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Natural Science Forum / Physics / Acoustics / January 2006Question about decibels
Are decibels an absolute measurement, like feet, or seconds, or are they just ratios? How would I measure decibels? Thanks... On 1/3/06 5:43 PM, in article 1136338989.323595.65480@o13g2000cwo.googlegroups.com, > Are decibels an absolute measurement, like feet, or seconds, or > are they just ratios? > How would I measure decibels? > > Thanks... Strictly speaking, they are just logarithms of ratios. Often however, for a specific application, a reference level is set that allows conversion to absolute levels. For example, dbmw (a bastard abbreviation) stands for decibels with respect to a milliwatt. IIRC, sound levels are often referenced to a sound pressure intensity in air of 0.0002 dynes per square centimeter rms. Bill -- Ferme le Bush > On 1/3/06 5:43 PM, in article > 1136338989.323595.65480@o13g2000cwo.googlegroups.com, [quoted text clipped - 9 lines] > absolute levels. For example, dbmw (a bastard abbreviation) stands for > decibels with respect to a milliwatt. No, dB's wrt 1 mW is written as dBm, not dBmw.  SignatureDave K http://www.southminster-branch-line.org.uk/ Please note my email address changes periodically to avoid spam. It is always of the form: month-year@domain. Hitting reply will work for a couple of months only. Later set it manually. The month is always written in 3 letters (e.g. Jan, not January etc) by using a reference quantity that is an absolute, you can express another quantity in decibels referenced to that absolute. However, the reference level must be clearly stated or understood for the result to have an absolute meaning. However, decibels should not be considered as normal units since something like a 3 dB difference between two results represents the ratio of the results and not the absolute difference between the results. > Are decibels an absolute measurement, like feet, or seconds, or > are they just ratios? > How would I measure decibels? > > Thanks... > Are decibels an absolute measurement, like feet, or seconds, or are they just ratios? > How would I measure decibels? The following sources have good explanations: http://en.wikipedia.org/wiki/Decibel http://www.phys.unsw.edu.au/~jw/dB.html Chris W SignatureThe voice of ignorance speaks loud and long, But the words of the wise are quiet and few. --- because the very wide range of sound pressure, this logarithmic scale is needed, in order to comprise in a new scale smaller and easily to manage. To make this scale a reference sound pressure was taken, then compared with the sound pressure in analysis and take the logaritmic value. > Are decibels an absolute measurement, like feet, or seconds, or > are they just ratios? Decibels refer only to ratios, just like percentage. "50%" has no physical meaning until you reference it. "50%" of the human population is male." > How would I measure decibels? Measure the real value of A. Measure the real value of B. the ratio of A to B is expressed in decibels as dB(of A vs B) i= 10*log(A/B) Since the the word root "Bel" is implicitly associated with elecrticty or sound (via the father of telephony, Alexander Graham Bell), one can infer that Bels have something to do with sound or electricity. Since about 1930, the connection has been that described above. Another convention has arisen that makes for great confusion amongst the novices; The decibel has additionally taken the connotation of power or quantity rather than amplitude. So "A" has to be the energy of a quantity; the speed of a body is called velocity, but its kinetic energy is (m*v^2)/2, so when using decibels to represent energy even though we only measure velocity, we would use (v^2) for A. For B we would use a reference speed, e.g. 1 m/s. for m, we would use linear m. for 2, we would use the log times 10. The kinetic energy of a body would then be expressed in decibels as dB(E) = 20*log(v)+10*log(m). The reference kinetic energy could be that of a kg going 1 m/s I leave it up to the student to detrmine whether 3 (that is, 10*log(2)) in addition belongs in the above formula. Other log sales in common use (that would be amenable to decibel notation if we were to so desire) are: chemical pH Richter scale (imagine hereupon the knietic energy example). sound power in Bels. Angelo Campanella On 1/6/06 10:21 AM, in article qyyvf.230784$qk4.197547@bgtnsc05-news.ops.worldnet.att.net, "Angelo Campanella" <a.campanella@att.net> wrote: >> Are decibels an absolute measurement, like feet, or seconds, or >> are they just ratios? [quoted text clipped - 47 lines] > > Angelo Campanella I always had trouble explaining why there were no differences between the so-called power decibels and voltage decibels. There is the confusion over nepers which are defined as the natural log of an amplitude ratio. There is additional confusion in photography in wihch the attenuation of a neutral density filter is often expressed in terms such as ND2. That really means an attenuation of two Bels. Even more confusion arises when signal-to-noise ratios are expressed in dB, especially with square law detectors. Even though the amplitude output of the detector is proportional to the square of the input amplitude, the SNR is usually proportional to the amplitude of the output, IIRC. Bill -- Ferme le Bush > I always had trouble explaining why there were no differences between > the so-called power decibels and voltage decibels. That's probably so because of your ignorance. There there is no such thing as power decibels and voltage decibels. 