118 decibel

.















yielding:

One can check that the quantity

equals 1 if yy = 00 and c≠0, and zero in every other

case. Rewriting steps 1 and 2 from the above algo-

rithm, we have:

January 1 of year mcyy falls on day number

where εis 1 if the year is a turn of the cen-

tury, but not the turn of a millennium, and

zero otherwise.

Thus, for example, consider New Year’s Day of the

year 3261. The millennium number here is m= 3, the

century number is c= 2, and we have yy = 61. Also,

, and, since this is not a turn of the

century, ε= 0. Thus New Year’s Day of this year will

fall on day 2 + (2 ×3) – (2 ×2) + 61 + 16 + 0 ≡4, a

Thursday. We can now compute the weekday of any

other day that year if we wish.

An Alternative Method

Mathematician Chris McManus has observed that what-

ever day of the week “March 0” (the last day of Febru-

ary) falls, so do 4/4 (April 4), 6/6 (June 6), 8/8 (August

8), 10/10 (October 10), and 12/12 (December 12). The

same is true of 9/5 (September 5) and 7/11 (July 11), and

their inverses 5/9 and 11/7. (One can remember this

with the mnemonic, “I work from 9 to 5 at the 7-to-11

store.”) So, for example, if you know that December 20,

2002, was a Friday, and you wish to determine the day

on which April 10 of that year fell, quickly compute that

December 12 was a Thursday, yielding April 4 also as a

Thursday, making April 10 a Wednesday.

decibel Denoted dB, a decibel is a measure of the

intensity of sound, with zero decibels representing the

lowest intensity at which a sound can be heard.

Decibels follow a base-10

LOGARITHMIC SCALE

.

This means that each increase of 1 dB represents a 10-

fold increase in the intensity of the sound. For example,

a note played at 1 dB is 10 times as strong as the soft-

est sound, and one played at 2 dB is 100 times as

strong as the softest sound. Normal human speech is at

a level of about 60 dB, and a whisper is around 20 dB.

The threshold of pain for the human ear is about 90

dB. Rock concerts have been known to reach levels of

120 dB at a distance of 50 m from the sound system.

The decibel level of a sound is computed by the

formula:

where Pis the intensity of the note being played, and P0

is the lowest intensity at which that note can be heard.

An interval of 10 dB is called a bel. Sound inten-

sity was originally measured in terms of bel, the name

being chosen in honor of the American inventor of the

telephone, Alexander Graham Bell. Today, however,

the unit of a decibel is considered more useful and

is the one most commonly used.

decimal representation See

BASE OF A NUMBER

SYSTEM

.

decomposition (factorization) The result of express-

ing a given object or quantity in terms of simpler com-

ponents is called a decomposition. For example, the

FUNDAMENTAL THEOREM OF ARITHMETIC

shows that

any natural number decomposes as a product of prime