“Full of sound and fury, signifying nothing”

SHADES of entropy, metacentric height, and degaussed heeling magnets—the Navy is full of decibels!

We have seen the compass “boxed” in lubberly degrees, the wind logged in freshwater miles by anemometer, and the “main engines” rated in pole combinations and power factor—now we find our boiler- rooms and living spaces, our radios and detectors, our telephones and motors, all being rated in decibels. Had Coleridge’s Ancient Mariner been a modern his mournful stanza might well have read,

The ice was here, the ice was there,

The ice was thick as hell;

It cracked and growled, and roared and howled,

In confounded decibel!

Today operators compare radio signals in decibels; sound men sputter in the same language about planes and submarines. Telephone engineers compute line “loss” or “gain” in “db.,” and manufacturers rate the “power” of amplifiers and similar equipment in this unit. Walt Disney’s new “Fantasia” with “stereophonic” sound effects is described as having a “volume range of 75 db.”; in the cafes on Hollywood movie lots you will find the “decibel” as common in the shop talk of directors and stars as “fadeout” or “long shot.”

But that is not all. Navy contracts for leased wires specify “power level” in db. The bureaus specify the requirements for such varied characteristics as “power level,” “frequency selectivity,” “gain,” and “output” in db. In an official technical bulletin even “personal equation” is expressed quantitatively in decibels, along with “field intensity” and “percentage,” in a dissussion of the increasing difficulty of finding a place to hang an antenna aboard ship.

All life is involved. A table shows that:

The mightiest roar of a lion in the Bronx Zoo is 90 decibels, a value comparable to the noisiest spot at Niagara Falls.

In a quiet office (pre-emergency!) the sound level may be as low as 40 db.

From a child’s whisper to a boatswain’s loudest shout a range of 60 db. is covered.

New York drivers whose horn power registers more than 75 db. at 100 feet on the traffic officer’s noise meter tell it to the judge.

Navy yard riveters and chip-hammers inflict over 100 decibels upon us who stay aboard during overhaul; and man cannot tolerate much above 120 db., the threshold of painful feeling.

Now all this indicates that the decibel has moved in on us and is here to stay. When I returned recently to Communications after a general line holiday—destroyer duty, gunboat cruise from China to Chicago (where you get used to three blasts in a fog), I found myself in an unfamiliar new world of high gain diversity antennas—miles of “rhombics,” “fish-bones.” “diamonds,” and what-not other types; “beam power” tubes, speech scramblers, automatic rebroadcast, cornet transmissions, and multiplex radio teletype. Television was no longer just around the comer, but was here, even in color; and Major Armstrong’s “FM,” the perfect quality, static-proof broadcast system with “frequency modulation” was beginning to sweep the country. A very different setup indeed from the navy radio of a few years before—and as for the still earlier spark gaps and electrolytic detectors of my first cruise, those had passed into the Umbo of the galleon, beautiful white battleships, and the “Armored Cruiser Squadron.” Everyone was talking the new decibel language, and if you didn’t know it you were just a has-been. What are all these various decibels? What is the relation between the roar of the Bronx lion and the “dit dah dit” of Washington’s radio signal?

In almost any textbook of physics or radio you can find that a decibel is a unit expressing a power ratio, abbreviated db., and defined by the relation

db. = 10 log_{10} *P _{1}*/

*P*;

_{2}but to learn why has required considerable effort because of apparent confusion. The fruits of the labor may be of general interest.

We find that the decibel originated innocently enough in connection with the telephone, whose inventor, Dr. Alexander Graham Bell, is honored by the name. The first telephone was “sound powered”; just two receivers connected by a pair of wires with no battery. At each end of the line between two rooms the speaker talked into the receiver, then placed it to his ear for the reply. With the addition of a microphone transmitter and battery the communication range was extended, but no really long distance telephony was possible until the development of vacuum tube amplifiers to compensate for line loss.

Calculations show that the attenuation in the transcontinental telephone line between New York and Denver is of such magnitude that if one amplifier were inserted in the middle to compensate for the entire loss it would have to be capable of a power amplification of about 10^{100}; i.e., would have to receive power of about l0-^{50} watts, and amplify it to about 10^{50 }watts. That such an arrangement is startlingly impossible will be clear from a translation of these figures. The received power would be less than the energy received by the naked eye from a star too faint to be seen with the most powerful telescope man could devise! The required amplification from this would be an amount of power incomparably greater than the combined power of all the world’s generating plants—greater even than the total amount of energy radiated by all the visible stars!

