It makes reasoning about amplifier chains and insertion loss so much more straightforward. It also means you can talk about transmitters and receivers in a comparable unit - in reality the signals are many many orders of magnitude apart.

kazinator8• 1 year ago

The confusing thing about decibels is not the Watts versus Volts thing.

It is the following.

If you mix two identical signals (same shape and amplitude) which are in phase, you double the voltage, and so quadruple the power, which is +6 dB.

But if you mix two unrelated signals which are about the same in amplitude, their power levels merely add, doubling the power: +3 dB.

cycomanic• 1 year ago

That has nothing to do with decibels at all, that's the fundamental physics (or mathematics if you want) of adding waves, i.e. interference.

kazinator8• 1 year ago

Sure, but people who are confused by the voltage vs power thing (also fundamental physics) will likely be quadruply confused by this.

mousethatroared• 1 year ago

If they're identical and in phase, the addition is obviously a multiplication by 2 -> 6dB.

If they're unrelated the signals can also cancel out. So not 6bB. If not 6 dB then what is it? An integral that has already been solved for us :D

calmbonsai2• 1 year ago

If you're specifying decibels in written form you always include the basis or you're simply being incomplete with your units. I don't understand the complaint there.

In casual conversation, the context implies the basis.

Dealing with decibels is also another shorthand to know the domain has a wide enough value gamut such that logarithmic values (where addition is multiplication) makes sense. See also, the Richter scale.

Aachen4• 1 year ago

If you're specifying decibels in written form you always include the basis or you're simply being incomplete with your units. I don't understand the complaint there.

It seems that a lot of people who are specifying decibels in written form aren't aware of what you just said

Did you ever see someone use p as a unit and expect anyone to understand it means pico? Because I've seen that with dB. In this very thread. You really don't have to look far for the tendency for dB to be used as incomplete unit

See also, the Richter scale

Looking at the article and trying to substitute Richter, I can't imagine what you'd plug in the different positions:

- it's not a derivative of another relative unit (no decirichter)

- it was not originally meant for something else (dB was originally meant for power, leading to difference in meaning of dB in dB(V) vs. dB(W), if I'm understanding the article correctly)

- it's not trying to indicate the magnitude of the actual unit (you don't specify Richter-Volts or something, just Richter, so you can't forget to specify the actual unit)

- there aren't different meanings depending on the field you're in (a –45dB microphone is mentioned in the article as referring to Volts whereas an acoustic 10dB loudness difference is apparently in Pascals; Richters are always Richters)

The article criticises a lot of dB's aspects but I'm not sure the exponentialness is one of them

viraptor12• 1 year ago

I don't understand the complaint there.

The problem is that almost nobody does. I can't remember the last time outside of HN comments here that I've seen dB(A) or similar in real world.

calmbonsai2• 1 year ago

I guess I'm biased from my Electrical Engineering background as we use different decibels all the time so the basis is essential.

It would be akin to saying 'kilo', but not specifying a 'gram', or 'meter'.

That's fine for bakers as they don't work with kilometers routinely, but not for physicists or antenna engineering.

BenjiWiebe4• 1 year ago

Exactly! I have seen temperatures specified as degrees, without specifying Fahrenheit or Celsius. It's a bit like that.

My exposure to dB is mainly the RF field, and it's simple. dB is gain/loss (power ratio, just like the dictionary says!) and dBm is relative to a milliwatt. In software defined radio, you've got dBFS - relative to maximum representable. And they're all labeled correctly.

badlibrarian4• 1 year ago

Horsepower is a unit of measurement. There's hp and bhp and hpE and...

"Other names for the metric horsepower are the Italian cavallo vapore (cv), Dutch paardenkracht (pk), the French cheval-vapeur (ch), the Spanish caballo de vapor and Portuguese cavalo-vapor (cv), the Russian лошадиная сила (л. с.), the Swedish hästkraft (hk), the Finnish hevosvoima (hv), the Estonian hobujõud (hj), the Norwegian and Danish hestekraft (hk), the Hungarian lóerő (LE), the Czech koňská síla and Slovak konská sila (k or ks), the Serbo-Croatian konjska snaga (KS), the Bulgarian конска сила, the Macedonian коњска сила (KC), the Polish koń mechaniczny (KM) (lit. 'mechanical horse'), Slovenian konjska moč (KM), the Ukrainian кінська сила (к. с.), the Romanian cal-putere (CP), and the German Pferdestärke (PS)." [1]

Decibel is not a unit of measurement. Decibels are a relative measurement. It tells you how much louder or powerful something is relative to something else. And frankly far less ridiculous than horsepower, which has a hilarious Wiki article if you read it with a critical mindset.

Deriving some of the constants without Googling is a fun exercise to verify that you're not as smart as you think you are. "Hydraulic horsepower = pressure (pounds per square inch) * flow rate (gallons per minute) / 1714"

[1] https://en.wikipedia.org/wiki/Horsepower

thaumasiotes2• 1 year ago

"Other names for the metric horsepower are [...]"

I'm not clear on what point you think you're making. Is it interesting that the same thing might have different names in different languages?

That subsection of the article, by the way, is obviously lying:

The various units used to indicate this definition (PS, KM, cv, hk, pk, k, ks and ch) all translate to horse power in English.

cv and ch translate to steam horse, which isn't hard to see even if you only speak English. What does "vapor" mean to you?

The opening of the article does suggest some problems, though not problems that wouldn't apply to the word "ounce". But you seem to have pulled an extended quote describing a completely expected state of affairs, while ignoring this:

There are many different standards and types of horsepower. Two common definitions used today are the imperial horsepower as in "hp" or "bhp" which is about 745.7 watts, and the metric horsepower as in "cv" or "PS" which is approximately 735.5 watts. The electric horsepower "hpE" is exactly 746 watts, while the boiler horsepower is 9809.5 or 9811 watts, depending on the exact year.

I don't get it.

badlibrarian4• 1 year ago

That a unit of power has a dozen metric abbreviations and converts to watts at different values depending on what it is measuring (and when) is precisely the point.

Decibels aren't ridicluous or a unit of measure. Horsepower, however...

marcosdumay3• 1 year ago

Yes, those are the reasons why nobody uses horsepower in an engineering context.

badlibrarian4• 1 year ago

I suppose if you don't count the engineers who work on engines. Or those expensive dynos that use the big font to report horsepower then plot it on the chart along with torque.

bob1029• 1 year ago

I think dB is a good way to represent certain user interfaces. I've always preferred to operate my audio equipment using a logarithmic scale. Changing the volume is much more intuitive to me this way than with some linear 0-100 mapping.

severusdd• 1 year ago

While I thoroughly enjoyed reading this piece of internet-rant, I've to argue that dB is still probably the best we have on this!

In RF engineering, expressing signal levels in dBm or gains in dB means you can add values instead of multiplying, which definitely appeared like a huge convenience for my college assignments! A filter with -3 dB loss and an amplifier with +20 dB gain? Just add. You can also use this short notation to represent a variety of things, such as power, gain, attenuation, SPL, etc.

I guess, engineers don’t use dB because they’re masochists (though many of them surely are). They use it because in the messy world of signals, it works. And because nobody knows anything that might work better!

modeless• 1 year ago

There's nothing wrong with using a logarithmic system, that's not the complaint here. The complaint is that using decibels instead of bels is weird, and also that it's a scale and not a unit but people use it as if it was a unit without specifying a reference point, and also that the scale changes for different base units. Crazy how many people here are missing the point.

blackguardx• 1 year ago

dBm is fully defined. Its reference is 1 mW into 50 ohms. I agree that using dB as a unit and not as a comparison (10 dB more power) is confusing, though.

em3rgent0rdr4• 1 year ago

For some reason, the bel — again, what started as a sensible 10× increment — was soon deemed too big to use. I don’t quite know why: in other aspects of life, decimal notation suits us just fine.

