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Subject:of Sound Forge and dB's
Posted by: kbouchard
Date:4/18/2005 7:25:46 PM

maybe this is a little "picky" but it's something I'd like to know and can't find a good answer:
The SF data window which displays a sound waveform, is calibrated in dB. In fact,the only two levels shown are -6 and -inf. (SF6)
Question: Are these "sound pressure level" dB's or "sound intensity" dB's?
There seems to be a rather large difference according to the stuff I've been reading, like whether a factor of 10 or 20 is used in the calculations.
The bottom line is whether the sound coming out of the PC's speakers should be half as loud when I cut a waveform down by 6 dB or 3 dB.
Have I confused everyone? Is this something people just ignore?

thanks for humoring me

ken prime

Subject:RE: of Sound Forge and dB's
Reply by: Rednroll
Date:4/18/2005 9:40:17 PM

The dB levels in Forge are referenced to "Full Scale" or dBFS. In digital audio 0dB is always as high as the waveform can go to, so the very top of the scale you are looking at is 0dB....or more precisely 0dBFS.

"The bottom line is whether the sound coming out of the PC's speakers should be half as loud when I cut a waveform down by 6 dB or 3 dB."

-3dB is definately not half as loud. Actually this is a debatable area as to what is "half as loud" or "twice as loud" is. Most audio reference books say that a +10dB boast is twice as loud and a -10dB reduction is half as loud. Most of the people that believe the 10dB twice as loud number base this information off of the "Fletcher/Munson equal loudness curves", which was a study done by Fletcher and Munson using pure tone sinewaves, which are not representative of a true complex waveforms like music. It is further supported by the original audio encyclopedia which stated +10dB is twice as loud. The problem there is that this study was done using music of that time in the 1930's, where the voice was mixed much louder than the background music. So what happened is when you raised the music level, your ear would go into a compression state due to the high mid-range level of the voice over the music, and it actually took a boast of +10dB to sound twice as loud. Today music is not mixed the same way and the music is much closer in level to the voice level. The problem is the books have never been rewritten and many people use the audio encyclopedia as a reference book, so the 10dB refernce continues to flourish.

I was taught +6dB is twice as loud by a well educated mastering engineer. All my audio listening experience tells me +6dB is twice as loud. So my answer to you is -6dB is half as loud and +6dB is twice as loud. I have a lot of background examples and information supporting this fact, that I won't bore you with at this time. I have further plans of doing an indebt study to prove the +10dB being twice as loud is inaccurate. I did a preliminary study using modern music on 5 different people and did A/B playbacks of audio that went from a reference level to a +6dB boost and then played the same reference level and did a +10dB boost. 4 out of 5 of the listeners said, the +6dB boost sounded twice as loud to them, and the +10dB boost sounded much louder than twice as loud. +10dB is actually closer to being 3 times louder with my theory.

Also if you expand the waveform window in Forge vertically the grid spacing on the left will expand with it, so you will see more marks than the -inf and -6dB mark.

You can also select a particular area or click your cursor at a specific point in the Forge wave editor window, then goto TOOLS>STATISTICS and it will give you the actual dB level of what you have selected with the "Maximum sample value (dB)" reading displayed.

Subject:RE: of Sound Forge and dB's
Reply by: Chienworks
Date:4/19/2005 4:13:45 AM

Sound Forge itself seems to agree with Red here. A 100% increase in volume level is +6.02dB and a 50% decrease is -6.02dB. I can't vouch for the dB scale in any quantitative terms, but 100% increase definately results in twice the energy under the curve and 50% is half. There's no disputing that. So, whatever it may supposed to be, Sound Forge uses 6dB as twice/half.

It took me a while to get used to this. My physics training taught that a 1 Bel increase was defined as 10 times the volume. This would result in each dB being a factor of about 1.2589254, and 3dB would then be a factor of 1.9952623, or just about 2. So, who is right? I dunno. What does Sound Forge do? That i do know: +6dB is twice the volume.

