For Whom The Decibel Tolls

By The Metric Maven

I’m old enough to recall the CB radio craze of the 1970s. Everyone ended up with a CB radio in their car, and in large cities, the radio traffic could be daunting at times. I was driving with my friend Ty one day. On his CB we were listening to a pair  of interlocutors, when one said “You look good, you’re pushing 12 pounds.” I had no idea what was being said. Ty began to laugh.

“They’re talking about the signal strength on the front panel meter, they think dB means pounds.”

I was a bit surprised. At that time, I did not have a real understanding of dB or decibels, but I knew they were not pounds.

I eventually learned from an electrical engineering professor that it was very important social skill be able to “talk about decibels with confidence at parties that other engineers might attend.” The origin of the decibel always seemed rather obscure. One would apocryphally hear that a unit called the Bel (after Alexander Gram Bell) had been created, and that one-tenth of that unit was considered of most use, and became known as the decibel. Early on, as an engineering student, I learned that 3 dB is a factor of 2 in power, and 10 dB is a factor of 10, so 13 dB is a factor of twenty. dB’s were used to express large numbers and large dynamic ranges (smallest to largest numbers in a set) in a tenable fashion.

The weird part was always the metric prefix, deci is attached to a logarithm, rather than to a fixed value, as is standard in the metric system. The decibel always requires a reference value. What this means is that one might receive 10 milliwatts of power in a system, and if the decibel reference value for that system is one milliwatt, the received power is 10 dBm, or 10 decibels with respect to a milliwatt. The m is an abbreviation of a metric prefix, so context is important to interpret this version of a decibel. As an engineer, one always wanted to know the defining reference power for the defined decibel under discussion. Without it, a value in decibels is void of meaning, other than as a ratio.

I’ve watched football games on television where the announcers would breathlessly claim the crowd was very loud. To demonstrate this in an authoritative manner, they would produce some measurement device and say: “it’s over 100 decibels in here, that’s like the sound of a jet aircraft.” I had done some acoustic testing during my career, and knew there are a number of different references for sound level. As I recall, I tested to something called A weighting, that had it’s own power definition, often called sound pressure level, and denoted dBSPL. The values were also in dBA, or dB A weighted sound. Without a reference value, the value of sound power the announcers were offering as an authoritative measurement, had no real units.

Recently, while doing some research, I had an excuse to look into this strange metric-sounding unit and its history. I heard a number of apocryphal tales about the origin of the dB, but the actual origin begins with the Bell Telephone Company in the late 19th and early 20th centuries. The telephone company had created a test where they set up:

… two common battery telephone sets of the type standard in the Bell System at the time this circuit was adopted, connected through repeating coils or transformers to a variable length of “standard cable.”

They knew that the longer the cable length between telephones was, the fainter the received voice would be. This set-up was called a “Standard Reference Circuit.”  The Bell System Technical Journal of 1924[1]  states:

The circuit then became the measuring or reference system for engineering the telephone plant and the “mile of standard cable” became the unit in which the measurements were expressed.

This comparison was on the basis of a speaker talking alternatively over the circuit to be measured and the standard circuit and a listener switching similarly at the receiving ends, the amount of cable in the standard circuit being adjusted until the listener judged the volume of sounds reproduced by the two systems to be equal. The number of miles of cable in the standard circuit was then used as the “transmission equivalent” of the circuit under test.

In some obscure book I read on measures, I recall a measurement “unit” that I believe was called the “whoop.” One person would stand and listen, while the second shouted “whoop!” and slowly moved away from the first. At the distance the first person could no longer hear the second person, he would wave his hand.  This became the length of the “whoop.” At the time I read this idea, it seemed rather ridiculous, but here was a version this old idea implemented in telephone design.

Rather than the whoop, the length of a “mile of standard cable” was the “unit” adopted, and often it was just called miles. A new design might be 16 miles better than the original design, and so on. Engineers realized the fuzzy and unscientific nature of this measurement setup, and wanted to improve the situation.

Bell System engineers then proposed a new unit they called “The Transmission Unit.” The new “unit” would be based on the ratio of the power into one end of a cable to that received at the other end. A logarithm would be taken of this ratio, but most importantly, in their list of six proposed qualifications for this new “transmission unit” was:

5. Approximately Equal in Effect on Volume to a “Mile of Standard Cable.” One reason for this is the practical of avoiding material changes in the conceptions which have been built up regarding the magnitude of such things as transmission service standards. Also, the sound power changes which can be detected by an ear are of the order of that corresponding to a mile of standard cable. …..

They go on to relate the properties of the new transmission unit:

A consideration of the above qualifications and of the various units suggested, led to the adoption of 100.1 as the most suitable ratio on which to base the unit of transmission efficiency. …… Its effect on the transmission of telephonic power corresponding to speech sounds is about 6 percent less than that of a mile of standard cable.

So in the end, it was important that the transmission unit or TU be as equivalent to the mile of standard cable measure as possible. There was no break from the past, only a mathematical estimation that would lead back to the measurements of a “standard ear.”

An article in a 1924 Bell System Technical Journal tried to rationalize this less than scientific definition a bit by arguing:

It will be noted that the TU is based on the same ratio 100.1 as the series of preferred numbers which has been used in some European countries and has been proposed here as the basis for size standardization.

If you are not familiar with preferred numbers, I recommend my essay Preferred Numbers and the Preferred Measurement System. This argument for the adoption of the TU seems a bit of a convenient post-hoc afterthought.

In 1929, it was announced in The Bell System Technical Journal, that the Transmission Unit was now named the Decibel.[2] In discussions with The European International Advisory Committee, Bell System representatives suggested the fundamental decimal unit be called the ‘bel’ after Alexander Gram Bell. Long time readers know what I think about the idea of naming units for humans. The final paragraph of the article states:

The Bell System has adopted the name “decibel” for the “transmission unit,” based on a power ratio of 10.1. This is in accordance with the terminology for the decimal unit, the prefix “deci” being the usual one for indicating a one-tenth relation. For convenience, the symbol “db” will be employed to indicate the name “decibel.”

The use of deci with a logarithmic ratio strikes me as a bit pigfish, and not really in the spirit of the metric system. The utility of the decibel is clear, as the Wikipedia page on this “unit” has dozens of examples of decibels used in every area of engineering and science. They do also offer criticisms of the logarithmic unit. The decibel has been suggested for inclusion in SI, but has not been. That seems very reasonable to me. The decibel only sounds metric, it has an almost infinite number of “units” depending on what the reference power is, and so it seems best that it should remain an expression used (and overused) by engineers and scientists. The decibel is more for quantity comparison, than as a unit in and of itself.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page.

[1] The Bell System Technical Journal July 1924 pp 400-408

[2] The Bell System Technical Journal January 1929 pp 1-2