Decibels of light and sound
DOI: 10.1063/1.3061786
The usefulness of logarithms in the measurement of many of the stimuli to which human beings are sensitive is almost too obvious to need argument. Three reasons are commonly given to justify the practice:
1. The intensity ranges of the physical stimuli are enormous—energy ranges of trillions to one are involved in vision and hearing.
2. To a rough approximation, discrimination follows a law of relativity: the just detectable increment in a stimulus is proportional to the magnitude of the stimulus (Weber’s law). Hence, to the extent that Weber’s law holds, the logarithmic difference that is just detectable is constant.
3. According to Fechner’s law, the subjective magnitude of a sensation is supposed to be proportional to the logarithm of the magnitude of the stimulus.
References
1. S. S. Stevens, The measurement of loudness, J. Acoust. Soc. Am. (in press).
R. M. Hanes, The construction of subjective brightness scales from fractionation data: a validation, J. Exp. Psychol. 30, 719–728 (1949).https://doi.org/JEPSAK2. W. H. Martin, The transmission unit and telephone transmission reference systems, Amer. Inst. Elect. Engr. Trans. 43, 797–801 (1924);
and W. H. Martin, Bell Syst. Tech. J. 3, 400–408 (1924).https://doi.org/BSTJAN3. W. H. Martin, Decibel—the name for the transmission unit, Bell Syst. Tech. J. 8, 1–2 (1929).https://doi.org/BSTJAN
4. H. Fletcher, Speech and Hearing in Communication (Van Nostrand, New York, 1953), p. 172.
5. A partial catalogue of the names thus far suggested for the standard logarithmic measure includes decilog, decilu, decilit, decibrigg, decomlog, logit, and decade. See, for example, the following articles:
J. W. Horton, Fundamental considerations regarding the use of relative magnitudes, Proc. Inst. Radio Engr. 40, 440–444 (1952); https://doi.org/PIREAE
J. W. Horton, The bewildering decibel, Elect. Engng. 73, 550–555 (1954); https://doi.org/EENGFQ
W. M. Hall, Logarithmic measure and the decibel, J. Acoust. Soc. Amer. 26, 449–450 (1954); https://doi.org/JASMAN
E. I. Green, The decilog: a unit for logarithmic measurement, Elect. Engng. 73, 597–599 (1954); https://doi.org/EENGFQ
V. V. L. Rao and S. Lakshiminarayanan, The decilit: a new name for the logarithmic unit of relative magnitudes, J. Acoust. Soc. Amer. 27, 376–378 (1955); https://doi.org/JASMAN
and R. V. L. Hartley, New system of logarithmic units, J. Acoust. Soc. Amer. 27, 174–176 (1955).https://doi.org/JASMAN6. C. T. Morgan, The statistical treatment of hoarding data, J. Comp. Psychol. 38, 247–256 (1945).
7. S. S. Stevens, On the theory of scales of measurement, Science 103, 677–680 (1946). https://doi.org/SCIEAS
See also Chap. 1 of S. S. Stevens (ed.), Handbook of Experimental Psychology (Wiley, New York, 1951).8. S. S. Stevens (ed.), Handbook of Experimental Psychology (Wiley, New York, 1951).
9. Mention should be made, however, of an unpublished report: Notes on Photometry, Colorimetry, and an Explanation of the Centibel Scale, by Wayne B. Nottingham, Radiation Laboratory (MIT) Report 804, 17 December 1945. In order to simplify its work on the luminescent properties of cathode‐ray tubes, the wartime group at the Radiation Laboratory devised a logarithmic measure of relative magnitude which they called a “centibel” and abbreviated “cb.” This measure, equal to a tenth of a decibel, serves all the useful functions of the decibel. A possible argument for using this smaller standard of relative magnitude in visual studies is that the eye is sensitive to smaller differences than is the ear. Under favorable conditions, the visible DL is of the order of a centibel. In any case, going from centibels to decibels and vice versa is as easy as changing millimeters to centimeters.
Another reason for the use of centibels rather than decibels seems to have been the approximate proportionality in a photocell between radiant power input and voltage output. Thus a 3‐db increase in light input doubles the voltage output, but the doubling of a voltage conventionally means a change of 6 db. I am informed by Pierre Mertz of the Bell Telephone Laboratories that he was concerned with this source of potential confusion when he proposed a decibel scale for measuring light in 1937.10. E. C. Watson, Reproduction of prints, drawings and paintings of interest in the history of physics: 37, Rubens as a scientific illustrator, Amer. J. Phys. 16, 183–184 (1948).https://doi.org/AJPIAS
11. A. Chapanis, How we see. In Human Factors in Undersea Warfare (National Research Council, Washington, 1949).
12. For a thorough table of conversion factors, see P. Moon and D. E. Spencer, Utilizing the mks system, Amer. J. Phys. 16, 25–38 (1948).https://doi.org/AJPIAS
13. See P. Moon, The Scientific Basis of Illuminating Engineering (McGraw‐Hill, New York, 1936), p. 545.
14. W. D. Wright, Researches on Normal and Defective Colour Vision (Mosby, St. Louis, 1947), p. 285.
More about the Authors
S. S. Stevens. Psycho‐Acoustic Laboratory, Harvard University.