Subject:RE: of Sound Forge and dB's
Reply by: mpd
Date:4/19/2005 4:46:38 AM

Most of the decibel confusion arises because power and voltage get mixed up. Most of the time in SF, you are dealing with a visial display of the "voltage," so the 20*log10() calculation is used. Generate some sine waves and use the Tools->Statistics window to see.

I can't really comment on the loudness perspective, but this article is pretty good, and as far as I can tell it is accurate (I am a DSP engineer by training):

Subject:RE: of Sound Forge and dB's
Reply by: jorgensen
Date:4/19/2005 11:04:30 AM

Not that foolish question.

Suddenly I came in doubt, and wanted to check it out, but the FFT SpectraLab program wouldn’t run, because of nVidia IDE driver problems.

But I am sure the indication of the data window, is in ‘level’ dBs, which means that 6 dB equals a factor 2 in level – e.g. 100% increase or 50% decrease in level.

The confusing about what dB actually indicates, is that it both can be ‘level’ and ‘power’ dBs. ‘power’ dBs are used for speaker system, where 3 dB equals a factor 2, because an increase in level means a similar increase in current and thereby the speaker power will be twice.

In the good old analog days, we had dBm, which indicated a reference level, but in the digital world, things tends to get mixed up, and terms like headroom is now obsolete.

To my knowledge, I haven’t seen any sound application using ‘power’ dBs for indication – but who knows

Subject:RE: of Sound Forge and dB's
Reply by: Rednroll
Date:4/19/2005 12:11:27 PM

Actually, Sound Forge doesn't quite support my theory of the 6dB being twice as loud scenario. A +6dB boast is definately twice the voltage, and a -6dB cut is half the voltage. So in other words a +200% increase in voltage with a +6dB increase and a 50% decrease in voltage with a -6dB cut. This is what Sound Forge's reference presets are set to. This fits into the equation 20 * Log of (Vnew/Vref). So if Vnew is twice the voltage of Vref you get 20* Log (200%)= +6dB or 20* Log (2)=+6dB

Here's some things to chew on regarding my viewpoint and my instructor's of +6dB being twice as loud:

The decibel is one of the most confusing terms in audio. History and Original Use: The unit was originally invented by Bell Telephone Labs as the Bel and given its name after Alexander Graham Bell. The decibel is 1/10 of this original unit. The Bel unit was defined as a ratio of power levels of 10 to 1(ten times the power or one-tenth the power). In Telephones, amplifiers are driving speakers and doing so over long lines. To drive speakers there needs to be a power transfer. So if you are in the business of driving speakers, you will analyze how much power there is available and how much power was lost in getting the signal to the speaker. What does Power have to do with Volume? More power means more volume can be achieved in the speaker but these two factors don't directly relate. Volume has to do with the amount of Sound Pressure there is. The EAR IS A PRESSURE SENSATIVE DEVICE. Power (in an electrical circuit) is not just the pressure but also the flow. In electricity, the pressure is the voltage and the amount of flow is the amount of current. If you put twice as much voltage into a device (say a light bulb) there would be twice as much current; because both the voltage doubled and the current doubled, the power has therefore, been multiplied by a factor of four. So in order to double the pressure of the sound pressure wave out of a speaker, you need 4 times the amplifier power to drive it.

Does Pressure and Voltage Directly Relate To Volume? For all practical purposes, yes. Although the ear is not exactly pressure sensitive, it is closer to being pressure sensitive than to being anything else. Many studies have been done regarding how changes in perceived loudness (volume) relate to level changes in dB. All of these studies suffered from problems in getting exact figures in that the personal opinion of listeners had to be consulted to get data for the studies. The results of the studies did show that the perceived change in loudness varied greatly (by some 30% difference) depending on the starting volume, the frequency of the sound and the complexity of the wave. [Howard W. Tremaine, The Audio Cyclopedia, Second Edition, pages 17-18] Furthermore, the greenest recording student listening to music played through a console with a meter can quickly discover that an increase in level of a certain number of dB is much easier to hear than a reduction of level by the same amount of dB. Someone (or some people) interpreted test data and made a generalization that a 10 dB change in level was twice (or half) the volume and many texts compound this useless and deceiving assertion. In practice the 6 dB change for full fidelity music represents twice (or half) the volume better than the confusing 10 dB. It has good scientific basis in that twice the pressure is an increase in 6 dB. The following is presented as factors supporting this:

1. For centuries, composers and conductors have used a formula that it takes four times the musicians to get twice the volume. If a composer/conductor wanted the violins to be twice as loud, they would specify 4 times as many. This is four times the power or a 6 dB volume increase. {ie dB=10*Log (P2/P1) => 10*Log (4)=+6dB}

2. If 10 dB is twice the volume, then 10 people talking (10 times the power) would be twice as loud as one person talking. {ie dB=10*Log(10)=+10dB} Any day care worker can tell you that 10 kids are much louder than twice the volume of one kid. If 6 dB is twice the volume, four kids would be twice the volume of one kid;{ie 10* Log(4)=+6dB} you might have a chance of a day care worker agreeing with you on this.

Modern Use of The Decibel Unit: Statements such as "voltage ratios cannot be expressed in decibels because decibels are, by definition, a ratio of power levels," it ignores the current use of the unit and published standard decibel notation. What is the case here is that the use of the term in the profession demands a new definition of the term. It is common in language for the manner that the word is used in society to be the final determining standard for what a word means and technical terms are no exception. When a technical term is being commonly used by professionals differently than the dictionaries say it should be, it is time for the dictionaries to be re-written. When you were little, it's possible that your teacher would not allow you to use the word "can" in asking a question. She may not have let you leave the room until you said, "May I go to the bathroom?" She was simply trying to get you to use words correctly. Most dictionaries of today allow you to use the word "can" when asking a question - it is too common in society for the writers of dictionaries to ignore. The same kind of thing has happened to the decibel. Except for the final amplifier that drives a speaker almost all equipment used in recording and sound reproduction is voltage sensitive. A change in voltage gain is a change in level, something to be measured, observed and used by recording engineers and design engineers. The dB, as read on meters, as specified for the level in and out of equipment, and as given in overload levels are voltage levels. The units dBV and dBu are based on standard levels of voltage completely divorced of current in the circuit or power levels.

When the original tests on this were made, it was the 1930's. They were reported in the first edition of the Audio Cyclopedia (c. 1936)

In the 30's you went to concerts and got recordings with the voice way up over the music (like 10 dB!). The ears were in compression in the midrange and therefore you would need to have 10 dB reduction in the input level (sound pressure going into the ear) to get half the loudness.

But when you played it for a while at the reduced volume, the ear would go into compression as you brought up the volume so 6 dB didn't sound twice as loud.

Now enter the 1950's where rock & pop had the voice much closer to the music track. Here 6 dB increases sounds more like 6 dB increases, more like "twice as loud."

Subject:RE: of Sound Forge and dB's
Reply by: kbouchard
Date:4/19/2005 3:42:28 PM

>Sound Forge's reference presets are set to<

I think we may be getting somewhere! :-)

The word "reference" rings a bell and red lights are flashing!
Is there ANY reference used for the data display or is that waveform strictly relative? Does the reference level of 20 micro pascals pressure (the faintest sound humans can hear) have any use at all in SF?

thanks, ken

Subject:RE: of Sound Forge and dB's
Reply by: Rednroll
Date:4/19/2005 3:51:10 PM

"Is there ANY reference used for the data display or is that waveform strictly relative?"

