Talk:Decibel

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[edit] Amplitude vs power

I'm still sketchy on the relationship between power and amplitude and dB. You can't convert from a power to a dB to a voltage, for instance, unless you know a load resistance. I'm especially confused because you can't convert amplitude --> dBFS --> power in digital land which doesn't even have load resistance. What does "power" even mean for digital?? - Omegatron 20:13, Apr 29, 2005 (UTC)

YEEARG - and I had explicitly edited this article to correct this, and it has been reverted.

decibels are DEFINED AS 10log10(x) - PERIOD. This 20log10 crap is WRONG! dB are NEVER 20log10 of ANYTHING.

Now, when you are talking about dBWatts (or any derived units like dBmW) you can compute the CHANGE in level by computing 20log10(V1/V2), but that is a simplification of the full formula 10log10( (V1*V1/R)/(V2*V2/R) ).

But it is also perfectly valid to speak of dBV - and a 10 dB increase of a 0dBv signal yeilds 10 volts, NOT 100!

dB absent any unit is a RELATIVE measurement - I can speak of a 6dB increase of my bank account (a thing much to be desired), but I cannot speak of having 6dB in my bank account - I can say I have 36dB$ in the bank, but I *have* to supply a unit for an absolute measure to be meaningful.

I design test equipment for a living, and this confusion causes us NO END of problems. People will increase the deivation of an FM signal by 2, and expect to see the audio spectrum analyzer increase by 6 dB. The spec-an is measuring deviation, so a x2 increase is 10log10(2) = 3dB. To get a 6dB increase we would have to be reporting (kHz deviation)^2 - now what physical property does that describe?

Please - dB is 10log10(x) ALWAYS - not 20log10!

Revert the reversion of my changes, please!

N0YKG 10 May 2005

Here's your chance to be bold and put the above explanation why 20 log 10(X/Xref) is wrong into the article. Though I admit I don't see why it's wrong to say 20 log ((V1/V2)) as opposed to 10 log((V1/V2)^2), assuming the circuit impedance is the same. dB should always be used to refer to ratios of power quantities, not to ratios of amplitude quantities...but we often cheat and say 20 log (amplitude/reference amplitude) --Wtshymanski 19:02, 10 May 2005 (UTC)
On the one hand, you say dB should only be used for power quantities, but then you say that dB could be used for your bank account. Also:
  • 0 VRMS = 0 dBV
  • 10 VRMS = 20 dBV
  • 100 VRMS = 40 dBV
According to this, which claims to be based on the ANSI T1.523-2001 definitions, which I would download, except it costs $175 - Omegatron 20:21, May 10, 2005 (UTC)

Mark Phillips 28 June 2005

Ref the statement above that "a 10 dB increase of a 0dBv signal yeilds 10 volts, NOT 100!", a 10 dB increase means an increase in power of 10(10/10), i.e. an increase in power of 10 times. Assuming that the circuit impedance doesn't change whilst this increase is happening (nearly always true when the 'before' and 'after' measurements are made at the same place in a circuit or system), then to achieve this 10 times increase in power the voltage must increase by the square root of 10 (because power is proportional to the square of the voltage, for a constant impedance), i.e. by a factor of 3.162 (approx). Since, in your example, you started off with a voltage of 0 dBV, i.e. 1 volt, the 10 dB increase will actually yield 3.162 volts (approx). (Note that I have written 0 dBV rather than 0 dBv, because from the context I think that is what the author meant. The lower case v is now falling out of usage in favour of a lower case u - these indicate a reference level of 0.775 volts rather than the 1 volt reference indicated by the upper case V. On a finer point it is always preferable to set a space between the value and the units, in line with SI standards, although the decibel is not yet accepted as a 'unit' by SI.)
Excellent. Thank you. - Omegatron June 29, 2005 23:07 (UTC)
Be aware that there is a slight usage inconsistency between different fields. Originally, dB was always strictly a measure of relative power. This usage is preserved in physics. One can use 20·log10 of an amplitude ratio, but only when the "impedences" are the same, so that the dB result is still a measure of power. This usage is not strictly preserved in engineering, where for example electrical engineers may express a ratio of voltages as 20\,\log_{10}(V_1/V_2), even when V1 and V2 are measured at different points in the circuit, where the impedence differs. Anyone who calls 10\,\log_{10}(V_1/V_2) a result in "dB", however, is simply mistaken. This unfortunate usage does, however, occur from time to time in engineering literature.--Srleffler 05:00, 28 November 2005 (UTC)
Confusion over this crept back into the "definition" section of the article. I have tried to resolve it. Again, for those unfamiliar with this: in physics, decibels are strictly a measure of power or intensity ratio. They are never a measure of voltage or amplitude. (This is not the case in engineering.) As long as the impedence is constant, 20\,\log_{10}(V_1/V_2) is equal to the power ratio. If the impedence is not constant, it would be incorrect in physics to call the result a value in "dB".--Srleffler 22:20, 4 January 2006 (UTC)

