# Frank Morgan's Math Chat - DECIBELS

September 14, 1999

OLD CHALLENGE. The Christian Science Monitor of July 8, 1999, reports that "according to the NRDC, the amount of ambient noise in the ocean may have increased by 10 decibels--in other words, 10-fold--between 1950 and 1975."

Is this correct?

ANSWER. Yes, 10 decibels is 10-fold, but that works only for 10, the base of the decibel system. 20 decibels is 100-fold (10x10), and an increase of 5 decibels is an increase by a factor of the square root of 10.

Al Zimmermann (whose name we have been known to misspell without the double n) mentions that the basic unit is "a bel which is equal to 10 decibels. . . The bel was named after Alexander Graham Bell. (Dare I opine that someone accidentally left off one of the L's at the end of his name?)"

NEW CHALLENGE (Colin Adams). A web comment claims that, "If the population of China walked past you in single file, the line would never end because of the rate of reproduction." Is this true?

Send answers, comments, and new questions by email to Frank.Morgan@williams.edu, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.