Audio Engineering

676 Chapter 23

The sensation of sound is caused by compressions and rarefactions of the air in the form
of a longitudinal oscillatory motion. The energy transmitted per unit area varies as the
square of the distance from the source. The rate with which this energy is transmitted
expresses the intensity of the sound, which directly relates to the sensation of loudness.
This incremental variation of the air pressure is known as sound pressure , which, for
practical purposes, is what is measured in determining the loudness of sound.

Sound pressure level ( SPL ) is defi ned as 20 times the logarithm to base 10 of the ratio of
the effective sound pressure ( P ) to the reference sound pressure ( Pref ):

SPL

P

P

20 log dB.

ref

(23.2)

Pref approximates to the threshold of hearing and numerically is 0.0002 microbar
(2 1 0 ^5 N/m^2 ).

The intensity ( I ) of a sound wave in the direction of propagation is

I

p

PC

Wm

P

C







2

0

2

0

118 2

340

/

. Kg/m
m/s.

(23.3)

The intensity level ( IL ) of a sound in decibels is

IL I

IL

I



 

10

10 12 2 2 10 5 2

log dB

w/m N/m.

ref

ref (23.4)

The relationship between IL andSPL is found by substituting Equation (23.2) for
intensity ( I ) in Equation (23.4). Inserting values for Pref and 7 ref gives

IL SPL

PC

 10

400

0

log dB. (23.5)