Decibels - Tech Note

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TECHNICAL NOTE

SOME NOTES ON DECIBELS The decibel is the most common unit used to measure the loudness of a sound. Many people know this, but few have a clear understanding of the concept or a real sense of what the numbers represent. This monograph provides a not-too-technical explanation of the decibel as applied to some common sounds and experiences.

T

O BEGIN, LET’S LOOK AT THE DEFINITION

and history of the word itself. The decibel (dB) is a unit of measurement that was originally developed to measure electricity, especially electrical power. It is also used in acoustics to measure the loudness of sound since there is a relationship between sound power and loudness. It is this acoustical use of the decibel which is most familiar to laymen. Actually, the original unit was the “bel.” It was developed in the 1920s at Bell Labs and named for Alexander Graham Bell. It turned out that the original bel was too large for ordinary purposes and that one-tenth of a bel (the deci-bel) was more appropriate. The decibel, then, is an objective numerical quantity used to measure the loudness of sound based on the amount of power produced by a sound.

It may seem strange to use an objective quantity for an experience that is so subjective, since it is well known that the sensitivity to loudness varies from person to person. In fact, this sensitivity also depends on the nature of the sound itself. For example, the alarm on my clock/radio, at 6 AM, seems louder than the music on the radio in the “wake up to music” mode. In reality, the alarm may just be more annoying, not necessarily louder. There seems to be an element of personal preference, taste, and psychological association in the perception of loudness.

Tech Note: Some Notes on Decibels

For scientific purposes, it is necessary to measure sound more objectively and precisely. To do this, we first establish a standard of loudness or reference level (usually expressed in pascals or watts). We then compare the loudness of any sound we wish to measure with this reference level. This comparison is done by a mathematical process resulting in a number (in decibels) which tells us how loud our sound is compared to the reference level. The whole computational process usually takes place inside a sound level meter, and the meter displays the numerical result. This same sort of procedure (comparison to a reference standard) is used for virtually all measurements including weight, length, color, etc. It’s just that the measurement of sound is not a common experience or need in daily life, so the “measuring sticks” for sound (sound level meters) are not common household items. Decibel readings provided by sound level meters are of little help to the average person since there is no intuitive relationship between decibels and common auditory experiences. To provide a subjective interpretation of decibel numbers, we ordinary use charts or tables that tell us the loudness levels of various common sound sources. One common version of a dB table is included at the end of this note. Take a look at this table now to get a feel for the loudness of various common sounds. The following provide some further elaborations:

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• Notice that the chart is not very precise. For example, we don’t see listed any information about the brand or model of the 80-dB vacuum cleaner, though we know that different vacuum cleaners can produce very different loudness levels. This chart (and all other similar charts) provides only an approximation of the loudness of typical sound sources. You may find a vacuum cleaner that produces 76 dB, or one at 85 dB. But, you probably won’t find one that produces 30 dB or 110 dB. • The ordinary range of dB values is between 0 and 120: these values are the “threshold of hearing” and “threshold of pain” respectively. You will rarely encounter any sound that is not within this range. • It is possible for a sound to be too quiet to be heard, i.e., below the threshold of hearing— below zero. It is, therefore, possible to have negative values of dB. Your sense of hearing cannot ordinarily detect such sounds, but sensitive sound level meters can. • The perception of loudness also depends on distance. From experience we know that the farther we are from a sound source, the quieter it appears to be. The standard rule for distance is that the sound level drops by 6 dB when you double the distance from the source. In your encounters with decibels, you may see references to various kinds of dB, e.g., “dB(A)” as in our dB table. You may also see dB(A) in specs for home audio equipment. dB(A) values are measured with sound meters equipped with an A weighting network, a set of electronic filters that approximates human hearing characteristics. You see, our ears are not very sensitive to high frequency (pitch) or low frequency sounds, but microphones and meters are. A meter with a dB(A) filter can, in effect, imitate the human ear and hear sound with about the same response as we do. Since we usually measure loudness to tell us something about human response to sound, most sound measurements are rendered in dB(A).