Obviously a more practicable method of amplification is required. The solution of this interesting problem which gave birth to the decibel will be apparent from a brief analysis of the electrical characteristics of telephone lines. Good quality transmission with present-day substation equipment is obtainable if the voltage and current received over a line are about one-tenth of the value delivered to the other end. Suppose a 20-mile length of a certain type of cable is just sufficient to produce these results. To receive the same current at 40 miles as that formerly received at 20 it is necessary to increase the input current 10 times, which, since power varies as the square of the current, means increasing the power 100 times. One-tenth of the input current arrives at the end of the first 20- mile section, and one-tenth of that, or 1 per cent, arrives at the end of the second 20-mile section. If we wish to increase the line to 100 miles, 10,000 times as much input current, or 100,000,000 times as much power input would be required as for the 20-mile line.

It is clear that with this rapid increase of required power with length we soon get into celestial figures, and that to keep the power within reason it is necessary to compensate for line loss at frequent intervals with small amplifiers, called “repeaters.” In the New York to Denver line a 50-mile interval was selected. There are about 40 repeaters in that distance of 2,000 miles and the power loss in each section is approximately 250/1. Each repeater is adjusted to compensate approximately for the power loss in the preceding section. At the transmitting end the power delivered is of the order of 10 milliwatts. This is attenuated in each section to about 40 microwatts, which value is raised by the repeater back to 10 milliwatts to start down the next section, and so on to the receiving end. Without repeaters, the attenuation in the whole 40 sections would be,

P_{1}/P_{2} = (250)^{40}, or approximately 10^{100}.

The important characteristic illustrated is that in properly constructed and adjusted long telephone lines an equal proportion rather than equal amount of current is attenuated in equal lengths of the same type of cable. For equal sections the ratio, A, of currents in adjacent sections is

*I _{1}/I_{2}= I_{2}/I_{3}= I_{3}/I_{4}…=A*

The ratio of the input current at the transmitting end to that available at the extreme end of the line is found by the product of the several ratios. For four sections it is,

*I _{1}/I_{2} X I_{2}/I_{3} X I_{3}/I_{4 }= A^{3},* and for n sections,

(1) *I _{1}/I_{ n=1}=A^{n}.*

If a number of sections with different attenuations (but of equal characteristic impedance) are connected together, with ratios of input current to output current in the sections as follows:

[EQUATION]

Equations (1) and (2) show that total “attenuation” is obtained by adding exponents and that any unit selected to indicate transmission losses, or attenuation, should be logarithmic in character.

After various experiments with units based on actual attenuation found in a given physical length of a certain type of cable, which units were accurate only for a given frequency, telephone engineers finally standardized on a unit obtained from the attenuation in a mile of standard cable at a frequency of 886 cycles, because this attenuation was

[EQUATION]

which value gave for A of equation (1) the base of the common logs, and for n a convenient decimal. Also, the resulting unit was independent of frequency and physical or electrical characteristics; it was applicable to any condition where ratios of power were involved. This unit was first called the “TU” or transmission unit. Later, a unit 10 times as large was adopted and called the “Bell.” It was found too large for practical purposes, and the original standard, now called the decibel, is used throughout the United States.

[EQUATION]

So the decibel began life as the logarithm of a telephone line power ratio. As it still requires some high power stretching to connect this with a Bronx lion, etc., we must see what caused it to stray so far afield. First, because the decibel was so convenient for calculations, and because it could be used for any two powers, whether in a telephone line or elsewhere, engineers began using it wherever there was any measurement of power required. It was still, however, nothing but a log of a ratio, and meant absolutely nothing unless one value of the power, which could be used as a “reference level,” was specified concurrently with the decibel data. There may be as many reference levels as there are systems for electrical communication. Today a number of generally accepted standard reference levels are in use. For high quality broadcast transmission 6 milliwatts has been arbitrarily chosen as the zero level. Broadcast engineers speak of an amplifier as capable of delivering plus 10 db. when it is capable of delivering 0.06 watts. This is derived thus:

[EQUATION]

In telephone testing the zero level is taken as one milliwatt, and other powers are referred to that level. In this case plus 30 decibels would be a power 1,000 times the standard, or one watt; and minus 30 decibels would be a power one thousandth of the zero level or one microwatt.