Decimal notation can be a tad cumbersome to write and speak. Meanwhile, decibel usage commonly results in nice simple numbers that range between 0 and 100, with the fractional digits often being too insignificant to say out loud. For instance, the dynamic range of 16-bit audio (which is generally all the range that our ears care about) is 96 dB, while volume increments smaller than 1 dB aren't really noticeable, so decibel makes it easy to communicate volume levels without saying "point" or writing a "." or breaking out exponential notation. Even in fields other than audio the common ranges also conveniently will be around 1 dB for being on the verge of significance to around 100 dB or 200 dB for the upper range. (Also the whole power vs root-power caveat is simply something users of dB have to be cognizant of because we need to stick with one or the other to make consistent comparisons, and at the end of the day physical things hapen with power.) So while decibels may seem ridiculous, they actually are quite convenient for dealing with logarithmically-varying numbers in convient range from 1 dB to around 100 dB or so in many engineering fields.

em3rgent0rdr4• 1 year ago

Its like why we use percent from 0% to 100% instead of speaking of ratios from 0 point something to 1.

cousin_it2• 1 year ago

Yeah. And don't get me started on the folks who think "6dB/octave" is a reasonable thing to say. Which is, apparently, everyone who works with audio filters except me.

jpc0• 1 year ago

How else would you describe what occurs other than 6dB/octave?

badmintonbaseba• 1 year ago

Notice how both dB and octave are ratios, but for some reason for frequency ratios we don't use bels or decibels. An octave is a ratio of 2, a bel is a ratio of 10.

cousin_it2• 1 year ago

For a 6dB/octave lowpass filter, I would say power gain is inversely proportional to frequency squared (1/f^2). There's precedent for this notation, for example pink noise is known as both 3dB/octave and as 1/f.

taneq2• 1 year ago

You use a unit that maps well between the thing you want to measure and the thing you want to know about it. If you do this enough with the same until you give it a name. I don’t get the author’s complaint.

mjaseem• 1 year ago

When you want to measure a related but different quantity, don't use the same name as the first one because that leads to confusion. This rule is not followed by Decibel and that is complaint.

undebuggable• 1 year ago

If decibels in acoustics confuse you, try learning decibels in optical communication. That's a witchcraft.

varjag3• 1 year ago

Decibels are not anywhere near as ridiculous as Marketing Kilobytes introduced in the 1990s. Pot, meet kettle.

nayuki10• 1 year ago

This is one of those cases where marketing is correct.

Oh tell me, if your CPU processes 1 byte in 1 cycle, and it runs at 800 MHz, how many bytes does it process in 1 second?

The answer is 800 million bytes, or 800 (real) megabytes. It cannot be 800 mebibytes. (Equal to 763 mebibytes.)

Similarly, let's say we have a 1-bit Boolean attribute for each person in the world, and the world population is 8 062 000 000 billion people. How many bits do we need in our database? It's 8.062 gigabits, not 8.062 gibibits. (Equal to 7.508 gibibits.)

The telecom industry has always used power-of-1000 prefixes on bits and bits per second. You have a gigabit Ethernet LAN, and assume no protocol overhead. How long does it take to transmit a 4.7 GB (real gigabytes) DVD image? Multiply by 8 to convert from bytes to bits, so that's 37.6 Gb, so that will take 37.6 seconds to transmit. But how long does it take to transmit a "700 MB" (actually MiB) CD image? Well, it's 734 MB (real megabytes), so 5872 Mb, which is 5.872 seconds.

The problem with the abusively overloaded definition that 1 kilobyte = 1024 bytes, 1 megabyte = 1048576 bytes, etc. is that it fails to align with the rest of the metric system, or even how we group decimal numbers into thousands and millions. The computer industry is wrong here.

And now you have the problem that you can't fit a memory dump of "16 GB" of RAM onto a "16 GB" flash memory card, because the former is actually GiB but the latter is real GB.

varjag3• 1 year ago

Oh tell me, if your CPU processes 1 byte in 1 cycle, and it runs at 800 MHz, how many bytes does it process in 1 second?

An interesting metric, used by noone in the Universe except you for the sake of this discussion. But let's entertain this: if the actual CPU speed is 838,860,800Hz, how many bytes does it process in 1 second?

Similarly, let's say we have a 1-bit Boolean attribute for each person in the world

I have no problem with definition of bits.

And now you have the problem that you can't fit a memory dump of "16 GB" of RAM onto a "16 GB" flash memory card, because the former is actually GiB but the latter is real GB.

Remarkable circular reasoning, since the Marketing Kilobyte was defined in the 1990s precisely to inflate actual storage sizes without getting class action suits.

it fails to align with the rest of the metric system

Look, byte is not derived from fundamental units. It is thus not a part of metric system so SI has zero business regulating information storage. On the other hand you can't buy a computer that does not address memory in anything other than powers of two. Nor you could ever buy a 1000 million bytes RAM chip, because they don't ever exist for basic reason that binary computers use 2^n addressable space.

nyanpasu64• 1 year ago

I have a vague report that "root-power" or voltage-like quantities (20 dB per order of magnitude) are signed or vector-like, while power-like quantities are unsigned scalars?

nabla9• 1 year ago

Decibel is ridiculously overloaded concept.

It can be used to express and calculate relative change in power, amplitude ratios, and absolute change. All of these are different units and should always use different notation, but sometimes it's skipped.

stephen_g• 1 year ago

But a lot of them can be combined - like you can take dBm of a microwave signal going into a filter, subtract the dB figure of loss through a filter, add the dB figure of gain through an amplifier, then add the dBi of antenna gain, and get a meaningful number (equivalent isotopic radiated power or EIRP, in dBm) out the end! It’s quite amazing!

amai• 1 year ago

Fahrenheit on the other hand makes sense...

pajko• 1 year ago

Loudness is not measured in dB, but in phon (https://en.wikipedia.org/wiki/Phon) or sone (https://en.wikipedia.org/wiki/Sone).

dubcanada• 1 year ago

Tell that to everyone on the planet who uses dB

mattclarkdotnet• 1 year ago

Or dB(SPL) as a ratio of the phon.

cesaref• 1 year ago

Generally speaking, the db scale is very useful for many practical situations, and this is overlooked in this critique.

As have been pointed out, it's just a power ratio on a logarithmic scale, but this has many benefits, the main one being that chaining gain/attenuation in a system is just a case of adding the db values together. 'We're loosing 4db in this cable, and the gain through this amp is 6db, so the output is 2db hotter than the input'. Talk to any sound engineer and you'll do this sort of thing successfully without necessarily understanding the science, so that's a massive win.

remram• 1 year ago

I didn't get that reading the article. The author acknowledge that ratios are useful, but that there are specific problems in how we use this unit and how we picked and express the reference scales.

On the face of it, the idea makes sense.

Your specific example is a pure ratio so there's no problem with it (there is no reference). Apart from the fact that I have to guess whether you are measuring volts or watts through your cables, of course...

BenjiWiebe4• 1 year ago

So what I learned today, via another comment and confirmed with a dictionary, is that decibels (unspecified reference) is NOT pure ratio - it's a _power_ ratio. So it will be Watts, not Volts.

Aachen4• 1 year ago

this has many benefits, the main one being that chaining gain/attenuation in a system is just a case of adding the db values together. 'We're loosing 4db in this cable, and the gain through this amp is 6db, so the output is 2db hotter than the input'.

I'm not a sound engineer, so to check my understanding: would this not be the case for any other scale indicator?

If you have a cable that loses 4m and you're sending 6m into it, you'd not get 2m out?

(The m being milli here, as in millivolts or whatever unit would be useful here — leaving it unspecified to keep the comparison to dB as close as possible)

BenjiWiebe4• 1 year ago

It's a ratio, not a fixed amount. The amount you lose depends on the amount you send.

bitdivision2• 1 year ago

No, because db is logarithmic. That's the key property that allows you to do addition instead of multiplication. Remember these are ratios here as well.