Tech Note: Some Notes on Decibels

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As you review the dB table you may notice some peculiarities, especially when you compare the loudness of different sounds. For example, you may ask: Is the rustle of leaves (20 dB) twice as loud as breathing (10 dB)? (Perhaps.) Is conversation (60 dB) twice as loud as a whisper (30 dB)? (That sounds more dubious.) You may have a sense that these are almost right, or could be, depending on how loud one is breathing, talking, or whispering. But things get more questionable as you move farther up the loudness scale. For example: Is a trailer truck (100 dB) twice as loud as the ambient level in the average home (50 dB)? If a trailer truck is 100 dB, will two trucks be 200 dB? And, if so, would those two trucks really be louder than a large jet takeoff at 50 feet away which our dB table lists at 140 dB? Our table is correct, but something is obviously amiss. There are two fundamental problems here. The first is that the decibel scale is logarithmic, not linear. Without delving into the math, let’s just say that decibel numbers, being on a log scale, cannot be combined like apples, or inches, pounds, years, nor most other quantities you are familiar with. The values used to describe these latter things are on a linear scale. (I’ll touch on log scales a bit more throughout this note, but with a minimum of math.) The second difficulty with decibels is that if you examine comparisons (e.g., twice as loud, half as loud) you will have trouble finding a correlation between dB values and your perception of loudness. This is because most of us have virtually no occasion to use decibels or logarithmic scales in everyday situations. The decibel scale does not conform with our expectations (based on experiences with other scales of measurement). For example, if you double the number of inches, you’ll see something that looks twice as long; if you double the number of decibels you probably won’t hear a sound that is twice as loud!

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One way to comprehend the decibel scale is to examine the notion of combining or adding sounds. But, as you may already suspect, a method for the addition and subtraction of decibels is not obvious. A rigorous explanation of decibel addition requires a real comfort level with logarithms. Since most people are uneasy and unfamiliar with logs, I will explain the concept through examples rather than mathematics. I will do this with the presentation of two rules of dB addition as simple numerical concepts, and then see how the addition of actual sounds would be perceived by a listener. The first rule of dB addition is that when you double the amount of sound (e.g., combine two equal* sound sources) the result will be 3 decibels louder. Stated as a rule: if you double the sound power, add 3 dB. This leads to some rather strange expressions: 60 dB

+

60 dB

=

63 dB

95 dB

+

95 dB

=

98 dB

Those look peculiar, but how about these: 3 dB

+

3 dB

=

6 dB

(Finally, that seems to make sense.)

0 dB

+

0 dB

=

3 dB !

Ordinary speech is about 60 dB measured at 3 ft. from the talker. The sound level of two people talking (simultaneously and at 60 dB each) would be about 63 dB. A single violinist is sustaining a tone at 78 dB. Two violinists sustaining the same tone (each at 78 dB) will produce a sound level of 81 dB. Let’s push this a little further: Together our 2 violins are producing 81 dB. If we add 2 more (i.e., double the number of violins for a total of 4), we will have 84 dB. Add 4 more for a total of 8 (another doubling) and we have 87 dB. Each doubling adds 3 dB! The second rule is that when you combine 10 equal sounds, the resulting sound will be 10 decibels louder. Simply add 10 dB to the level of one of the 10 levels. For example: If you combine 10 equal sound sources, each producing 15 dB, the result is 25 dB. If you write this out as 10 separate sources at 15 dB each, it looks a bit odd: 15dB + 15dB + 15dB + 15dB + 15dB + 15dB + 15dB + 15dB + 15dB + 15dB = 25 dB Another example:

(But that really looks strange!)

All four examples are correct and follow directly from applying the rule stated above.

10 sources at 86 decibels each is: 10 @ 86 dB = 96 dB The following will summarize our two rules:

Let’s see how this rule would be applied to some realworld examples:

* I am taking some liberty with the idea of two “equal” sounds. In the examples on this page, there could be a lot of debate about how equal two talkers or two violinists might be. For now, let’s assume we have a perfect world and that our equal sound sources are able to produce sounds that are identical in every way.