But, like “Rochester” and the gas man, we still haven’t explained the lion. Well, the ear itself happens to be so constructed as to fit right into a system using logarithmic units of power. The ear perceives such units of sound power as equal intervals. Stated more simply; just as a man who is very sober may be made quite drunk on a few highballs, the ear will find the chirp of a cricket quite loud on a quiet night in the country; and just as a man who has crowded three months’ drinking into his first liberty after a cruise won’t be made much drunker with a few more highballs, so the chirp of a cricket wouldn’t register significantly to your ear in a New York subway. This is just an illustration of Weber’s Law that the minimum change in stimulus necessary to produce a perceptible change in response is proportional to the stimulus already existing. Daylight movies, for example, are not very satisfactory because the eye perceives relative intensity; the actual absolute difference of intensity of lights and shadows in the projected image is the same as in a darkened room. Research workers on hearing, engaged in the determination of ear sensitivity, and intensity differential sensitivity, soon saw the advantage of adopting the electrical system’s decibel, and did so.

The decibel is used in acoustics to express ratios of sound intensity. Sound intensity, in ergs per second per square centimeter, may be expressed in watts per square centimeter (having nothing to do with the watts of associated electrical gear), and the reference level of sound intensity for acoustics work has been chosen as 10-^{16} watts per square centimeter. With this zero level established we now see that when our lion roared 90 db. the sound intensity was 90 db. about 10-^{16} watts per square centimeter, which has no more connection with the strength of our radio signals, the power of our amplifiers, or the discrimination of our radio circuits than if his roar were labeled in “Strombolis.”

Now the decibels in acoustics have several interesting features. The reference level which has been standardized coincides with the threshold of audibility at 1,000 cycles for binaural (both ears) reception for young people. That is to say, the least intense sound of a frequency of 1,000 cycles that can be heard is that sound produced by a free field intensity in a plane progressive wave of 10-^{16} watts per square centimeter. With this definite standard established the acoustics decibels may be pegged at concrete values which the mind can refer back to without translation. Values of sound, whether it be noise, voices, gunfire, planes, or the water noises from submarines, may be compared to the known levels of familiar sounds that have been measured and tabulated. The mind has no difficulty whatever in grasping the import of decibels used in this manner; starting from scratch anyone of ordinary intelligence could study a decibel table of sound levels and thereafter estimate other sounds fairly accurately in decibels. Sound operators, engineers, builders, and naval constructors have something definite to work with.

Confusing to the worker is the broad statement in some texts that one decibel is the minimum sound intensity perceptible to the human ear. This is almost true for a frequency of 1,000 cycles; but at 400 cycles the minimum perceptible intensity is 10 decibels; at 100 it is 30 db.

It is a coincidence that the differential intensity sensitivity of the ear, that is, the minimum change in field intensity of the sound wave that can be detected by the ear, is approximately one decibel; from an intensity level of about 40 to 80 db., at frequencies within the audio range of about 300 cycles and up. But too much importance should not be attached to this, for if the original sound intensity at these frequencies is of 5-db. level above threshold a change of 3 db. is the least the ear can detect; and from a 5-db. level above threshold at 60 cycles the ear cannot detect much less than a 6-db. change.

[GRAPH-AUDITORY SENSATION AREA]

A certain pamphlet recently stated that one advantage of using decibels was that decibels:

“. . . following a logarithmic law themselves, need only to be added to be representative. For example: A ten decibel signal sounds approximately twice as loud to the ear as a five decibel signal, etc.”

While the italicized statement may be true for certain conditions that were clear to its author, the struggling amateur, clutching at such straws of knowledge in the effort to save himself from drowning in a sea of confusion, may be, as I was, further confused by the failure to make clear that such a law applies only to the variation of the effect upon the ear of changes in the field intensity of a sound wave in air. Any attempt to extend this law to the effect upon the ear of the response of headphones or a loud-speaker connected to a radio receiver whose output signal from a distant station is first 5, then 10 decibels as measured by the decibel meter connected to the receiver, would be illogical and futile. The 10-db. signal from Washington which the radioman reports does not necessarily sound twice as loud as another 5-db. signal from Washington; if it does it is accidental and due to a purely local combination of circumstances. The connection between acoustic decibels and readings of decibel meters in communication networks and radio receivers is academic; not something for the operator to reconcile.