So the original example in linear units would be: We're reducing the signal by 63% in the this cable, and the gain through this amp is 199.5%, so the output is...

0.63 * 1.995 = 1.26

126% which is 20log10(1.26) db or around 2db.

-4 + 6 = 2 is a little easier to do.

layer82• 1 year ago

Tangential question: Are there any sound meters that can actually measure down to 0 dB? The best I’ve seen specify 20 dB, which to me is still very audible.

(Note that, as the article mentions, 0 dB doesn’t mean “zero sound pressure”, but just “threshold of hearing”.)

danadam2• 1 year ago

Some laboratory-grade equipment probably.

0 dB doesn’t mean “zero sound pressure”

From the decibel definition, zero of anything is -∞ in dB_suffix scale.

layer82• 1 year ago

Some laboratory-grade equipment probably.

I wasn’t able to find any listings, that’s why I’m asking.

867-5309• 1 year ago

still doesn't answer what 0.3 Sone is in dBA

dogman1050• 1 year ago

His first equation is wrong. It should be P=V^2/R, not P=V^2R.

halayli• 1 year ago

this is one of the best videos to understand what a dB is and when it is used, and how to interpret them. what's unique about this unit is it relies a lot on the context.

https://www.youtube.com/watch?v=1mulRI-EZ80

numpad0• 1 year ago

I just can't understand why "[specialized domain] uses these stupid wrong units, it should be [unit that no educated smart SMEs use]" types don't do their researches to understand why those are used at all. This type of weird non-SI units appear when means of measurement and unit is related to one another and has downstream dependencies.

Just look at aviation. An airplane's:

  - speed is measured in knots, or minute of angle of latitude per hour, which is measured by ratio of static and dynamic pressure as a proxy.
  - vertical speed or rate of climb is measured in feet per minute, which is a leaky pressure gauge, probably all designed in inches.
  - altitude is measured in feet, through pressure, which scale is corrected by local barometric pressures advertised on radio, with the fallback default of 29.92 inHg. When they say "1000ft" vertical separation, it's more like 1 inHg or 30 hPa of separation.
  - engine power is often measured in "N1 RPM %" in jet engines, which obviously has nothing to do with anything. It's an rev/minutes figure of a windmilling shaft in an engine. Sometimes it's EPR or Engine Pressure Ratio or pressure ratio between intake and exhaust. They could install a force sensor on the engine mount but they don't.
  - tire pressure is psi or pound per square inch, screw tightening torques MAY be N-m, ft-lbs, or in-lbs, even within a same machine.

Sure, you can design a battery charging circuits in Joules, fly an airplane with a GPS speedometer, analog audio-radio circuitry in millivolts. Absolutely no one does. I think that cognitive dissonance should trigger curiosity circuitry, not rant mode.

I mean, just type in "use of decibels[dB] considered harmful" at the box at chatgpt.com. It'll generate basically this article with an armchair version of the top comment here as the conclusion.

anilakar• 1 year ago

Wait until you hear about unit conversions in aeronautical mental math. 1 NM across ground corresponds to 1000 or 100 feet of altitude in many conversion formulas. For small angles, sines and tangents are approximated by degrees of azimuth × distance in NM = 60.

tim3332• 1 year ago

The author gives the downsides but not the upside of why it is like that.

It's basically so it describes sound levels on an understandable scale with 0db being just audible and 100dB being very loud.

It also corresponds to the energy carried by the sound - 0 dB is 1 pW per square meter so it is kind of a scientific unit. It's probably easier to have a measure that is understandable by the public and let engineers do conversion calculations for signal levels in networks than the other way around.

jeroenhd2• 1 year ago

I assume you mean dB(A) here, because the sound level at dB(SPL) depends on the reference pressure chosen (20 mPa for db(A) with a calibrated microphone) and the constants for dB(A) are applicable to a large part of human sound perception. Though, if you use human perception as a reference, you'll also need to take dB(B) and dB(C) into account, depending on the sound you're playing and where you're playing that sound.

You can't use "dB" standalone. You need to specify what kind of dB you're talking about, because every field has different dBs that measure different units or are adjusted to different constants.

10dB is like 10k. 10dB is a tiny number if you're talking about volume, but blows your audio equipment if we're talking dB(u) or dB(v) (not to be confused with dB(V). In the same sense, 10k is a low number if it's the price for a new electric car, or an election changing amount of voters when talking about a population.

tim3332• 1 year ago

Ah - it's complicated I guess. I was looking at this stuff https://en.wikipedia.org/wiki/Sound_intensity#Sound_intensit...

cb321• 1 year ago

Abbreviation confusability is relative to { in fact one might say measured by ;-) - number? entropy? etc. } the listener/reader's knowledge/exposure, much as sound levels need a reference distance.

I have heard "bare K" refer to a great many different things, not just kilobits (transmission) or kilobytes (storage) or kilograms (drug trade) or kilometers (foot races) and on & on, but pages or items or etc.

The fundamental problem is that some humans like to abbreviate while others get caught and annoyed by the necessary ambiguity of such abbreviation. Sometimes this can be the very same human in different contexts. ;-)

In fact, there even seems to be some effect where "in the know people" do this intentionally - like kids with their slang - as a token of in-group membership. And yes, this membership is at direct odds with broader communication, by definition/construction. To me this article seems to be just complaining about "how people are". So it goes!

This is the primary complaint. The secondary one about voltage and power and the ambiguity of the prefix itself was addressed in another comment (https://news.ycombinator.com/item?id=44059611).

nayuki10• 1 year ago

I have heard "bare K" refer to a great many different things

The worst of the worst is when it refers to kilometres. Like, "I'm selling my car on the used market and its odometer is 150k", where they mean "150k km", but stacked prefixes are not allowed in metric, so the correct notation is "150 Mm" or "150 megametres".

I get immense pushback whenever I point this out - the response is usually along the lines of "but you know what I meant", and it inherently assumes that km is the universal unit for talking about distance traveled by car.

I point out that this is as ridiculous as saying "the hard drive is 4k GB" because they grew up with gigabytes; no, the correct notation is either "4000 GB" or "4 TB".

Also regarding bare k or kilo (especially キロ in Japanese), you can say something ridiculously ambiguous like "My scooter goes up to 30k for 90k and weighs 20k" (respectively km/h, km, and kg).

bombela• 1 year ago

In 3D printing, I often catch people talking acceleration in kilo-milli-meter/second². Written and pronounced "16k accel". Instead of writing "16m/s²" and pronouncing "16 accel".

I have nightmares of 150km meaning kilo-miles instead of kilo-metre. And when I say that my car has 260 mega-meter on the odometer, even people born metric look at me funny.

And don't get me started on MB vs MiB. I have seen so many stupid production outages because of people miss-allocating resources by confusing SI and IEC bytes.

/rant

lambdaone2• 1 year ago

It's a bit like hating numbers, and saying "What do you mean by 'three'; what is it - three volts, three amps, three metres? Clearly 'three' is meaningless, and we should stop using it and all the other numbers besides."

decibels are simply a dimensionless ratio, used as a multiplier for some known value of some known quantity.

In every context where decibels are used, either the unit they qualify is explicitly specified, or the unit is implicity known from the context. For instance, in the case of loudness of noise to human ears in air, the unit can be taken to be dBA (in all but rare cases which will be specified) measured with an appropriate A-weighted sensor, relative to the standard reference power level.

And similar (but different) principles apply to every other thing measured in dB; either theres an implicit convention, or the 0 dB point and measurement basis are specified.

People who assume that everyone is an idiot but themselves are rarely correct.

I look forward to the author discovering about (for example) the measurement of light, or colorimetry, and the many and various subtleties involved. The apparent excessive complexity is necessary, not invented to create confusion.

weinzierl2• 1 year ago

"decibels are simply a dimensionless ratio, used as a multiplier for some known value of some known quantity."