Yes, I explained that in my first post, they're referenced to 0dB Full Scale. The top of the display is 0dB Full scale and the bottom is "-inf", or in other words no sound, no voltage, no waveform. This has nothing really to do with DBspl levels that you're hearing coming from your speakers except for the fact that lowering the levels in Sound Forge will lower levels coming from your speakers, because you're lowering the level of the voltage coming out of your sound card, which then maybe connected to an internal amplifier stage within your sound card, or an external amplfier connected to your sound card, which then powers your speakers.

The dB by the very unit is a unitless value. dB = 10 x Log of P1(watts)/P2(watts). So you can see in this equation the units of reference (ie watts) cancel out. This is why there are so many different dB units, because they add an additional reference unit. ie dBu, dBspl, dBfs, dBv...etc.

Message last edited on4/19/2005 3:59:41 PM byRednroll.
Subject:RE: of Sound Forge and dB's
Reply by: kbouchard
Date:4/19/2005 8:09:22 PM

OK Red, let's see if I got this straight:
It sounds like we're talking about "sound pressure" coming from the speakers so I'll be using a factor of 20 in my calculations. (from what I can see in different web pages, the factor of 10 is used for power and 20 is used for pressure)
I'll use two different sound files, the first "scans" at 0 dB RMS, (our reference file,so to speak. You said 0 dB is the reference, right?) the second "scans" at -34 dB RMS.
Using my trusty scientific calculator which does logs and all that, I figure that the second file has a ratio of 50:1 (I keep seeing this formula, dB=20 log (pressure 2/pressure 1)
Question: When I play the two files, can I expect the first file to be 50 times louder than the second? Am I all wet?

thanks, ken

Subject:RE: of Sound Forge and dB's
Reply by: Rednroll
Date:4/20/2005 12:03:59 AM

Here's a table to use: Notice as you double the number on the left you add 6dB on the right.

1.5 x Louder= +3dB
2 x Louder = +6dB
3x Louder= +9dB
4x Louder= +12dB
8x Louder= +18dB
16x Louder = +24dB
32x Louder= +30dB
64x Louder=+36dB

And yes a 34dB level difference would be 50 times louder. (ie 34=20 * Log (Y x Louder) = Inv Log (34/20)

and yes, you would use the factor of 20. The original equation is in reference to power levels. Which is 10*Log (P2/P1). To get the other equation what they did was substute in Ohm's Law, which is V=I*R and Watts Law of P=V*I. If you combine these two equations you get P=V^2/R. Now you substitute this equation into the 10*Log (P2/P1). The R value is the same in the top and the bottom (ie your speaker resistance is the same), so it cancels out of the equation. So you have dB=10*Log((V2)^2/(V1)^2). The Voltages squared (ie ^2) can now be moved outside of the Log equation so it becomes dB=2*10 Log (V2/V1), or your final equation of dB=20*Log (V2/V1). The waveform you are seeing in Sound Forge is a Voltage representation of the audio, therefore you are solving this equation for the ratio of the voltages(ie V2/V1).

Clear as mud yet? :-)

Message last edited on4/20/2005 12:07:02 AM byRednroll.
Subject:RE: of Sound Forge and dB's
Reply by: airon0
Date:4/20/2005 1:23:43 AM

You forgot the Bell multiples.
Voltages and basically everything except power:
+20 dB -> 10 times as loud
+40 dB -> 10 * 10 = 100 times as loud

Power (PA systems, speakers and so on):
+10 dB -> 10 times as loud

This corresponds to the factor of 20 or 10 in front of the logarythmic component. I'm shure most of you can find the theory and developed equation in any physics reference. This forum lacks formula language to properly display it Red :) .

Btw, did you know that the Space Shuttle produces 180 dB SPL (Sound Pressure Level - Reference is 2 * 10^(-5) Pascal at 0dB SPL) during takeoff at 100 meters distance ? That's another reason people sit so far away on the grandstand to watch a launch. Standing near a commercial jet when it's rolling is usualy around 140 dB SPL.. Double the distance, quarter the volume, which is -12 dB. To get down to 132 dB SPL you would thus have to double your distance to the space shuttle four times, which results in a distance of 1600 meters, and will still hurt. At 6400 meters you'd still be going with very loud levels of 108 dB.