On the other hand acoustic decibels are essential for the man who masters the binaural sound locators, fire-control phones, or the announcing system. The boatswain’s mate may not need to know that articulation increases rapidly in the range from 10 to 40 db., and that from 50 to 90 db. there is little further improvement, but the word will be passed over the loud-speaker or the fire-control phones better if someone aboard makes use of that knowledge. If the noise level in the engine-room is 100 db., and no more than 80 db. can be tolerated in the engine control-room, the constructor knows he must sound-proof the latter to provide an insulation of 20 db.; which can be done by selecting the required amount of a specific material of given absorption coefficient.

As an example of the confusion which has prompted this article, a well-known communication authority once wrote:

The use of transmission units in describing power levels emphasizes the advantage of using logarithmic units in connection with such phenomena as hearing, which itself follows a logarithmic law. The practice should not, however, be carried to the point where the reference level is lost sight of.

That was written 10 years ago. It is very apropos today. Telephone engineers with their one milliwatt reference level and broadcast engineers with their 6-milliwatt level ran into confusion when they got together in chain broadcasting. To obviate this and also because in speech and music a wide band of frequencies is involved, they devised a new logarithmic volume unit called “vu” for joint operations. They use a volume indicator calibrated to read zero vu on one milliwatt of 1000-cycle power in a 600-ohm impedance. Although in speech and music there is no direct correlation between vu and milliwatts, the fact that the meter is calibrated at a reference level of one milliwatt permits the volume indicator to be used to measure transmission losses and gains directly in decibels from its vu scale.

An important use of decibels in the operation of radio is the measurement by meter of the ratio of received signal to the “noise level” in the receiver. In this case we mean the “noise” in the receiver output circuit caused by atmospheric disturbances (static) or by the radio tubes themselves. For this purpose a voltmeter is connected in the receiver output circuit. This meter may be calibrated to read directly in db. referred to 6 milliwatts.

It is often necessary in certain electrical work to determine the contributions made by two or more sources when the quantities are expressed in decibels, such as determining the combined level of several noise sources, or combining the various components of a complex tone. It is possible to use special devices for this purpose as a result of an interesting characteristic of decibels. For example, 2 components of equal magnitude will have a combined level exactly 3 decibels higher than that of the lower, no matter what the original levels were. Combining 2 db. and 2 db. will produce 5 db.; combining 50 db. and 50 db. will produce 53 db., etc. The explanation of this is found in a table of logarithms. Adding 2 equal quantities is equivalent to multiplying by 2, and 10 times the log of 2 is 3. Hence the increment in decibels is 3. Also, adding 2 components differing by 3 db. is equivalent to multiplying the higher of the two powers by 1.5, or (from log tables) adding 1.8 db. to the higher level, no matter what the absolute levels are. Extending this principle shows that if the difference is zero the increment in decibels to be added to obtain the sum is 3; and if the difference is more than 20 db. the increment becomes quite small indeed.

A practical simplification for the worker is obtainable from the log tables:

P_{1}/P_{2} 10 log_{10} P_{l}/P_{2}

1.0...................................................... 0

1.26........................................ 1

1.58 ( = 1.26X1.26).................... 2

2.0 ( = 1.26X1.26X1.26).............. 3

4.0 ........................................... 6

8.0 ........................................... 9

- 10

From this it is apparent that when we hear these confounded decibels again we can make horse sense out of them by calling 1 decibel a power ratio of 1.26; 3 decibels, double the power; 6 decibels 4 times the power; 9 decibels, 8 times the power, and 10 decibels, 10 times the power. A change of 3 decibels doubles the power ratio in every case. A power ratio of 100 is represented by 20 db.; of 1,000 by 30 db.; of 1,000,000 by 60 db.; that is, for power ratios expressed by even powers of 10 such as 100, 1,000, etc., multiply the number of zeroes by 10 to obtain the decibels.

Tables of decibels are published in textbooks and in bureau pamphlets, but if the basic principles are understood you won’t need them. It all seems very simple, if true, after a year of investigation. If you want to get a lot of different answers now just start asking, “What is a decibel?”

There is no such thing in war as absolute certainty; risk cannot be eliminated from any military situation, whether of passive defence or of offensive action. ... A reasonable preponderance of chances in one’s favor is all that can be assured. —Mahan, The Problem of Asia, 1900.