Except they are not. 1 dB can sometimes mean a ratio of ~ 1.26 and other times it can mean a ratio of ~ 1.12.

"In every context where decibels are used, either the unit they qualify is explicitly specified, or the unit is implicity known from the context."

Maybe in university, but certainly not in the real world.

20k• 1 year ago

I have a feeling that a lot of people here haven't read the article. There's lots of "Its just a dimensionless ratio" comments

hgomersall6• 1 year ago

It's a power ratio. 1dB always means a power ratio of 1.26. That might mean a voltage or current ratio, say, of 1.12, but that is because the relationship between voltage ratios and power ratios is a simple square.

tpoacher• 1 year ago

This sounds more like a problem with the 'real' world then.

lambdaone2• 1 year ago

In the "real world", techically competent people understand decibels just fine.

But this is not arcane knowledge only known by a priesthood. Since you are clearly confused about what a decibel is and how and why it is used, you can read

https://en.wikipedia.org/wiki/Decibel

and all will be revealed.

sanderjd17• 1 year ago

In every context where decibels are used, either the unit they qualify is explicitly specified, or the unit is implicity known from the context.

The author's whole point is that this is not true.

To adapt your analogy, it's not like being mad at the number three, it's like being mad about people not attaching any units to the number three, arguing that it's clear in context. It isn't!

klodolph9• 1 year ago

Sure, but the author is wrong.

“How old is your son?” “He’s 3.”

Clear in context. People write things like dB SPL (A-weighted) in spec sheets because spec sheets benefit from being unambiguous. Most of the time it’s really clear, like you’re talking about insertion loss or amplifier gain and there’s only one reasonable way to interpret it.

drob5189• 1 year ago

Just because the author is ignorant of the context doesn’t mean that the engineers working in those fields are. They use it because it all makes sense in context.

BobaFloutist• 1 year ago

I mean it's always a little bizarre when the default unit used to measure something is dimensionless. Why not set a default (like STP) that's assumed to be the baseline unless otherwise specified? It would be like if Celsius had no reference point and every time you said water boils at 100 degrees Celsius people came out of the word work to smugly correct you "Only if you first say 0 degrees C is when water freezes, which you can't assume. What if 0C is actually absolute 0?"

beloch• 1 year ago

Many scientific measurements are entirely contextual. e.g. What is 0 V? Ground? Is ground across the globe always at the same potential? Nope. What's ground on a space station? Ground potential is whatever we want it to be. You don't need to define what ground potential is in, say, a computer, relative to some global standard for things to work.

How about velocity? What's 0 m/s? What does it mean to be absolutely still? All motion is relative, and being still is entirely a matter of perspective. You might be sitting still on a train, but traveling very quickly relative to a cow standing still while you blow by.

Bels are a relative measure that confuse some because they pop up in different contexts that seem unrelated. However, they are useful when dealing with quantities for which most pertinent relationships are exponential. e.g. They work for sound because humans perceive exponential increases in volume in a linear fashion. Something that is 3dB louder is twice as loud in terms of pressure levels, but we only perceive it as a little bit louder. Sound pressure levels are both relative measures and an attempt to reflect human perception . That makes them, necessarily, a bit odd.

xeonmc• 1 year ago

Interviewer: "So what's the fastest you've gone on your bike?"

Kid: "Thirty."

Interviewer" "Thirty what?"

Kid: "Umm..."

Kid: "Speed."

[0] https://www.youtube.com/watch?v=OYt1kqDNlMY

dotancohen• 1 year ago

KSP measures funds in some unitless value, it drives me nuts. Everything else is almost (but not quite) perfect.

UncleMeat• 1 year ago

"I was doing 70 down the highway" is absolutely the sort of thing people say. From context (this conversation takes place in the US, most highways have a speed limit somewhere around 60-70mph) people understand that you are talking about miles per hour.

JoeDaDude• 1 year ago

Maybe you can say "6 dbm/s"

skrebbel2• 1 year ago

To be frank, your comment just reads to me as a "stockholm syndrome" type reaction to a needlessly complex unit that you're intimately familiar with.

You see the same in HN threads where people complain that eg Git or Rust are needlessly complex, there's a swath of people who are so emotionally invested in how well they understand the ins and outs of Git resp Rust that any suggestion that maybe things could be better makes them angry.

It's possible for decibels to be usable and generally fine and also for them to needlessly complex, ie for there to exist better alternatives in each place they're used.

As an example, it makes no sense to me that eg in audio software, volume sliders start at 0 dB and then go down to negative $MUCHO, until complete silence at -Infinity. And then this same unit is also used to measure how loud my coffee machine is, somehow, but then it's suddenly positive and not a relative number at all? That's just weird shit, it's like expressing the luminosity of a pixel (in HSL terms) in lumen instead of a unitless percentage.

In the audio software context, it would be much more intuitive for "no sound" to be 0, and "full volume" to be 100, a bit like percentages. The "but volume needs to be logarithmic because that's how we hear it!" argument doesn't disallow that at all. Just because a slider goes from 0 to 100 doesn't mean that a 10 must mean 10% of the power output. Decibels are ridiculous.

amluto• 1 year ago

As an example, it makes no sense to me that eg in audio software, volume sliders start at 0 dB and then go down to negative $MUCHO, until complete silence at -Infinity.

This one doesn’t bother me. Those sliders, and especially the real analog sliders they’re modeled after, don’t have an absolute scale — they are attenuators that reduce voltage. So 0dB is the same as no slider at all, -20dB reduces voltage by a factor of 10, etc.

CamperBob2• 1 year ago

dB is always relative, even when it appears to be an absolute unit. The 0 dB marking at the top of the volume slider on pro audio gear (more likely +3 or +6 or something similar to leave some headroom) means "0 dB relative to the maximum rated power level." In pro gear this will be an absolute industry standard of some sort, likely one where the load impedance is also defined. 1 milliwatt into 600 ohms or something like that. The distinction between voltage and power is always going to confuse people, but that's not the dB's fault.

A major reason decibels are used is to make it easy to assess the overall gain or loss of an entire chain of processing stages: you simply add the numbers. The equipment's output can only go down from 0 dB, so the rest of the scale is negative.

As for sound pressure levels in dB, those are given relative to a 0-dB point that corresponded originally to the faintest sound people were generally considered capable of perceiving. These days "0 dB" refers to a specific amount of acoustic power, which I don't know off the top of my head, and that might or might not be near the threshold of perception for a given listener. But the reasoning still applies: amplification or attenuation of power levels is a simple matter of addition when expressed in dB. Arbitrarily defining a system's reference level to be 100 dB instead of 0 dB would be of no use to anyone.

nyeah6• 1 year ago

It makes perfect sense that the sliders start at 0dB and go down to -inf. Maybe you don't understand it, but it definitely makes sense. Everyone who uses dB has also tried a % scale with 100% as 0dB, and then later made a conscious choice to figure out how dB work.

Maybe they're all in a conspiracy to make things needlessly complex. But that's not the only possibility.

regularjack• 1 year ago

There is no such thing as full volume, and there is not such thing as zero volume.

klodolph9• 1 year ago

If you want 0 = no sound, then you can’t use a logarithmic scale. You end up with sound being measured as Pascals in the micro to unit range.

“0 dB SPL” is 20 micro pascals which is roughly the threshold of hearing. A loud rock concert at 120 dB SPL is 20 pascals (no micro). The dB figures are a lot more convenient to work with.

It’s intuitive for 0 to be silent and 100 to be full, but if you work with audio you learn that dB are more convenient. Long-term convenience for experts tends to win out over short-term intuition for non-experts. This is why musicians continue to use sheet music and all of its seemingly ridiculous conventions—and likewise, decibels only seem ridiculous to people who don’t work in audio.

