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DISTANCE TO THE FAR FIELD OF A LINE ARRAY*
(* from AES Convention paper Presented at the 110th Convention 2001 May 12-15 Amsterdam)
The analysis of line arrays relies on a far fi eld assumption, that is, that the distance to the point of observation P is large
compared to the length of the array. The far fi eld is characterized by sound pressure level decreasing at 6dB for every
doubling of distance. In the near fi eld the sound pressure level
undulates and decreases nominally at 3dB per doubling of distance.
The transition point can be estimated if we set as a criterion that
the far fi eld is reached when the distance to P from the centre point
of a line array is within a quarter-wavelength of the distance to P
from the endpoint of the array.
Referring to the previous fi gure , the far fi eld is obtained when
where r is the distance to P from the centre point and r’ is the distance from the endpoint. Solving for r’,
where l is the length of the array. Rewriting, the distance to the far fi eld is
the square of the array length and inversely proportional to wavelength. For most applications, the second term can be
dropped. For convenience, the far fi eld equation for a line array can also be expressed in terms of frequency rather than
wavelength. Two useful forms are:
(l in meters, ∫ in Hz)
and
(l in feet, ∫ in Hz)
SYSTEM CONFIGURATIONS
In practice, not all line arrays can be straight lines, i.e., depending on the application and needs, it may be
necessary to curve the array in order to achieve sufficient coverage throughout the audience areas. For this
reason, each box that makes up the “line array” must incorporate a rigging system that allows aiming in the
vertical plane. It is important to note that the rigging system, as well as being integral to the units, needs to al-
low for hinging at the front of the box so that the separation between the speakers remains the same (hinging
at the back of speakers would increase the vertical spacing, which works against line array theory). Thus, curved
systems are frequently used.
Geometric construction for far fi eld distance
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