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Appendix A
Vertical Array theory
Vertical arrays, commonly referred to as line arrays, have earned enormous popularity among profes-
sional users. The fundamental principals used as a basis of the design and operation of these electro
acoustic systems unfortunately have not enjoyed the same proliferation as the systems themselves. In
this appendix, we will briefly analyze the phenomenon of interference which serves as a base for the
control of directivity of bass frequencies which is exploited in vertical arrays, and the conditions which
need to be satisfied by a high frequency source used in the same.
First of all, we repeat two definitions that help to clarify the meanings of two oft-misunderstood
terms. The definition of Array is: "an ordered arrangement", therefore the definition of line array is "an
ordered linear arrangement". In electro-acoustic texts you find the more precise definition: "a group of
omnidirectional sources, arrayed in a straight line in close proximity one to the other and radiating in
phase with equal levels".
Very often a line array is confused with a line source. While a line source is a hypothetical, linear
source, the line array is only an approximation of this.
A.1 The Lobing Phenomenon
Briefly analyzing the emission of an array along its vertical axis without resorting to any mathematical
formulae, here we refer to a few simulations. The simulated array here (see figureA.1) is composed of 16
omnidirectional sources spaced at 32 cm intervals, for a total length of about 5 meters. You can see how,
because of the phenomenon of interference, the array is extremely directional at low frequencies but as
frequencies rise, the phenomenon becomes increasingly discontinuous until it disappears altogether.
Therefore, with spherical sources there is always a precise frequency above which it is not possible
to exploit the effect of directivity control due to the interference between sources. This frequency is
determined by the distance between the various sources, referred to as "step".
The phenomenon is due to the different composition of summation and cancellation in different di-
rections in function of frequency. It is possible to schematize this principle with a design:
In the primary direction of radiation the contributions of the various sources are summed coherently,
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