I don’t know what more usable alternative there would be, to decibels.

_kb2• 1 year ago

volume sliders start at 0 dB and then go down to negative $MUCHO, until complete silence at -Infinity. And then this same unit is also used to measure how loud my coffee machine is.

They're not the same unit, at all.

The audio software is a skeuomorphism from an analogue mixing console that is applying a change to a signal. 0 is unity gain and deviation from this describes an amplitude variation. This is important, as it means you are either discarding information by lowering the level and reducing dynamic range, or interpolating new information (/ decreasing SNR) by applying gain. This is less important today with floating point, but has strong historical reasons for existence across both analogue and digital domains.

If you look at an audio power amp, you will likely have some form of positive number as this is applying gain. Depending on the context this may have some specific meaning or it may be a screen print of a Spinal Tap logo and the numbers 1..11. These are all just UI decisions and part of doing that well is presenting coherent information for the target user group.

When you're talking about an acoustic noise source this is dB SPL which is a quantifier against a physical reference. That reference level quantifier is omitted a lot, which leads us to a lot of the angst in this post and the comments here. These are precise measurements, with very specific meaning. Their expression is often sloppy, but the units aren't to blame.

(excuse me while I got "full HN" here - I appreciate the irony in this response noting your first few sentences)

The reason people respond strongly to comments like this (or those about Git, or Rust) is because details matter. When you immerse in a domain, you learn the reason for those details. That does not mean things can't be improved, but this also does not imply those details can be removed or are wrong. A lot of the world, particularly when working outside of the bounds of a computer, depends on necessary complexity.

davrosthedalek14• 1 year ago

Ok, I bite. Please come up with a mapping of 0 to 100 to -inf dB to 0 dB attenuation.

And then put two in series. Is there a simple formula to calculate the total attenuation?

This works flawlessly with dB. Just add. And it doesn't matter how you break it: -20dB and -20 dB in series is the same as -40dB and 0dB.

baxtr• 1 year ago

People who assume that everyone is an idiot but themselves are rarely correct.

Print this, frame this, put this up on walls in schools, offices, heck even outdoor on large billboards!

anthomtb• 1 year ago

And before doing any of that, get it tattooed onto your own forearm.

DonHopkins4• 1 year ago

Some people just hate certain numbers.

Many buildings don't have a 13th floor because superstitious people think it's unlucky.

Some people lose their shit at 8647 because paranoid delusional people think it's out to kill them.

lxgr10• 1 year ago

It's a bit like hating numbers, and saying "What do you mean by 'three'; what is it - three volts, three amps, three metres?

No, it’s a bit like saying “for chocolate M&Ms, 3 obviously means 9, to compensate for the fact that they’re much smaller than the peanut ones”.

timerol4• 1 year ago

Can I get 3 M&Ms? Obviously I mean 3 serving sizes, how else would you measure M&Ms?

DonHopkins4• 1 year ago

At least the Mel-frequency cepstrum is honest about being a perceptual scale anchored to human hearing, rather than posing as a universally-applicable physical unit.

https://en.wikipedia.org/wiki/Mel-frequency_cepstrum

Mel-frequency cepstral coefficients (MFCCs) are coefficients that collectively make up an MFC. They are derived from a type of cepstral representation of the audio clip (a nonlinear "spectrum-of-a-spectrum"). The difference between the cepstrum and the mel-frequency cepstrum is that in the MFC, the frequency bands are equally spaced on the mel scale, which approximates the human auditory system's response more closely than the linearly-spaced frequency bands used in the normal spectrum. This frequency warping can allow for better representation of sound, for example, in audio compression that might potentially reduce the transmission bandwidth and the storage requirements of audio signals.

https://en.wikipedia.org/wiki/Psychoacoustics

Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.

jampekka• 1 year ago

For instance, in the case of loudness of noise to human ears in air, the unit can be taken to be dBA (in all but rare cases which will be specified) measured with an appropriate A-weighted sensor, relative to the standard reference power level.

This was covered in the article. But also it was discussed why things aren't this simple.

People who assume that everyone is an idiot but themselves are rarely correct.

Indeed.

timerol4• 1 year ago

multiplier for some known value of some known quantity

Of course, unless it's a multiplier for an unknown value of a known quantity, like every amplifier, filter, and sensor specified in dB.

For instance, in the case of loudness of noise to human ears in air, the unit can be taken to be dBA

Unless you're using dBB or dBC, but of course we all know exactly why you'd use dBC (more suitable for figuring out safety of high impulse, short events) or dBB (it's somewhere in between - you'll know it when you see it).

The apparent excessive complexity is necessary, not invented to create confusion.

Wait, so writing dB instead of dBA is now necessary, not just convenient?

WhitneyLand• 1 year ago

People who assume things are not complex because they understand them are rarely correct.

The complexity absolutely is not necessary. Maybe you mean to say it’s understandable or it’s coherent if you know the rules.

Physics doesn’t require us to create ambiguity by assigning DB to mean multiple possible ratios. If it needs to be disambiguated, then they both didn’t need to be DB in the first place.

mystified5016• 1 year ago

Exactly, the log(x) function is stupid and useless! It's the log of what? 6? Pi? Little-g? Same for logn(x). Who the hell is n?!

IvyMike• 1 year ago

People who assume that everyone is an idiot but themselves are rarely correct.

This is an off-by-one error.

ok_computer• 1 year ago

I think college undergrad physics and engineering is an important time to gain exposure to a variety of concepts and measures. Then you learn the people who discovered or invented these concepts were writing by candlelight and not washing their hands and didn’t have modern mathematics or computers and didn’t want to piss off the church. Oftentimes working at the pleasure of a rich sponsor family or king.

Like you have to describe relative intensity of waves in some way and these were experimental scientists, not commerce merchants looking for absolute interchangeability like weights and measures.

Computer blog people like standards and languageisms but science isn’t determined by big tech sponsored committee. It’s the best tool put forward so far and db is a physics concept and with a reference denominator you can calculate the absolute value. It’s fine. If you dabble with physics and expect the universe to make intuitive sense then you need an education.

Read books not blogs.

ttoinou• 1 year ago

Love this kind of articles but I wished the author suggested solutions.

I go even further than this author : sometimes decibels are computed using logarithms and what we put inside the logarithm has a physical unit. But I can prove mathematically that this is wrong and that whats given to a log function has to be dimensionless. Hence a lot of dB calculus is mathematically wrong and physically meaningless

adrian_b• 1 year ago

Decibels are not ridiculous, but very frequently the notations for quantities expressed in decibels are ridiculous.

The decibel is an arbitrary unit for the quantity named "logarithmic ratio".

Logarithmic ratio, plane angle and solid angle are 3 quantities for which arbitrary units must be chosen by a mathematical convention and these 3 units are base units, i.e. units that cannot be derived from other units. For a complete system of base units for the physical quantities, there are other 3 base units for dynamic quantities that must be chosen arbitrarily by choosing some physical object characterized by those quantities, i.e. a physical standard (originally the 3 dynamic quantities were length, time and mass, but in the present SI the reality is that mass has been replaced by electric voltage, despite the fact that the text of the SI specification hides this fact, for the purpose of backward compatibility), and there also are other 2 base units for discrete quantities (amount of substance and electric charge) which must be established by convention.

Like for the plane angle one may choose various arbitrary units, e.g. right angles, cycles, degrees, centesimal degrees, radians, or any other plane angles, for the logarithmic ratio one may choose various arbitrary units, e.g. octave, neper, bel, decibel.

So if we choose decibel all is OK. Decibels have the advantage that for those used to them it is very easy to convert in mind between a logarithmic ratio expressed in decibels and the corresponding linear ratio, so it is very easy to make very approximate computations in mind, but good enough for many engineering debugging tasks, in order to replace multiplications, divisions and exponentiations with additions, subtractions and rare simple multiplications, for a quick estimate of what should be seen in a measurement in a lab or in the field.