6dB corresponds to a factor of four in power and a factor of two in amplitude. > There is the > confusion over nepers which are defined as the natural log of an [quoted text clipped - 13 lines] > > -- Ferme le Bush If confusion indeed exists, it would appear that it exists only in your mind. >That's probably so because of your ignorance. There there is no such thing >as power decibels and voltage decibels. 6dB corresponds to a factor of >four in power and a factor of two in amplitude. Not to mention that 10 dB corresponds to a factor of two in loudness. Or the position taken by some that the decibel was developed as a mathematical formalization of the attenuation of a mile of standard telephone cable. I love decibels. Particularly the way those factors of two and four are good to about the precision of a ten inch slide rule. Ken Plotkin >>That's probably so because of your ignorance. There there is no such >>thing as power decibels and voltage decibels. 6dB corresponds to a >>factor of four in power and a factor of two in amplitude. > > Not to mention that 10 dB corresponds to a factor of two in loudness. True, but only in the mid-frequency range. As you probably know, the slope of the loudness function is reflected in the spacing between the equal loudness contours. At low frequencies the equal loudness contours are much more closely spaced than at mid frequencies, which means that the growth of loudness is more rapid at low frequencies than at mid frequencies. > Or the position taken by some that the decibel was developed as a > mathematical formalization of the attenuation of a mile of standard [quoted text clipped - 3 lines] > are good to about the precision of a ten inch slide rule. > Ken Plotkin Not to mention their simplicity. One only needs to memorize a few basic associations and quite precise first-order calculation can be done very easily in one's head. For example, 121dB SPL corresponds to X Pascals? Subtracting 94dB we have that X is 27dB above 1Pa, which is approximately 10% (1db) above 20Pa (26dB), or 22Pa. The exact answer is 22.39Pa. On 1/6/06 7:52 PM, in article QVGvf.160946$z82.101149@fe12.news.easynews.com, "The Ghost" <theghost@hotmail.com> wrote: > If confusion indeed exists, it would appear that it exists only in your > mind. There is no confusion in my mind. If you were really able to read and comprehend, that would be obvious. -- Ferme le Bush > On 1/6/06 7:52 PM, in article > QVGvf.160946$z82.101149@fe12.news.easynews.com, "The Ghost" [quoted text clipped - 7 lines] > > -- Ferme le Bush Your exact words were "I always had trouble explaining why there were no differences between the so-called power decibels and voltage decibels." If that isn't an admission of confusion, I don't know what is. On 1/7/06 12:56 PM, in article _VVvf.134747$ND2.131943@fe01.news.easynews.com, "The Ghost" <theghost@hotmail.com> wrote: > Your exact words were "I always had trouble explaining why there were no > differences between the so-called power decibels and voltage decibels." > > If that isn't an admission of confusion, I don't know what is. That is a statement that I had trouble explaining not of understanding. No matter what I said, the subject came back to what if dBs were voltage dBs instead of power dBs. -- Ferme le Bush > On 1/7/06 12:56 PM, in article > _VVvf.134747$ND2.131943@fe01.news.easynews.com, "The Ghost" [quoted text clipped - 8 lines] > matter what I said, the subject came back to what if dBs were voltage dBs > instead of power dBs. You might just say that since power is the square of voltage (to a resistive load if qualification is necessary) one multiplies by 20 instead of 10. Bob Signature"Things should be described as simply as possible, but no simpler." A. Einstein > You might just say that since power is the square of voltage (to a > resistive load if qualification is necessary) one multiplies by 20 > instead of 10. That sounds pretty reasonable. It reinforces the notion that decibel notation wants to be one about quantity, that when the measurement is in one mode (voltage or pressure) while the entity we want to represent (electricity of energy, or ions) is in another, namely power, we use 20 (to connotate "squared") instead of ten. Another use of logs is in astronomical visual "magnitude", which is stated to be "a factor of just over 2.5". That amounts to almost exactly 4 decibels, similar to our notion of just noticeable difference in sound level; 3 dB. The factor od 2.5 almost certainly relates to light intensity, which is power or energy. In astronomy, the reference zero seems to be unclear. My old (Baker, 1930-46) astronomy book says "...the brightest star, Sirius, is -1.6 (magnitude); Canopus is -o.9, Vega, Capella, Archturus.. are about o.2. Altair (o.0) and Aldebran (1.1) are nearly standard first magnitude stars." And now note that the astronomy 'zero' magnitude is really the "first" magnitude or