--- "This 20log10 crap is WRONG! dB are NEVER 20log10 of ANYTHING." Decibels are used for all sorts of physical quantities - some where the power concept is obvious and others, such as sound pressure and vibratory acceleration, where it is not so obvious. I agree completely that decibels always express a power-like ratio - ie, 10log(power-like ratio). But decibels are widely used for many non-power quantities, such as sound pressure when it becomes 10log(ratio of pressure squared) and hence 20log(pressure ratio). So it's not wrong to say 20log(pressure ratio) but writing it that way tends to facilitate confusion by encouraging people to think that "sometimes it's 10log and sometimes it's 20log. For that reason I edited the sound pressure level page which originally said something like SPL = 20log(pressure ratio) = 10log(pressure squared ratio) so that it became SPL = 10log(pressure squared ratio) = 20log(pressure ratio). I think we should always use 10log() as the starting point in Wikipedia - not because 20log is wrong, but because 10log keeps the decibel concept clear and consistent. Richardng 17:35, 2 June 2006 (UTC)


Decibels always express power ratios. dB = 10*log10(x), where x is a ratio of powers p1/p2. A dB can be "mapped" to a voltage if either the impedances are known or it is assumed that both components (p1 and p2) are into the same impedance. —Preceding unsigned comment added by 71.70.224.93 (talk) 21:29, 28 January 2008 (UTC)


[edit] Noise floor of air

Earlier we discussed the maximum SPL possible in air (when it turns to vacuum during rarefaction). On the other end of the scale, what's the minimum noise always present in still air in a perfect anechoic chamber due to thermal motion? I'm sure it depends on temperature. Is it ever relevant? (Probably not.) — Omegatron 15:27, 26 February 2007 (UTC)

In water of density ρ, sound speed c, the noise floor of mean square pressure is given by A T f2, where A = 4 π k ρ/c= 0.00012 nPa2/(K Hz3), T is absolute temperature, f is frequency and k is Boltzmann's constant k =1.381 10-23 J/K. It comes out as about -15 dB re 1 μPa at 1 kHz, and is important at frequencies above 100 kHz. That doesn't answer your question but perhaps it helps. Thunderbird2 17:34, 31 July 2007 (UTC)

Hmmm... I found some references that give formulas, but I don't think I'm understanding the formulas correctly. To rewrite yours for water:

\overline{P}^2 = {4 \pi \rho k T f^2\over c} \quad \left (\tfrac \mathrm{Pa^2} \mathrm{\sqrt{Hz}}\right )

So:

{P}^2 = \int_{f_1}^{f_2}{4 \pi \rho k T f^2\over c}\, df = {4 \pi \rho k T \over c} \int_{f_1}^{f_2}{f^2}\, df = {4 \pi \rho k T \over c} {{f_2^3 - f_1^3} \over 3} \quad (\mathrm{Pa}^2)

So RMS pressure would be:[1]


P = \sqrt{{4 \pi \rho k T \over c} {{f_2^3 - f_1^3} \over 3}} = 303\ \mathrm {\mu Pa}

which is +50 dB re 1 µPa. Is your "at 1 kHz" measurement a narrow bandwidth? — Omegatron (talk) 17:53, 4 May 2008 (UTC)

Goodness, I'd forgotten about this. It looks like I was being lazy. What I meant was a spectrum level of -15 dB re 1 μPa2/Hz at 1 kHz. What values are you using for f1, f2? Thunderbird2 (talk) 18:02, 4 May 2008 (UTC)

20 Hz to 20 kHz. Sound pressure lists +67 dB for the auditory threshold for divers, so it seems correct. — Omegatron (talk) 18:07, 4 May 2008 (UTC)

Does this mean that the noise is not white?

Refs for air:

The "softest," or quietest sound that humans can perceive is nearly the same as the softest sound that all animals (or insects) can perceive: the vibrational amplitude of the air at zero decibels (the softest sound) is only about the diameter of a hydrogen atom, and any further sensitivity of the listener would be overcome by the ambient "hiss" of the Brownian motion associated with the thermal agitation of molecules.[2]
How sensitive can one really hear? Vibrations of the ear-drum at the threshold of hearing can correspond to about the diameter of a hydrogen atom! As stated before, some people, especially those living in the countryside away from machinery and big city sounds can actually hear random motion of air molecules bouncing against their eardrums![3]
The amplitude range is substantially broader, beginning at a level so low that we can almost "hear" the fluctuations in air pressure due to random motion of air molecules near the ear drum[4]
At 4 kHz, which is about the frequency of the sensitivity peak, the pressure amplitude variations caused by the Brownian motion of air molecules, at room temperature and over a critical bandwidth, corresponds to a sound pressure level of about -23 dB. Thus the human hearing system is close to the theoretical physical limits of sensitivity. In other words there would be little point in being much more sensitive to sound, as all we would hear would be a 'hiss' due to the thermal agitation of the air! [5]
According to Watson, Franks, and Hood (1972), who were the first to control the signal duration (125 ms), the absolute threshold at 1000 Hz is about 9 dB SPL. The energy of this signal is approximately 10−16 W s/cm2. We estimate the N0 of Brownian motion over the same area to be about 1.7×1020W s/cm2. Thus, the ratio of signal energy to noise power density at absolute threshold is about 5000. Our ability to hear weak auditory signals is impressive, but the fundamental limitation is not the thermal agitation of molecules of the air. Is human hearing limited by Brownian motion? David M. Green and Huanping Dai