The problem is that whenever a logarithmic ratio is specified in decibels, it must be accompanied by 2 quantities, what kind of physical quantities have been divided and which is the reference value. Humans are lazy, so they usually do not bother to write these things, assuming that the reader will guess them from the context, but frequently the context is lost and guessing becomes difficult or impossible.

An additional complication is that one never uses logarithmic ratios for electric voltages or currents, but only for powers. When it is said that a logarithmic ratio refers to a voltage or a current, what is meant is that the logarithmic ratio refers to the power that would be generated by that voltage or current into an 1 ohm resistor. A similar problem exists for sound pressures, because logarithmic ratios are used only for sound intensities, so where sound pressure is mentioned, actually the corresponding sound intensity is meant.

This complication has appeared because voltages, currents and sound pressures are what are actually measured, but powers and sound intensities are frequently needed and using logarithmic ratios with different values for related quantities, while omitting frequently to mention the reference value, would have caused even more confusion than the current practice.

FRidh• 1 year ago

The problem with using decibels is that since it is a relative unit you need to know what it is relative to, and that is often not just the unit but also the quantity. Unfortunately, this part is (as expressed) at times omitted or put in the wrong place. And its often also the engineers in the respective fields that keep using this incorrect notation spreading the confusion for those outside the domain.

E.g., acoustic engineers often write db(A) for A-weighted sound pressure levels. Yes, it is often noted this way, but it is incorrect. The correct way is to specify the quantity and that the quantity is A-weighted, `L_{p, A} = 80 dB` for example to express an A-weighted sound pressure level of 80 dB.

Regarding sound pressure and sound power. Sound power is not expressed using A-weighting because it does not make sense. Sound power is a property of the source. A-weighting is a property of the receiver, that is, the human listener.

rightbyte• 1 year ago

The problem with using decibels is that since it is a relative unit you need to know what it is relative to

Ye but that is also the point. The author seem to prefer to memorize dozens of absolute values.

thinkingtoilet• 1 year ago

Not surprisingly, Tom Scott has an interesting video on this:

https://www.youtube.com/watch?v=Is_wu0VRIqQ

lamename• 1 year ago

I appreciate the sentiment, but I've found this resource [0] much more direct and comprehensive. It explains all of the nuance regarding dB and related terminology from audio engineering to perception (voltage, power, intensity, volume, loudness, etc.)

The format is a bit circular; just enjoy getting lost in it for half an hour.

https://sengpielaudio.com/TableOfSoundPressureLevels.htm

HPsquared• 1 year ago

It's a bit like "percent". A shorthand for dealing with ratios, often with hidden assumptions.

colejohnson66• 1 year ago

Sure, but you never say "the production is at 50%". 50% of what? Peak possible output? Typical output? That's what the author's complaint is: dB, while arguably useful, is annoying because people leave out the part that it's relative to. And then people, when talking about dB, assume the other party has knowledge of what their ratio is relative to. dBm, dbSPL, etc.

davrosthedalek14• 1 year ago

In every communication, the sender assumes that the other party has some knowledge. For example, I assume that you can read my badly worded English text. There is rarely confusion with the people in the fields that use dB a lot. That other people often get confused by dB is not a failure of dB, not even of its common use, the same way I can't blame English for not being Chinese, or for Americans use F instead of C, or K, for temperatures.

BlueTemplar6• 1 year ago

Insert mandatory complaint about percentages being misused : their point is the approximation : 1.02×1.03~1.05 <=> +2%+3%~+5%, which only holds up to low tens +/-%.

nayuki10• 1 year ago

There is a solution for you - log points! https://en.wikipedia.org/wiki/Relative_change#Logarithmic_ch... , http://a-loonie-saved.blogspot.com/2008/08/log-points.html

An example of deceptive arithmetic: A mutual fund's 5-year history of annual returns is −70%, +30%, +50%, +20%, +40%. Naively, the total return for the 5-year period looks like +70%. But in fact it's −1.72%, because the reciprocal function makes the −70% very “heavyweight” compared to the positive changes.

Using log points instead, the 5-year sequence is approximately −120.4, +26.2, +40.5, +18.2, +33.6. The sum of these rounded numbers is −1.9 (nowhere near +60.0), which agrees well with the correct result of about −1.735 log points (i.e. −1.72%).

kragen6• 1 year ago

This is an incredibly valuable article for anyone who's trying to make sense of decibels in some context. Michał clearly explains almost all of the gotchas you have to understand.

I realized recently, after years of doing it for signal powers, that dB are a pretty convenient way to do mental logarithmic estimates for things that have nothing to do with power or signals, with only a small amount of memorization. Logarithms are great because they allow you to do multiplication with just addition, and mental addition isn't that hard. For example, if you want to know how many pixels are in a 3840×2160 4K display, well, log₁₀(3840) ≈ 3.58 (35.8dB-pixel) and log₁₀(2160) ≈ 3.33 (33.3dB-pixel), and 3.58 + 3.33 = 6.91 (69.1 dB-square-pixel), and 10⁶·⁹¹ ≈ 8.13 million. The correct number is 8.29 million, so the result is off by about 2%, which is precise enough for many purposes. (To be fair, though, 4000 × 2000 = 8000, which is only off by 3.5%.)

The great difficulty with logarithms is that you need a table of logarithms to use them, and a mental table of logarithms is a lot of rote memorization. You can get pretty decent results linearly interpolating between entries in a table of logarithms, so you can use a lot more logarithms than you know, but you have to know some.

It's pretty commonplace in EE work to make casual use of the fact that a factor of 2× [in power] is about 3 dB, which is a surprisingly good approximation (3.0103dB is a more precise number). This is related to the hacker commonplace that 2¹⁰ = 1024 ≈ 1000 = 10³; 1024× is 30.103dB, while 1000× is precisely 30dB.

To the extent that you're willing to accept this approximation, it allows you to easily derive several other numbers. 4× is 6dB, 8× is 9dB, 16× is 12dB, and therefore 1.6× is 2dB. ½× is -3dB, so 5× is 7dB (10-3). So with just 2× = 3.01dB we already know the base-10 logarithms of 1, 2, 4, 5, and 8, to fairly good precision. That's half of the most basic logarithm table. (The most imprecise of these is 8: 10⁰·⁹ is about 7.94, which is an error of about -0.7% when the right answer was 8.)

If we're willing to add a second magic number to our memorization, 3× ≈ 4.77dB. This allows us to derive 6× ≈ 7.78dB and 9× ≈ 9.54dB. So, with two magic numbers, we have fairly precise logarithms for 1, 2, 3, 4, 5, 6, 8, and 9.

The only multiplier digit we're missing is 7. (Shades of the Pentium's ×3 circuit: http://www.righto.com/2025/03/pentium-multiplier-adder-rever....) So a third magic number to memorize is that 7× ≈ 8.45dB. And now we can mentally approximate products and quotients with mentally interpolated logarithms.

You can do my example above of 3840×2160 as follows. 3.8 is 80% of the way from 3 (4.8dB) to 4 (6.0dB), so it's about 5.8dB. 2.2 is 20% of the way from 2 (3.0dB) to 3 (4.8dB), so about 3.4dB. 35.8dB + 33.4dB = 69.2dB, which is between 8 million (69.0dB) and 9 million (69.5dB), about 40% of the way, so our linear interpolation gives us 8.4 million. This result is high by 1.2%, which is much better than you'd expect from the crudity of the estimation process.

For a more difficult problem, what's the diameter of a round cable with 1.5 square centimeters of cross-sectional area? That's 150mm², half of 300mm², so 24.77 dB-square-millimeters minus 3.01, 21.76dB. A = πr². Divide by π by subtracting 5dB (okay, I guess that's a fourth magic number: log₁₀(π) ≈ 4.97dB) and you're at 16.76dB. Take the square root to get the radius by dividing that by 2: 8.38dB-millimeters. That's less than 7× ≈ 8.45dB by only 0.07dB, so 7-millimeter radius is a pretty decent approximation, 14mm diameter. The precise answer is closer to 13.82mm.

