User Guide

Sound System Design Reference Manual
Inverse Square Relationships
When we move away from a point source of
sound out of doors, or in a free field , we observe that
SPL falls off almost exactly 6 dB for each doubling of
distance away from the source. The reason for this is
shown in Figure 2-5. At A there is a sphere of radius
one meter surrounding a point source of sound P
1
representing the SPL at the surface of the sphere. At
B, we observe a sphere of twice the radius, 2 meters.
The area of the larger sphere is four times that of the
smaller one, and this means that the acoustical
power passing through a small area on the larger
sphere will be one-fourth that passing through the
same small area on the smaller sphere. The 4-to-1
power ratio represents a level difference of 6 dB, and
the corresponding sound pressure ratio will be 2-to-1.
A convenient nomograph for determining
inverse square losses is given in Figure 2-6. Inverse
square calculations depend on a theoretical point
source in a free field. In the real world, we can
closely approach an ideal free field, but we still must
take into account the factors of finite source size and
non-uniform radiation patterns.
Consider a horn-type loudspeaker having a
rated sensitivity of 100 dB, 1 watt at 1 meter. One
meter from where? Do we measure from the mouth
of the horn, the throat of the horn, the driver
diaphragm, or some indeterminate point in between?
Even if the measurement position is specified, the
information may be useless. Sound from a finite
source does not behave according to inverse square
law at distances close to that source. Measurements
made in the “near field” cannot be used to estimate
performance at greater distances. This being so, one
may well wonder why loudspeakers are rated at a
distance of only 1 meter.
The method of rating and the accepted
methods of measuring the devices are two different
things. The manufacturer is expected to make a
number of measurements at various distances under
free field conditions. From these he can establish
Figure 2-6. Nomograph for determining inverse square losses
2-6
Figure 2-5. Inverse square relationships