Tech Note: Some Notes on Decibels

If

1 person talking is 60 dB, 2 would be 63 dB, 10 would be 70 dB.

If

1 violin is 78 dB, 2 would be 81 dB, 10 would be 88 dB.

(If you are adventurous, try extending the 3-dB rule to 4, 8, or 16 sounds; the 10-dB rule to 100, 1,000, or 100,000. Then try some combinations, e.g., 20 or 400.)

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Let’s take a break from numbers. What does it sound like when sounds are combined? We’ll look at some common experiences for help. Have you ever attended a concert where a solo violin played with an orchestra? Let’s say, for simplicity, that there are 10 violins in the orchestra. Do those 10 violins (when playing together) sound 10 times louder than the solo violin? No! Not really. How about a choral concert with a vocal soloist? Does a 100voice chorus sound 100 times louder than the soloist? No! Of course not. How about 2 vacuum cleaners? Do they sound twice as loud as one? This last example is less obvious. But, by now you might be wondering what is meant by “twice as loud.” It is not a precise concept. Acousticians realized that there was little correlation between the decibel scale and the human perception of loudness. To find a relationship, tests were conducted with thousands of people. Each subject sat in a soundproof chamber in front of a loudspeaker. A sound was played and the listener adjusted the loudness until the sound was judged to be “twice as loud.” As a result of these subjective tests we have a good idea of how the average person responds to loudness, and some basic “rules-of-thumb” for acoustics: 1.

If you increase the sound level of a tone by 10 decibels, it sounds about twice as loud. Conversely, if you decrease it by 10 dB, it sounds about half as loud.

2.

It takes an increase of about 3 decibels for a listener to hear any difference in loudness. In other words, one sound would have to be 3 decibels louder than another for you to hear any difference in loudness. A change of 3 dB is, therefore, referred to as a “justnoticeable difference.” (NB: In a laboratory and under ideal conditions, this just-noticeable difference is about 1 dB. The 3-dB value is for more common real-world situations.)

You may want to keep these rules in mind the next time you’re shopping for a stereo. If a salesperson tells you that for a $100 more you can buy a 200-Watt stereo which will sound twice as loud as a 100-Watt system, you will see that this sales pitch is false. You now know

Tech Note: Some Notes on Decibels

that your “$100 more” for twice the power will buy you only 3 dB, i.e., a “just-noticeable difference” in loudness. Remarkably, it would take a 1,000-Watt system (10 times the power for a 10-dB increase) to “sound” twice as loud as a 100-Watt system. If you now combine the rules and examples above, you can come to some surprising but reasonably accurate conclusions. For example: 1.

It takes 10 violin players to sound twice as loud as 1.

2.

All other things being equal, a crowd of 100 people will be just a little bit noisier than a crowd of 50 people. That’s because you have twice as many people and twice as much sound. But, twice as much sound power produces an increase of 3 dB which is our “just-noticeable difference.”

3.

If two vacuum cleaners are running and are disturbing you, then turning off only one of them will have little effect. If each one alone produces 80 decibels, then both together will produce 83 dB. Now if you turn off one of them, the sound level drops from 83 down to 80. That is the “justnoticeable difference.” Surprised? Try it yourself sometime. You will be surprised! (Have you ever noticed that it is difficult to tell when one of your stereo speakers is disconnected? That is because the loudness drops by only 3 dB!)

There are two major conclusions to remember from this discussion. First, although the decibel is a well-defined quantity in acoustics, the relation between decibels and the human perception of loudness is not straightforward. Second, expressions such as “twice as loud” or “half as loud” have no formal scientific definitions. We do have some rules-of-thumb to help us work with these concepts. But they are imprecise and subjective: they vary greatly from person to person. This is true of most human senses. (Compare the notion of “twice as loud” with “twice as hot” or “twice as bright.”)

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Summary No pedantic discourse would be complete without the traditional brain-teaser to let you test your own understanding of the concepts presented. Here are a few to think about. 1.

