Los Senderos Studio
Decibels
 Issue 73 October 2015 
dB Meter

Words from the Glossary

This month we explore the wonderful world of decibels.

This month's terms: decibel, bel, dB, dBA, dBB, dBC, dBf, dBm, dBr, dB-SPL, dBu, dBV, dBw, dBr, 0 dBFS, 0 dB-SPL, sound pressure level.
(Note: Click on the term to view its definition in the glossary.)

Decibel

The decibel is one of those terms that most people think they understand, but few actually do. Most people associate the decibel with sound levels and loudness. But that is just one small part of its purpose. So let's take a closer look at the decibel.

Sound Pressure Level
Sound Pressure and Sound Pressure Level

The basic unit for this measurement is the bel, named for Alexander Graham Bell. It is a logarithmic unit, which basically means that we are looking at exponential measurements, things that vary by factors of 10.

For example, if you look at the chart at right, you will see that the measurements on the right run from 20 to 100,000,000. The largest value is 5 million times greater than the lowest. If we plotted this on a linear scale, most of the items on the chart would be squashed into the bottom tenth of an inch. To make this more readable, we use a logarithmic scale. However, the bel is too large for what we want to measure. So instead, we use a tenth of a bel, or a decibel.

Although we think in terms of sound level, the decibel is actually a ratio of two power levels, one of which is a reference value. In the case of sound levels, we use the ratio of the item being measured to the threshold of hearing—the quietest sound that a human ear can hear, which is defined as 20 micropascals. (A pascal is a unit of pressure equal to about 0.00015 pounds per square inch. So you can see that we are dealing with extremely small values of pressure.) So a decibel for sound pressure level (SPL), which is designated as dB-SPL is the log of the ratio of the measured sound level to the threshold. For example, if loud rock music has an SPL of 10,000,000 μPa, the dB-SPL will be 20 times the log of 10,000,000 divided by 20 or about 114. (We'll discuss where the first 20 came from in a moment.)

Human hearing also tends to be logarythmic. See graph below. Also because human hearing does not perceive all frequencies equally, engineers are fond of throwing in fudge factors. A-weighting is one such factor and is an attempt to make hearing measurement more like the human ear. A decibel scale using A-weighting is designated dB(A) or dBA. There are also B-weighting and C-weighting, which use dBB and dBC.

Perceived Hearing

As mentioned, the decibel is the log of a ratio of two power levels. One unit of measuring power is the watt. Using a reference power of one watt, dBW = 10 x log (P), where P is the power being measured. (The first 10 is to convert from bels to decibels.)

In the recording studio, audio signal levels are usually measured in volts, but since the levels can vary from a few microvolts to several volts, a linear scale usually is not convenient. So the decibel would be a much better unit. So the decibel would be 20 times the log of the ratio of the voltage being measured to some reference, but what reference? And why 20? As it turns out, power is proportional to the square of the voltage. So when you have a ratio of two things that are squared, it is equivalent to twice the logarythm of the ratio not squared. The 10 of course is the bel to decibel conversion.

As for the reference, how about using one volt? So we could define dBV = 20 x log (V). That is the unit usually associated with consumer electronics. However, just to be stubborn, someone decided that in the studio, we are dealing with RMS voltage. RMS voltage is the effective voltage because a one volt alternating current is constantly varying and only averages about 0.775 volts. So another decibel is defined as dBu = 20 x log (V/0.775). This is the unit usually encountered in the studio and other professional applications. And 0.775 volts is equal to zero on the VU scale. Most of the time when dealing with decibels in the studio, we are discussing dBu which is a measure of voltage, although most musicians are probably thinking in terms of loudness.

There is one more definition we need to consider. And that is dBFS or dB(FS). This is a decibel scale where the audio reference level is equal to full scale. Zero on this scale represents the absolute maximum voltage level and has a digital code consisting of all ones (111111111111). Therefore, no digital level can exceed 0 dBFS. When voltage exceeds that level clipping occurs and the tops of the peaks are chopped off. That is why levels in the studio are always negative. You start at a maximum of zero and go down.

So the next time you encounter a decibel, think about all the possibilies it represents.

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Music Trivia

In October, 1966, "96 Tears" by Question Mark (?) and The Mysterians reached number one on the Billboard chart. Originally the song, written by lead singer Rudy Martinez (Question Mark), was entitled "Too Many Teardrops," but he changed the title to "69 Tears." Realizing a song with such a title would never get any radio airplay, he again changed the name. It was recorded in the living room of their manager's house in Bay City, Michigan.

On October 17th, 1990, the album To The Extreme by Vanilla Ice reached number one on the album chart. This marked the first time that the No. 1 album in the United States was only available on CD or cassette. It had not been issued on vinyl.

The soundtrack for the movie "Saturday Night Fever," written and and performed primarily by the Bee Gees, went platinum fifteen times over. Despite this success, Robin Gibb, who died in 2012, never saw the movie.

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