Handbook for Sound Engineers

Fundamentals of Audio and Acoustics 37

(2-21)

This is the sound intensity level LI of the source and
represents the amount of power flowing through the
surface of a sphere of 1 square meter. Again, this is the
highest intensity level that could be achieved by an
omnidirectional device of 100% efficiency. LI can be
manipulated by confining the radiated energy to a
smaller area. The level benefit gained at a point of
observation by doing such is called the directivity index
(DI) and is expressed in decibels. All loudspeakers suit-
able for sound reinforcement should exploit the bene-
fits of directivity control.
For the ideal device described, the sound pressure
level LP (or commonly SPL) at the surface of the sphere
will be numerically the same as the LW and LI
(LP= 120 dB) since the sound pressure produced by
1 W will be 20 Pa. This LP is only for one point on the
sphere, but since the source is omnidirectional, all
points on the sphere will be the same. To summarize, at
a distance of 0.282 m from a point source, the sound
power level, sound intensity level, and sound pressure
level will be numerically the same. This important rela-
tionship is useful for converting between these quanti-
ties, Fig. 2-21.

Let us now consider a point of observation that is
twice as far from the source. As the wave continues to
spread, its total area at a radius of 0.564 m will be four
times the area at 0.282 m. When the sound travels twice
as far, it spreads to cover four times the area. In decibels,
the sound level change from point one to point two is

This behavior is known as the inverse-square law

(ISL), Fig. 2-22. The ISL describes the level attenuation

versus distance for a point source radiator due to the

spherical spreading of the emerging waves. Frequency

dependent losses will be incurred from atmospheric

absorption, but those will not be considered here. Most

loudspeakers will roughly follow the inverse square law

level change with distance at points remote from the

source, Fig. 2-23.

2.11.2 The Line Source

Successful sound radiators have been constructed that

radiate sound from a line rather than a point. The infi-

nite line source emits a wave that is approximately

cylindrical in shape. Since the diverging wave is not

Figure 2-21. This condition forms the basis of the standard
terminology and relationships used to describe sound radia-
tion from loudspeakers. Courtesy Syn-Aud-Con.

LI 10 1W/m

2

10

12–

W/m

= log---------------------------- 2

=120 dB

dB

dB

dB

dB

1 W

1 W

W

Source 1 m^2

m^2

m^2

20 Pa

0.00002 Pa

W

'Lp 20 0.564

0.282

= log-------------

=6 dB

Figure 2-22. When the distance to the source is doubled,

the radiated sound energy will be spread over twice the

area. Both LI and LP will drop by 6 dB. Courtesy

Syn-Aud-Con.

Figure 2-23. The ISL is also true for directional devices in

their far field (remote locations from the device). Courtesy

Syn-Aud-Con.

0.282 m 0.282 m

source 1 m^2

4 m^2

10log^41 

6 dB