2.

3.

Joshua returned to Jericho only to find that the wall had been rebuilt with stronger materials. (Space-age carbonfiber composites, I suppose.) The new structure can withstand a trumpet blast of 115 dB, but no more! The loudest sound Joshua can play with his trumpet is 100 dB. Can Joshua plus 39 other equally gifted trumpeters make the wall come tumbling down? AC/DC (a popular music group) was performing in a large theater. During rehearsal they found that with 20 loudspeakers, they could produce sounds of 120 dB at row M (60 ft. away). How many more identical speakers will they need to produce the same level at row Z (120 ft. away)? My apologies to AC/DC for using the “threshold of pain,” 120 dB, for this example. If the cooling fan on one IBM computer produces 55 dB, how loud are 4 fans? How loud are 20? 320? 8,000? — OK, for laughs, how loud are 64,000,000 fans?

Answers 1.

Yes, 40 trumpets at 100 dB each will produce 116 dB.

2.

80 loudspeakers. If you double the distance, the loudness drops by 6 dB. (See page 2, paragraph 4.) This means that 20 loudspeakers will produce 114 dB at row Z. If you double the number of speakers you will have 117 db at row Z; double again to get 80 loudspeakers at the level at row Z will be 120 dB.

3.

4 fans = 61 dB; 20 = 68 dB; 320 = 80 dB; 8,000 = 94 dB; 64,000,000 = 133 dB.

• The decibel is a unit used to measure the loudness of sound. Decibel numbers are based on a logarithmic scale and do not combine like ordinary numbers. Loudness measurements are typically done with sound level meters.

• In daily life, where sound level meters are uncommon, loudness is estimated by making subjective comparisons with sounds listed on dB tables. This procedure, though inexact, is generally sufficient since the human perception of sound is imprecise and subjective.

• To work with decibels in most common situations, you can apply the two basic rules listed below. However, you must make a distinction between the objective form of these rules (what the numbers say) and your subjective experience of loudness (what your ears will hear). 1. If you double the amount of sound power, there will be an increase in loudness of 3 dB. This 3-dB increase will sound louder, but only justnoticeably louder. It will definitely not sound twice as loud. 2. If you increase sound power by 10 times, there will be an increase in loudness of 10 dB. To the average listener, this 10-dB increase will sound about twice as loud. The following table summarizes these rules: IF YOU INCREASE SOUND POWER BY

THE I NCREASE IN MEASURED SOUND LEVEL WILL BE

THE PERCEIVED INCREASE IN

LOUDNESS WILL BE

2 times

3 dB

just noticeable

10 times

10 dB

twice as loud

— also (as a corollary) — If you double the distance between the sound source and the listener, the power per unit area at the listener’s position will decrease by a factor of 4: the measured sound level will decrease by 6 dB.

Tech Note: Some Notes on Decibels

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COMMON NOISE SOURCES AND SOUND LEVELS Source of information: National Bureau of Standards Handbook 119 (July 1976)

SOUND LEVEL in dB(A)

NOISE SOURCE

140 ...................................

Large jet at takeoff; 15 m (about 50 ft.) away

130 ...................................

Air-raid siren; 15 m (about 50 ft.) away

120 ...................................

Threshold of pain

110 ...................................

Thunder, sonic boom

100 ...................................

Trailer truck at roadside; 5 m (about 16 ft.)

90 ...................................

Power lawn mower; 2 m (about 6 ft.)

80 ...................................

Vacuum cleaner, garbage disposal; 2 m (about 6 ft.)

70 ...................................

Freeway traffic; 15 m (about 50 ft.) away

60 ...................................

Conversational speech; 1 m (about 3 ft.)

50 ...................................

Ambient level in a typical residence

40 ...................................

Ambient level in a typical bedroom

30 ...................................

Soft whisper; 5 m (about 16 ft.)

20 ...................................

Rustle of leaves

10 ...................................

Breathing

0 ...................................

Tech Note: Some Notes on Decibels

Threshold of hearing

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