a "one"!. Oh well, happy new year.... Angelo Campanella >> You might just say that since power is the square of voltage (to a >> resistive load if qualification is necessary) one multiplies by 20 >> instead of 10. > > That sounds pretty reasonable. snip...snip > Angelo Campanella Not to me. It is perfectly legitimate and accurate to say that +6dB represents a factor of two increase in voltage across purely reactive load (eg. an ideal capacitor), even though the power both before and after the increase is zero. Furthermore, by definition, an increase of 6dB SPL indicates a factor of two pressure increase regardless of whether the sound intensity is purely resistive or purely reactive. So, in a sense, the very act of attempting to relate amplitude and power units when explaining decibels leads to the very confusion that one wants to avoid. > Not to me. It is perfectly legitimate and accurate to say that +6dB > represents a factor of two increase in voltage across purely reactive load [quoted text clipped - 4 lines] > very act of attempting to relate amplitude and power units when explaining > decibels leads to the very confusion that one wants to avoid. While I tend to agree with this, one will still be asked why and when one multiplies by 20 rather than by 10. Bob Signature"Things should be described as simply as possible, but no simpler." A. Einstein >> Not to me. It is perfectly legitimate and accurate to say that +6dB >> represents a factor of two increase in voltage across purely reactive [quoted text clipped - 10 lines] > > Bob The answer is very simple. 20 log Vo/Vi is a totally arbitrary definition that is used solely for practical convenience even though the power gain does not equal the square of either the voltage or current gain (such as in the frequency response of an electrical filter). 20 log is used instead of 10 log only because one is dealing with a ratio of voltages as opposed to a rato of powers involving a purely resistive load. > The answer is very simple. 20 log Vo/Vi is a totally arbitrary definition > that is used solely for practical convenience even though the power gain > does not equal the square of either the voltage or current gain (such as in > the frequency response of an electrical filter). Well, actually in the LTI regime the ratio of power will go as the square of the ratio of voltage regardless of the type of load other than at certain physically unrealizable limits. Bob Signature"Things should be described as simply as possible, but no simpler." A. Einstein >> The answer is very simple. 20 log Vo/Vi is a totally arbitrary >> definition that is used solely for practical convenience even though [quoted text clipped - 6 lines] > than at certain physically unrealizable limits. > Bob While that may well be true in the fantasy world of technical incompetence in which you reside, it is certainly not true in the real world of physics, science, engineering and mathematics. In order to prove that your assertion is false, one only needs to consider the operation of a simple first-order (RC) low-pass filter in which the output is taken across the capacitor. 20 log Vo/Vi shows the low pass response characteristic as a function of sinusoidal frequency. Po/Pi is zero at all frequencies because even real-world capacitors that are used to build real-world filters consume virtually zero power. > Po/Pi is zero at all frequencies because > even real-world capacitors that are used to build real-world filters > consume virtually zero power. Virtually? If they consume _any_ at all, then for a given signal the ratio of powers goes as the square of the ratio of the voltages and that principle encompasses all of what is physically realizable in the real world. Bob Signature"Things should be described as simply as possible, but no simpler." A. Einstein >> Po/Pi is zero at all frequencies because >> even real-world capacitors that are used to build real-world filters [quoted text clipped - 5 lines] > world. > Bob First of all, from a purely theoretical perspective, in a circuit contianing idealized elements, the power across the output capacitor of the low-pass filter is zero and your lame argumet falls flat on its face. More importantly, however, the fundamental issue is whether or not in general 20 log Vo/Vi identically equals 10 log Po/Pi. The answer is that it does not, and that is why 20log and not 10 log is used, by definition. The fact that 20 log Vo/Vi equals K + 10 log Po/Pi, as you correctly infer, is irrelevant. > Not to me. It is perfectly legitimate and accurate to say that +6dB > represents a factor of two increase in voltage across purely reactive load [quoted text clipped - 4 lines] > very act of attempting to relate amplitude and power units when explaining > decibels leads to the very confusion that one wants to avoid. I think that the main reason that "20" has become so common, especially in electrical engineering, is that the voltage of a signal or situation is the easiest variable to observe... most everyone has a voltmeter (VOM or VTVM), while relatively fewer users have a power meter at their beck and call. Most things talked about in EE consider volts as the variable. Thus, they, when doing circuit analysis and systems analysis become