For approximating small corrections like that, it can be useful to keep in mind that ln(10) ≈ 2.303 (a fifth magic number to memorize), so every 1% of a dB (10¹·⁰⁰¹) is a change of about 0.23%. So that leftover 0.07dB meant that 7mm was high by a couple percent.

More crudely: 150mm² is 22dB, ÷π is 17dB, √ is 8½ (pace Fellini), 7×.

It's pretty common in engineering and scientific calculations like this to have a lot of factors to multiply and divide, increasing the number of additions and subtractions relative to the number of logarithmic conversions; this is why slide rules were so popular. Maybe you derived the 1.5cm² number from copper's conductivity and a resistance bound, or from the yield strength of a steel and a load, say. 3840×2160 pixels × 4 bytes/pixel / (10.8 gigabytes/second), as I was calculating last night in https://news.ycombinator.com/item?id=44056923? That's just 35.8 dB + 33.3dB + 6dB - 100.3dB = -25.2dB-seconds, which is 3.0 milliseconds to memcpy that 4K framebuffer. (I didn't do that mentally, though.) Even 36 + 33 + 6 - 100 = -25, so π ms, is a fine approximation if what you want to know is mostly whether it's more or less than 16.7 ms.

So here's a full list of the seven magic numbers to memorize for these purposes:

  2× ≈ 3.01dB (∴ 4×, 8×, 5×)
  3× ≈ 4.77dB (∴ 6×, 9×, 1.5×)
  7× ≈ 8.45dB
  π× ≈ 4.97dB
  ln(10) ≈ 2.303 (∴ 0.01dB ≈ 0.23%, etc.)
  1.259× ≈ 1dB (+1dB ≈ +25.9%)
  (1 - .206)× ≈ -1dB (-1dB ≈ -20.6%)

I haven't been applying this approach long; I'll try to report on results later.

kragen6• 1 year ago

I wrote:

So with just 2× = 3.01dB we already know (...) 8, to fairly good precision. (...) (The most imprecise of these is 8: 10⁰·⁹ is about 7.94, which is an error of about -0.7% when the right answer was 8.)

This is slightly mixed up. It's true that approximating 8× as 9dB gives you an 0.7% error. But I was talking about 3.01dB, and approximating 8× as 9.03dB gives 7.998×, only about 0.02% low.

The errors for the logarithms of the 10 digits thus approximated are:

  >>> print('\n'.join([f'  {10*p:.2f}: {100*(10**p-i-1)/(i+1):+.3f}%' for i, p in enumerate([0, .301, .477, .602, .699, .778, .845, .903, .954])]))
  0.00: +0.000%
  3.01: -0.007%
  4.77: -0.028%
  6.02: -0.014%
  6.99: +0.007%
  7.78: -0.035%
  8.45: -0.023%
  9.03: -0.021%
  9.54: -0.056%

oddthink2• 1 year ago

I've been using decibels as a scale for log-odds for a while when reporting results. It works pretty well, since the relevant part of the scale is wide, unlike using nepers, which I had never heard of until I started noodling around with this.

kragen6• 1 year ago

Like, how many decibels of evidence does this observation provide for this hypothesis? That seems potentially pretty workable, as long as you can ensure conditional independence.

hatthew• 1 year ago

Does this have anything to do with decibels specifically or is it just general log-space arithmetic?

kragen6• 1 year ago

Decibels specifically are just general log-space arithmetic. (Usually.)

kragen6• 1 year ago

It occurs to me that 100 is 2% more than 7×7×2, so you could reasonably approximate 7× (if you didn't know it) as follows. Since 1dB is about 23%, 2% is about 0.09dB, so 98× is about 19.91dB, 49× is about 16.90dB, and so 7× has to be half that: 8.45dB. And so it is.

elfrinjo2• 1 year ago

I'll summarize: It's annoying that dB is often used as a physical unit without the necessary suffix. It's annoying that the suffix seems quite random for most units It's annoying that the factor for power differs from the factor for voltage, etc. It's slightly annoying that it's usually decibel instead of Bel.

However, we all agree that dBs are really useful.

Aachen4• 1 year ago

However, we all agree that dBs are really useful.

Which part of the article was that again? I was surprised to see that conclusion as summary because it's not what the takeaway seemed like to me, so went back to the article and I don't see this mentioned, perhaps I'm overlooking it because I didn't do a careful read a second time

elfrinjo2• 1 year ago

oh sorry; thats the comments

DonHopkins4• 1 year ago

Almost as annoying as Euler angles, which force you to choose an arbitrary ordering (XYZ, ZYX, ZXZ, …), while each choice is equally valid yet mutually incompatible, so there is no canonical “true” yaw-pitch-roll.

Not to mention gimbal-lock singularities, wrapping discontinuously at +/-PI, mapping one orientation to many triples, and forcing you to juggle trig identities just to compose two spins.

To pure mathematicians obsessed with elegant unambiguous coordinate-free clarity, Euler’s pick-any-order gimmick is like hammering tacky street signs onto the cosmos: a slapdash, brittle hack that smothers the true geometry while quaternions and rotation matrices sail by in elegant, unambiguous splendor.

49pctber2• 1 year ago

The idea that helped make decibels click for me is that they're a way to quickly do both dimensional analysis and gain/attenuation calculations at the same time.

"Plain" decibels are simply (power) ratios. These can describe multiplicative changes in power. These are positive for gains (like in a power amplifier) or negative for attenuations (like path loss). They are unitless quantities.

Decibels add. A ten 10 dB gain (x10) followed by a 20 dB loss (x0.01) is -10 dB (x0.1).

"Flavored" decibels are in reference to some power quantity. For example, dBm uses one milliwatt as its reference. So 2 mW / 1 mW = 2 = 10^(3/10) = 3 dBm. These quantities have associated units, but they're still technically dimensionless.

Here's the key insight. You can only have one "flavored" decibel value per computation. Say you have some 3 dBm signal (2 mW). You can add as many regular decibel values as you want, but the unit is still dBm. 3dBm + 4 dB - 7 dB = 0 dBm. In linear units, 2 mW * 2.5 * 0.2 = 1 mW

If you were to do something like 3 dBm + 0 dBm, the linear units would be 2 mW * 1 mW = 2 mW^2, which is probably not what you want.

dBs are confusing. Different fields have slightly different conventions. People talk about any factor of 2 as a 3 dB change, when technically it should only be relative to power-like quantities. It's weird that some of these "units" can be added together, while others can't. The factors of 10 and 20 can be confusing.

But if you consider the units from a dimensional analysis standpoint, decibels are much more sane and intuitive than they appear.

timerol4• 1 year ago

2 mW / 1 mW = 2 = 10^(3/10) = 3 dBm

It's worth noting that this is wrong, in exactly the way that makes decibels confusing. 3 dBm is an absolute power figure (about 2 mW). 2 mW / 1 mW is a ratio of 2 (about 3 dB).

2 mW / 1 mW = 2 = 10^(3/10) = 3 dB.

2 mW = 2 * 1 mW = 10^(3/10) * 1 mW = 3 dB (1 mW) = 3 dBm.

49pctber2• 1 year ago

Yeah, that's a better way of thinking about it. That way you don't have any phantom bookkeeping like the way I was taught. The units are still right there.

tbihl• 1 year ago

Similarly, but in a very different context:

I have to teach non-engineers C programming for an undergrad course, which is basically trying to teach very explicit attention to punctuation (among many other things). "Watch those double quotes!", "single quotes, not double!", "where's your semi-colon??", and so on.

