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Decibel Flavors Part 1 – L Values

Over the next few articles I will explain some of the different meanings of the word “decibel” as it relates to sound.  ”Decibel,” by itself, is not a unit of measurement of loudness.  Decibels are a way of counting large numbers, very similar to the Richter scale.  For people to be talking apples to apples about noise, they need to be clear about what flavor of decibels they’re using.

In this article I will talk about the different kinds of L Values.  In the next article I will talk about weighted values and sound spectra.  You need both of these pieces to determine what “decibel” means.

Sound level measurements are taken over time.  If you have an inexpensive sound level meter, it probably just has a screen with a single number that bounces up and down on the screen depending on what it’s measuring right at that moment.  While this is useful for getting a general idea of what sound levels you’re measuring, it’s not very useful for making numerical comparisons.  The type of sound level meter used by acoustical engineers makes a complete measurement with a beginning and an end; basically a short recording.

This chart shows a basic sound level measurement.  The curve is the Sound Pressure Level (SPL), which is the sound level at a specific moment.  SPL fluctuates with time.  If you were making this measurement with an inexpensive meter, you would see the value on the meter move up and down in time in a way that resembled the curve below.

The problem is a sound that lasts over time never has a single SPL value.  Since it fluctuates over time you have to find a way of describing the entire curve with a single number.  It turns out there are several ways of doing just that.

Very frequently, the metrics Leq, Lmax, and Lmin are used.  These refer to the Equivalent Level, the Maximum Level, and the Minimum Level.  Lmax and Lmin are the easiest to understand, they’re simply the highest and lowest values the sound level meter saw during the measurement:

Leq is trickier to understand.  Technically the following charts aren’t a correct representation, because Leq depends on the actual numerical value for sound pressure level, not the decibel value.  But understanding that is not necessary for understanding the idea behind Leq.

Leq is the Time Weighted Equivalent Level. That’s kind of a mouthful but it’s not too complicated.  Weighting is a way of averaging.  Here’s how it works out:

The below chart shows everything below the curve highlighted in red.  The size of the red area is, essentially, the SPL multiplied by the amount of time of the measurement.  In order to multiply something by a curvy line, you have to use calculus, which is actually what an “integrating sound level meter” is doing.

If you take the entire red area and rearrange it so that it makes a nice square shape, you’ll have something like this:

This red square has the same area as the red area under the curve in the previous figure.

The Equivalent Level, Leq, is the sound level that would result in a square with the same area as the curve.

Leq and Lmax are used quite frequently.  Lmin is not used as often, but is usually recorded alongside Leq and Lmax anyway.

Another method of deriving a single number from a sound level measurement is with a Statistical Analysis, or “Ln values.”  ”Ln” by itself describes the methodology and isn’t an actual level.  The actual levels are written with a number in place of the letter n.  Typical Ln metrics are L10, L50, and L90.  You can have any Ln value you want, L37.5, for example.

What the number refers to is the “percentile” of the value.  Specifically, the amount of time the sound level was above the Ln value.  L10 is the level, in decibels, that the sound level exceeded for 10% of the time.  L50 is the value that the sound level was above for 50% of the time and can be considered the median value.  L90 is the value that the sound level was above 90% of the time.

Graphically speaking, Ln values are calculated by adjusting a line up and down until exactly the correct percentage of the line is below the curve.  The L10 line is adjusted until 10% of it is below the curve, the L50 line is adjusted until exactly half of it is below the curve, and the L90 line is adjusted until 90% of it is below the curve. Once those lines are adjusted to the proper height, you read the value from the left axis of the graph to determine your Ln values.

So on the following chart, if our Lmax was 80 dB and our Lmin was 40 dB, L10 would be about 78 dB, L50 would be about 65 dB, and L90 would be about 45 dB.

The chart below shows the lines without showing the SPL curve.  The sections in red are what would appear below the curve.  For L10, the section below the curve (red) is 10% of the total length of the line.  For L50, the red portions make up half of the length of the line.  For L90, the red portions make up 90% of the length of the line. The length of the lines left to right is equal to the amount of time of the measurement.

Ln values are very useful for long term noise measurements, such as what you would use for an environmental noise study.  Such studies often have measurements that last for several days.  L90 is commonly used to determine the ambient, background level.  If your L90 value is 45 dB,  that is the same as saying “the sound level was 45 dB or higher 90% of the time.”

In the next article I will write about the different ways of combing all the different frequencies of a given sound into a single number.  This includes A-weighted decibels, or dBA, which are the most commonly used single-number flavor of decibels, and what the great majority of noise ordinances refer to.

Is something still unclear?  Did I make a mistake?  If so, please ask any questions or share any comments in the comments section of this article.  I will attempt to clarify anything I didn’t explain well or correct any mistakes I may have made.

11 Comments

  1. Cliff Adams says:

    Joshua, I am interested in getting in touch with folks who are concerned about the loudness of Nutty Brown concerts. Do you have any contact info for those groups or individuals (such as yourself)that are trying to make a difference?

  2. David says:

    Could you explain how L10 and L90 are actually calculated from sound level measurement data?
    That is, given a one hour sound level measurement at 10 second intervals, how would you calculate the L10, practically speaking? Is there a way to do it in the Excel spreadsheet program?

    Thanks

    • Hi David. Very good question!

      It’s really a matter of counting more than a matter of calculating. Ln values are called statistical measurements because they’re a result of analyzing a group of samples, rather than performing a calculation. During a measurement the sound level meter continuously adds the current SPL to a histogram. The interval between samples is constant and internal to the meter, and certainly less than a second. L10 then becomes the value that is lower than 10% of the measurements and higher than 90% of the measurements.