Physicians state that exposure to 95 dB SPL can occur for 15 minutes without causing permanent damage to your ears, and for 45 minutes at 85 dB SPL. Another reason to wear those plugs at concerts :) .

Message last edited on4/20/2005 1:29:30 AM byairon0.
Subject:RE: of Sound Forge and dB's
Reply by: kbouchard
Date:4/20/2005 2:23:55 PM

This is making sense. (somewhat)
The human sense of hearing is complex to say the least!
I have this book that says we're "wonderfully made", the author was on to something I think. :-)

thanks for your patience, ken

Subject:RE: of Sound Forge and dB's
Reply by: mpd
Date:4/20/2005 5:55:39 PM

Your explanation is pretty good, but your analogies of more people isn't totally accurate.

The issue has to do with coherent versus noncoherent signal summation. Basically, assume you have two signals, x and y, with power P dB. Now, assume that you sum x and y (what audio engineers call mix). What is the new power?

The answer depends on whether the signals are coherent or not. For those unfamiliar with this term, it has to do with the phase relationship between the two.

Try this in SF. Create two mono signals. Generate 2 sec of DTMF in each; choose the digits 1 for the first and 9 for the second. These two signals are noncoherent (they share no fundamentals). Set the amplitude to -11.8. The RMS power of each should be about -18 dBFS.

Now, do a select all of signal one, and create two new instances of it. To the first new instance (lets call it signal 3), mix signal 1. To the second new instance (lets call it signal 4), mix signal 2.

Run statistics on both. Signal 3 should be about -12 dBFS, signal 4 should be about -15 dBFS. Also notice that they peak at about the same value.

What happened here?

When we added signal 1 to itself, we essentially doubled the voltage, which quadrupled the power, hence a +6 dB power increase. A signal is by definition coherent with itself, so it obeys the cohenent signal summation equation, which is increase in dB is 20*log10(n), where n is the number of siganls of equal power.

When we added signal 1 and 2 together, we ended up with four sinusoids with no relation to each other (this is how DTMF works), so by definition, they were non-coherent. The non-cohenent signal summation equation is increase in dB is 10*log10(n), where n is the number of siganls of equal power.

Additional musicians playing the same instument and score would be coherent to each other. People talking in the same room would for the most part be non-coherent.

Subject:RE: of Sound Forge and dB's
Reply by: Rednroll
Date:4/20/2005 6:42:36 PM

Yes, I totally agree. Thus, the first example which is a fact known by orchestra conductors and these would be coherent, but there are very few orchestra conductors in this forum so not many could grasp this example. The day care children example is definately a non coherent example but more of one that most people can identify with. I still feel pretty comfortable saying that 4 people talking at the same time at the same level, regardless if they're saying the same thing at the same time at the same tone/timbre is much closer to being twice as loud as 10 people doing the same thing. Thanks for the suggestion of doing the exercise in SF, but I think I have a pretty good understanding of phase and signal addition and subtraction.

If you want to do a more representative exercise of my 4 children/ 10 children example then create 10 seperate white noise files in Sound Forge and place each of them on seperate Vegas tracks and tell me which one sounds closer to being twice as loud, 4 tracks of simultanous white noise playing or 10 tracks of simultaneous white noise. Now that would be more representative of non coherent signals playing at the same time with all of them at the same level.

Subject:RE: of Sound Forge and dB's
Reply by: jumbuk
Date:4/20/2005 7:43:05 PM

For a good in-depth discussion of dB and SPL, I recommend a book: "Mastering Audio: The Art and the Science", by BobKatz.

Subject:RE: of Sound Forge and dB's
Reply by: kbouchard
Date:4/21/2005 9:36:13 AM

sounds like this topic of coherent/incoherant sound might be analagous to synchronous/asynchronous . Am I out in "left field"?

thanks, ken

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