concerned about voltage values, and the 20log situation recurs. That practice has spread into acoustics. On the other hand, for instance, mechanical engineers still think in terms of direct and linear variables in vibrations analysis. For them, it's all mills and millimeters. However, I find myself crossing that line in my field measurements of vibrations, having my LD2900 scales calibrated in "dB re one micro-g" for accelerometers, and "dB re one nano-inch per second" for the seismic velocity sensor. There, dB's work out OK; it becomes again 20 log, however... Angelo Campanella > I think that the main reason that "20" has become so common, especially in > electrical engineering, is that the voltage of a signal or situation is [quoted text clipped - 14 lines] > > Angelo Campanella One explanation to definitions LI = 10 lg(I/I0) and Lp = 20 lg(p/p0) is that in old times the plane wave was used as a model or reference. Concerning this plane wave case we have the impedance z = p/v = rho c (with no phase lag between p and v) and by definition I = p^2/z = p^2/(rho c). If we want to have Lp = LI, we must define also I0 = p0^2/(rho c), or p0 = sqrt(I0 rho c), as well as Lp = 20 lg(p/p0). If we define I0 = 10^-12 W/m^2, we get p0 = 20 myPa (about). Some remarks Loudness of a tone N = k [prms^2]^(1/3) = k [prms]^(2/3) = 0,01 prms^0,6 (about) p = sound pressure in myPa, k = "transfer constant" Sone/myPa. prms = sound pressure, root mean square value, myPa. (in many papers sound intensity related stimulus intensity is used instead of prms and the plane wave correspondence is assumed between LI and Lp). The ear is a nonlinear sound pressure detector. We may say that the ear compress the sound pressure signal the more the higher the pressure is. For a 1 kHz tone we have approximately [4 phones corresponds here about the assumed random neural noise level, 0 dB sound pressure level at 1 kHz corresponds about 50 % detectability]: - range of LI and Lp: 4...120 dB (1:30) - range of loudness, N: 0,2...250 sone (1:1250) - range of loudness level, LN: 4...120 phone (1:30) - range of sound pressure, p: 32 myPa...20 Pa (1:320000) - range of intensity, I: 3 pW/m^2...1 W/m^2 (ca. 1:10^11) All scales are arbitrary that regards how the ear detects and measure sound. For example, 1 sone is by definition the loudness of a 1 kHz tone having the sound pressure prms 40 dB and duration 1 s. If we assume that the ear is a sound pressure sensitive detector, we could also use a sound pressure scale L'p= 10 lg(p/p0) dB. This scale had a range 2...60 dB. As far as my memory serves me well, the range of the "volume information" of neural signals from the ear to the brain is about 60 dB, too. [BTW: Did the creator of the ear know what definitions we use, for example,. for sound pressure and intensity level?] We could also define L''p = 5 lg(p/p0). In this case the range is 1...30 dB. Kari Pesonen >> Not to me. It is perfectly legitimate and accurate to say that +6dB >> represents a factor of two increase in voltage across purely reactive [quoted text clipped - 10 lines] > in electrical engineering, is that the voltage of a signal or > situation is the easiest variable to observe... I think it's because voltage is generally the variable of relevance, except where mixed variables are concernied, such as impedance, admittance and transducer sensitivity (which I comment on below), which are commonly plotted as 20 log x/y, even though x and y do NOT have the same units. > most everyone has a > voltmeter (VOM or VTVM), while relatively fewer users have a power > meter at their beck and call. Irrelevant. You still have theory and I challenge anyone to point to a reference in the literature where the response of an electrical circuit that isn't purely resistive is quantified in terms of 10 log (Pout/Pin). > Most things talked about in EE consider > volts as the variable. Thus, they, when doing circuit analysis and > systems analysis become concerned about voltage values, and the 20log > situation recurs. That's not necessarily true. For example, an electrical impedance measurement would involve Vout/Iin and is justifiably plotted on a dB scale as 20 log Vout/Iin. The equivalent situation in acoustics is Pout/Uin where p is the pressure that is produced by a known volume velocity across an unknown acoustic impedance. > That practice has spread into acoustics. On the other hand, for > instance, mechanical engineers still think in terms of direct and [quoted text clipped - 8 lines] > There, dB's work out OK; it becomes again 20 log, however... > Angelo Campanella Sorry, but I don't see it as crossing any so-called line. It's all a matter of definiiton, and the appropriate definition for expressing ratios of amplitudes in dB is 20 log x2/x1 regardless of whether the units are mills, inches per sec or micro-gs.....or even mixed units such as mV/Pa which are commonly used to stipulate the sensitivity of a microphones. For example -60dB re 1V/Pa means 1mV/Pa, or 20dB re 1Pa/V at one meter means that the speaker produces 10Pa at one meter for 1Vrms input. Complicating these definitions by inappropriately introducing power ratios is nonsensical and only leads to total confusion. |
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