Also [6] and doi:10.1121/1.1906831, which gives the equation:

\overline{P}^2= {8 \pi \rho \nu^2h \nu \over c(e^{h \nu/kT}-1)} d \nu

  • ρ = density of gas
  • c = velocity of wave
  • ν = frequency
  • dν = bandwidth
  • h = Planck's constant
  • k = Boltzmann's constant
  • T = temperature in K

— Omegatron (talk) 18:12, 4 May 2008 (UTC)

That last equation is in the same form as the one I mentioned, provided that h.ν/k.T is small, but there is a factor of 2 discrepancy between them that I don't understand. Perhaps one is defined for negative frequencies and the other not. I'll dig up my source reference for thermal noise. (re whiteness: In the sea the audible noise spectrum is certainly not white, but it's not blue either because thermal noise is not important at audible frequencies. The actual spectrum depends on conditions but is usually reddish) Thunderbird2 (talk) 18:35, 4 May 2008 (UTC)
Is that environmental noise or thermal noise, though? — Omegatron (talk) 19:03, 4 May 2008 (UTC)
The red noise is environmental (often caused by wind-generated breaking waves) and dominates up to about 100 kHz. Above that the thermal noise takes over. The reference I was looking for is [R. H. Mellen, The thermal-noise limit in the detection of underwater acoustic signals, J. Acoust. Soc. Am. 24, 478-480 (1952).]. Thunderbird2 (talk) 19:24, 4 May 2008 (UTC)
That's relevant to the Colors of noise article, then, which is confused and lists "red noise" as a separate oceanographic spectrum rather than a synonym for Brownian noise. Can you fix it and add a reference? — Omegatron (talk) 20:10, 4 May 2008 (UTC)
I removed the statement about ocean noise, which was incorrect. In fact it's rare to hear the terms "red" and "blue" applied to ocean acoustics, so the relevance to the "colors" article is questionable. Instead, spectra are usually described in the form "N dB per octave". Is there a still a reference you'd like me to add? Thunderbird2 (talk) 20:57, 4 May 2008 (UTC)
Thanks for the Boyarsky 1951 reference. (It's not mentioned by Mellen so I was not previously aware of it). I don't understand his Eq. (4) because the total energy density is mean square pressure divided by (ρ c2), and not half that as he claims. If you correct for that factor of 2 and assume small h.ν, you end up with Mellen's formula, which I think is correct. Thunderbird2 (talk) 19:56, 4 May 2008 (UTC)

[edit] The lede

This sentence is poor: "The decibel is useful for a wide variety of measurements in acoustics, physics, electronics [...]". Acoustics and Electronics are a part of Physics, not separate entities as the sentence seems to implies. It's better to say "[...] of measurements in physics, (such as in acoustics and electronics) [...]. —Preceding unsigned comment added by 75.12.148.193 (talk) 05:19, 1 January 2008 (UTC)

No, it's just fine. Not everyone agrees that acoustics and electronics are part of physics. I mean, by that argument, everything is part of physics. It is clearer and more understandable in its current version than what you propose. jhawkinson (talk) 05:31, 1 January 2008 (UTC)
The decibel is overwhelmingly used by engineers rather than scientists. Therefore I don't agree that "The decibel is useful for a wide variety of measurements in science and engineering (e.g. acoustics and electronics)" is an improvement over "The decibel is useful for a wide variety of measurements in engineering (e.g. acoustics and electronics)". Thunderbird2 (talk) 14:16, 2 January 2008 (UTC)

[edit] Broken link no. 3

Link no. 3 "Decibel chart, small spectrum " is broken. Who can correct this? Georgegh (talk) 16:10, 28 January 2008 (UTC)


[edit] Real life examples that people can use

A lot of encyclopedias etc. have examples of what various decibels might sound like e.g a bee is .. a concorde is ... a train is ... . This would be more for kids, and might make the subject a bit more approachable?? —Preceding unsigned comment added by 41.241.5.105 (talk) 09:45, 9 May 2008 (UTC)

You mean like this? Thunderbird2 (talk) 10:26, 9 May 2008 (UTC)

[edit] Doubling

Our article says an increase of 3 dB corresponds to a perceived doubling of sound volume. http://www.phys.unsw.edu.au/jw/dB.html says: "Experimentally it was found that a 10 dB increase in sound level corresponds approximately to a perceived doubling of loudness". Can anyone clear this up? Boris B (talk) 22:43, 19 May 2008 (UTC)

This has come up before, but I don't recall it ever being resolved. One problem for me is that I don't understand what is meant by "perceived doubling of sound volume". Do you? Thunderbird2 (talk) 22:51, 19 May 2008 (UTC)