      Here’s a very simplified example. Suppose we turn on our SLM long enough for it to collect 20 samples and we ask it to tell us the L20 of the measurement. The samples it collects, in chronological order, are:

      58, 59, 58, 57, 56, 55, 55, 56, 56, 57, 58, 59, 60, 61, 62, 62, 61, 62, 63, 64

      To determine L20, we look for the value that is below 20%, or 4 out of 20, of the samples. The easiest way to do this is to sort the samples in descending order:

      64, 63, 62, 62, 62, 61, 61, 60, 59, 59, 58, 58, 58, 57, 57, 56, 56, 56, 55, 55

      L20 will be the value below the top 4 values and above the bottom 16. The 4th and 5th samples (in descending order) are 62 and 62, so L20 is 62. In other words, 20% of the time, the measured sound level was above 62 dB.

      We can also determine the L50 (or any other Ln from our data) by using a similar analysis. Instead of the top 20% of samples, we would instead determine the top 50%, or 10 out of 20. The 10th and 11th samples, in descending order, are 59 and 58. So the L50 is somewhere between 58 and 59 dB.

      The only way you could really do this calculation in Excel is if you had access to frequent periodic samples of the measured sound level meter. Generally the only way you can collect that type of data is with an advanced sound level meter, and such a meter will almost certainly have Ln functionality built in, so it’s sort of pointless to do it yourself. In a real Ln measurement the SLM will collect far more than 20 samples, so doing it by hand in a spreadsheet could be quite an undertaking.

      If you had a quick pencil, you could approximate Ln values by watching a simple SLM and recording the value at regular intervals; every 10 seconds for an hour, to use your example, would work well, giving you 360 samples. You would watch a clock with a second hand and every 10 seconds write whatever value was on the SLM at that moment. You would then enter all of your samples into a spreadsheet and sort them in descending order. You could then determine your approximate L10 by seeing what value had 10% (36 out of 360) of the samples above it.

      -Joshua

  3. seti says:

    hello hye..
    joshua
    thanks alot for details explaination..u’re really help me to find out the L10, L90 and Ln manually.
    actually for noise level measurement i used sound level meter and the value will appear digitally
    but for manually, if we can’t read the Leq so we can use L10 L90 l50 to calculate Leq,is that right joshua?
    good jobs dear.

  4. David says:

    Joshua:
    Thanks, I discovered a function / formula in Excel that calculates L10 and L90 automagically from a data set

    It is the “percentile” function.

    • Determining Ln values from a data set isn’t too difficult, though it’s tedious, so the percentile function would certainly make that task more simpe (“percentile” is another term used to describe statistical values). The trick is actually collecting the data. Generally the types of sound level meters that can collect the type of data appropriate for determining Ln already have Ln functionality built in.

  5. Ralph says:

    Thanks for the useful explanation Joshua. Would the L90 figures have to be calculated from the actual numerical value for sound pressure level, not the decibel value, in the same way as in the LEQ calculations?

    • Hi Ralph. There’s no point in converting decibels to sound pressure, since you’re not actually “calculating” L90 in a strict sense of the word. It’s really just a statistical examination of the data, and each individual SPL sample the meter takes is not added/subtracted/multiplied or otherwise mathematically combined with any of the other samples. 60 dBA will always be higher than 59 dBA, regardless of whether you’re talking in decibels or Pascals of sound pressure, so it works no matter what you do. Better to just stay in decibels.

      Another perspective that might help you understand the process is to consider that finding L50 is the same process as finding the median. The median value of any group of data falls below 50% and above 50% of the group. The L90 value falls below 90% and above 10% of the samples.

  6. Ralph says:

    “60 dBA will always be higher than 59 dBA, regardless of whether you’re talking in decibels or Pascals of sound pressure”
    Thanks Joshua, I realise that was a kind of dumb question now! (Like asking if I need to change a box of jelly babies into chorus girls before counting them. Actually, there would be some point in doing that….) :)

    I’ve got the percentile formula working in Excel now. Just as a point of interest for those trying it, the syntax is:

    PERCENTILE(Range,xValue)

    Because of the way the formula works, For L90 the xValue is 0.1, for L10 it is 0.9. The only Ln value that is the same as the xValue obviously is L50.

  7. Don says:

    Hi, I have a dilemma. During monitoring noise at a certain location, overall 15-minute L90 values (linear) were recorded. However, I am after the A-weighted 15-minute L90 value. There is no spectrum for the L90 values and only have spectrum data for Leq,1min. Is there any way the A-weighted L90 value,15minute could be derived from the available data? Any help would be appreciated.

    • There’s no way to do a direct conversion, since Leq and L90 are calculated in fundamentally different ways.

      I can think of two ways you can make an approximation. Neither of them are great, but I can’t think of any better options.

      The first thing you can do is make the assumption that the Leq spectrum is similar in shape to the L90 spectrum. This is not a reliable assumption to make, since the L90 spectrum can be quite different from Leq, depending on what sounds you were measuring. Subtract the difference between your unweighted (overall) Leq and A-weighted Leq from your unweighted L90 and that will approximate the A-weighted Leq.

      L90 (dBA, approx) = L90 (unweighted) – [Leq (unweighted) - Leq (dBA)]

      If you don’t have the unweighted Leq already, you can calculate it by adding up the 1/3-octave or octave bands using decibel addition.

      The other approach you can take is to do some research and dig up some Ln spectra for a similar measurement. L90 captures a good representation of background, ambient noise, so if you can find a measurement done in a similar location chances are decent the background spectrum will be similar to what it was for your measurement. Again, approximate the A-weighted L90 for your data by subtracting the difference between the unweighted and A-weighted numbers for your reference measurement.

      Hopefully you weren’t in an unusual environment. If you were somewhere typical, like an outdoor rural area, then comparing your data to a measurement in a similar environment should yield decent results.

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