Martin Audio Wavefront W8CT, Application Manual

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SPL = SWL(line) - 10log(4 p r)
For a line source this results in only a 3dB reduction in sound pressure
level per doubling of distance in the nearfield . . .
But note: This nearfield -3dB/doubling distance varies with frequency
and straight line array length
Plane Sources
For a plane source (e.g. a flat wall of sub-woofers), integrating an infinite number of
point sources distributed in two dimensions produces a flat surface. Thus, propagation
away from a planar source approximates a plane wave. The sound energy of each
point source is therefore assumed to propagate in a straight line perpendicular to the
plane, meaning that no geometric spreading need be considered as there is no change
in distributed surface area as the wave propagates.
Obviously there will be some at the edges of an finite planar source, however, at close
range near the centre of the plane there is no diminution with distance. Therefore, the
sound pressure level can be written as:
SPL = SWL(plane)
Unfortunately, most real line and plane sources are of a finite size. This means that
their overall behaviour becomes a definite integral. Considering this, it is easy to
imagine that, at a very great distance or very small size, both sources will ultimately
approximate an ideal point source.
This suggests that for such sources, there is a gradual change in behavior as a function
of both size and distance.
A straight line array will maintain it's low loss characteristics (3dB decrease in spl per
doubling of di air absorption) for a distance that depends on it's length with
respect to the wavelength of the sound being projected. Beyond this distance the line
effect breaks down and the spl characteristic weakens from -3dB/doubling of distance
plus air absorption to -6dB/doubling of distance plus air absorption. This transition
distance depends on the square of the straight line array's length and is proportional to
frequency following the generally accepted formula:
Where distances and length are given in metres and the frequency is in Hertz.
The speed of sound is approximately 340metres/second but varies with temperature.
Simplified, this means that you need a long line array to project low-mid frequencies
efficiently. Doubling the line array length will almost quadruple its low-mid
frequency nearfield throw. See
Section 5.4 .
All material © 2007. Martin Audio Ltd. Subject to change without notice.