Then, three weeks into the course, we're passing values by reference with &, and I get the question, "isn't that scanf missing the and-sign in front of the string name?", and I'm forced to answer, "that punctuation doesn't matter, this time," because the C standard makes & do nothing in front of a string specifically because so many people were confused about that fact that a string's variable name is already passing by reference.

nayuki10• 1 year ago

"Plain" decibels are simply (power) ratios. / "Flavored" decibels are in reference to some power quantity.

I think this is analogous to https://en.wikipedia.org/wiki/Affine_space . If I understand correctly, an affine space has absolute points and relative vectors.

In terms of types: point ± vector = point; point + point = illegal; point - point = vector; vector ± vector = vector.

Similar with datetimes - you have absolute datetimes (e.g. 2025-05-23T05:16:35Z) and relative offsets (+1 minute, -1 day, etc.). You cannot add two datetimes together.

A plain decibel would be a vector, and a flavored decibel would be a point.

etskinner• 1 year ago

Here's another related one that always bothers me: When you say something's loudness in decibels, you also need to specify a measurement distance.

The author of this article even accidentally makes this omission:

It’s 94 dB, roughly the loudness of a gas-powered lawnmower

And that distance is very important; the actual sound pressure measured is proportional to distance^2. So for a lawnmower measuring 94dB, let's say we assume that we're measuring at 1m. At 2m away, the sound is actually 91dB.

And don't get me started about the fact that a halving in power is 3dB, that's just wacky. I wish we used base 2.

duped• 1 year ago

And that distance is very important; the actual sound pressure measured is proportional to distance^2.

While we're sniping nerds, the inverse square law only applies in the far field (which is tautologically "far enough away for the source to behave as a point source and follow the inverse square law"). That's probably a good bit further than 1m for a lawnmower in the physical world. For loudpseakers you have to be about 2m away before the inverse square law kicks in, unless they've been designed to operate as line sources which decay linearly for a very long distance. For loud sound sources near barriers like the ground they behave like half point sources, which will eventually act like point sources but there's a good bit of distance before it is really measurable.

filterfish• 1 year ago

Whether something is near field or far field is frequency dependent

RicoElectrico• 1 year ago

This difference in mindset makes me comfortable as an EE that all the laid-off SWEs aren't going to take my job. Granted, demand side of the job market isn't rosy due to macro conditions, but at least supply isn't.

stdbrouw• 1 year ago

One way to illustrate some of the weirdness of dB is to look at the documentation of unit libraries, e.g.:

https://pint.readthedocs.io/en/stable/user/log_units.html

https://painterqubits.github.io/Unitful.jl/v0.7/logarithm/

karmakaze• 1 year ago

The writing style is antagonistic like a clickbait title. I find it bothersome. I would have much preferred an organized breakdown of all the different ways dB are used and what they mean instead of a random rant. It complains about how unscientific 'the' unit is, knowing that it's not a single unit then adds little to sort it out.

timerol4• 1 year ago

The one thing that really resonates with me from this article is also the silliest thing: Why decibels instead of bels? Everyone has multiplied in scientific notation before, and making a power ratio of 10^4 = 4 B would be so much more intuitive for conversion to absolute figures. It's a completely silly complaint, given that it's literally just a decimal point instead of a d, but it would make mental math of absolute conversions that much faster, especially for people who don't live and breathe amplifier chains all day.

I want to live in a world where a radio can be specified as a -10.2 Bm sensitivity. -9 is three SI prefixes down from 1 mW, so less than 0.1 pW.

aimor• 1 year ago

Yes, dB is a mess and if we could do it again we ought to use something more explicit like just annotating the units with log10 such as log10(W). Then it's easy to use other convenient units like log2(W) or if you want to reproduce dBV: 20log10(V). dB is fine shorthand, but it gets used all the time in places where things should be explicit.

stevage• 1 year ago

Gosh, I didn't know it was that bad - I didn't know it was used for so many different things.

amelius2• 1 year ago

Speaking of which. Does anyone know why, in Physics, we only use the operators +, * and exponentiation? And why higher operators in the hyperoperation sequence are never used?

https://en.wikipedia.org/wiki/Hyperoperation

mik1998• 1 year ago

You would use it if it was useful or convenient

amelius2• 1 year ago

It was more of a question about the nature of our universe, similar to: why are there only n spatial dimensions?

gregschlom• 1 year ago

"The bel is named in the honor of Alexander Bell; this is in the same tradition that prompted us to name the “wat” in honor of James Watt."

This line killed me. I literally laughed out loud.

teknopaul• 1 year ago

"This is nuts: it’s akin to saying that the milli- prefix should have different meanings depending on whether we’re talking about meters or liters."

Were were here recently with "mega": Sometimes mega is squared as in megapixels. Sometime not as in megabytes.

No biggie.

Db in audio is a relative scale and that makes perfect sense. If you mixer goes + or - 6db that makes sense but can't be measured as power, your mixer might not be plugged in to any speakers so relation to real power is moot in the digital realm.

3 eq bands with -+6db makes sense too. Doesn't need to be precisly specified to be of immediate value, +-12db is clearly something else and users know what.

perching_aix5• 1 year ago

Sometimes mega is squared as in megapixels.

Is that right? A pixel is a 2D object already. It's not like e.g. with centimeters, where it's a 1D unit, so it becomes centimeters squared to form a 2D unit.

davrosthedalek14• 1 year ago

it's (cm)^2, not c(m^2). If there would be the one-dimensional equivalent to pixels, say pix, then 1pixel = 1pix^2, and then 1 megapixel = (kpix)^2

StableAlkyne• 1 year ago

Sometimes mega is squared as in megapixels. Sometime not as in megabytes.

Even worse is Mega in Megabytes could be 1,000,000 or 1,048,576 and it's more or less up to you to know what's what

(Yeah, there are formally megabytes/mebiibytes/MiB/MB, but I honestly cannot recall the last time I heard anyone use anything other than just "megabyte" for 2^20 bytes... Or even wanted to refer to exactly 1,000,000 bytes. Other than decades ago when disk manufacturers wanted to make their hardware seem higher capacity than it really was)

BlueTemplar6• 1 year ago

Wait, when did they stop ?!

klysm• 1 year ago

I see MiB in usage a lot and I always make the distinction myself

jameshart3• 1 year ago

Megapixels aren’t ‘squared’ though?

Ah, unless you’re trying to make ‘pixels’ the same unit as in ‘pixels per inch’…

The problem there isn’t how ‘mega’ is applied but how ‘pixel’ means both an area pixel as well as the linear size of a pixel.

strbean2• 1 year ago

I think the biggest issue by far is that many of the different contextual uses for dB are all in the same domain, or very close.

When you're talking about the loudness of sound, in the same exact context you might care about SPL, perceived loudness, AND gain.

If it was just a matter of "in electrical engineering / physics, dB implies this unit + baseline, when dealing with acoustics, it implies this other unit + baseline", it would be less problematic.

waffletower• 1 year ago

This is an armchair rant with a very narrow complaint. The decibel unit has objective utility in both analog and digital signal processing and the field of audio engineering. It is far from meaningless in filter design and a useful reference for software and hardware interfaces that employ them.

bsteinbach• 1 year ago

The power vs voltage thing I think comes from the historical connection of dB to sensing waves. Because you can change impedance to match any sensor, but power is conserved, power was just more often more important to discuss than voltage. I still have to look it up every time whether 10x is 10 or 20 dB.

vt240• 1 year ago

I see dB scale units used without contextual issues in near uniformity. Unfortunately, I have to agree with the OP, that microphone capsule manufactures seem to be an edge case. I'm not sure where dBV/Pa became the standard. I can understand why given 94dBSPL@1000Hz calibration standards, and the measurement equipment of the time, but I've run into my own fair share of datasheets with lines such as 'Sensitivity -45dB' with no units or other call outs for the standard in use. Thankfully, it seems like most modern datasheets use mV/Pa which seems like a much better unit in my book.

The scientific “unit” we call the decibel

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