Environmental Engineering FOURTH EDITION

Noise Pollution 427

where

SPL (a) = sound pressure level (in dB),

P = pressure of sound wave, and

PEf = some reference pressure, generally chosen as the threshold of hearing,

0.00002 N/m2.

These relationships are also derivable from a slightly different point of view. In 1825,

E. H. Weber found that people can perceive differences in small weights, but if a person

is already holding a substantial weight, that same increment is not detectable. The same

idea is true with sound. For example, a 2 N/m2 increase from an initial sound pressure

of 2 N/m2 is readily perceived, whereas the same 2 N/m2 difference is not noticed if

it is added to a background of 200 N/m2 sound pressure. Mathematically, this may be

expressed as

dW

ds = K-

W’

where

ds = is the minimum perceptible increase in a sensation (e.g., hearing),

W = the load (e.g., background SPL),

K = aconstant.

dW = the change in the load, and

The integrated form of Eq. (22.6) is known as the Weber-Fechner Law

This idea is used in the definition of a decibel

W

dB = 1010g,o -,

Wref

(22.6)

(22.7)

(22.8)

where the power level W is divided by a constant WEf, which is a reference value, both
measured in watts.
Since the pressure waves in air are half positive pressure and half negative pressure,
adding these would result in 0. Accordingly, sound pressures are measured as root-
mean-square (m) values, which are related to the energy in the wave. It may also be
shown that the power associated with a sound wave is proportional to the square of the
rms pressure. We can therefore write

P

(22.9)

W P2

dB = 10log1, - = lologlo 2 = 2Olog10 -1

Wref Pref PEf