Specifications

TI 323 (6.0E)
16 - 36
R
2R
A
4A
Point
source
5. Sphere or line ?
This chapter investigates the differences between
spherical and line sources.
5.1. Spherical sources
An ideal spherical source is an infinitely small point.
Energy radiated from such a point source is
distributed spherically. Doubling the distance from the
source quadruples the surface of the sphere, while the
total acoustic power remains constant, therefore the
acoustic power density is quartered and the sound
pressure level is halved.
In other words, the sound pressure level drops 6 dB
by doubling the distance from the source, this
behaviour is known as the Inverse Square Law.
This behaviour is valid not only for ideal spheres, it is
valid for all radiators where both the horizontal and
vertical angle diverge.
With this knowledge it is possible to calculate the SPL
for a specific loudspeaker at a given distance (D).
Usually the SPL of a loudspeaker is defined at a
distance of 1 metres (3.3 ft) on axis, therefore the
level drop can be calculated using the following
formula:
SPL
(D )
= SPL
(1m)
- 20log
D
1m
As any loudspeaker has a maximum SPL capability, it
maybe necessary to use a quantity of loudspeakers in
order to increase the SPL over greater distances.
5.1.1. Combining spherical sources
Combining spherical sources to obtain various
horizontal and vertical dispersion patterns requires
loudspeakers that perform in a very specific manner.
Placing spherical loudspeakers adjacent to each other
always causes interactions between the sources.
These interactions are known as comb filter effects
and are described in chapter 4. To minimize the
comb filter effects the loudspeakers must produce
precisely controlled dispersion patterns. Splaying the
cabinets to match the –6dB isobars results in minimum
overlap and therefore minimizes the areas affected
by comb filter effects. Usually the spread of the
cabinets to the maximum possible angle can be
obtained in the horizontal plane, where a very even
energy distribution is essential. In the vertical plane it
might be necessary to adjust the angle between the
cabinets to suit the distance that has to be covered. A
large vertical overlap is used between a number of
boxes for the far field, while in the near field the
vertical overlap decreases and a single speaker will
provide sufficient coverage.
It is not possible to achieve a coherent coupling
between spherical sources, especially in the HF region,
as the distance between the acoustic centres is too
great. A coherent addition of two loudspeakers is
only possible on the axis between cabinets where
both path lengths are equidistant.
5.1.2. Signal tuning
Due to their directional behaviour, arrayed spherical
sources can be seen as single, independent
components, addressing a defined part of the listener
area. Coupling only happens with adjacent cabinets,
below the frequency of defined directivity. Depending
on the amount and arrangement of the individual
cabinets a shelf filter can be applied to compensate
this coupling effect.