X-Treme Audio MISI User Manual
LINE ARRAYS
LINE ARRAYS
User’s manual
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User’s manual
LINE ARRAYS
User’s manual
CONTENTS
1. Free-field acoustics
2. Sound power and pressure levels
3. Physical-mathematical model: brief description
4. Linear sources: introduction
4.1 Infinite length linear source
4.2 Finite length linear source
5. Description of the sound field of a linear source
5.1 Directivity analysis
5.2 In-axis response analysis
6. Arc, J and progressive sources
7. Line arrays: “the state-of-the-art”
8.
X-Treme Vertical Line Array: product range
9.
X-Treme Vertical Line Array
10. MISITM system: from “AS IS” to “TO BE”
11. Types of installations
12. Stacking instructions
13. Suspension guidelines
13.1 X-Treme Installer (XTI)
13.2 Suspension instructions
: system design
13.3 “Straight to the… angle”
13.4 LSA: flying and lifting
1. Free-field acoustics
An unlimited acoustic space without discontinuities or obsta cles
can be defined as a “free-field” and clearly is an idealization of
the real conditions in which the sound usually propagates itself,
whether it is generated by a “natural” source or by a sound re inforcement system. However, this can lead to two situations in
which the free-field conditions may be approximated in a more or
less correct way. The first one refers to an open space (such as
an area where great events and rock, pop music concerts can
take place) provided that weather conditions are stable and homogeneous, and no surfaces or obstacles are found in a suitably
large area all around the source. The second one can be created
artificially in a laboratory with special conditions, known as “ane-
choic” chamber, where all the surfaces limi ting it absorb completely the sound acting on them; the sound inside the chamber
is just the one produced by the source, as no sound is reflected
by the surfaces.
The acoustic field generated by a source in free-field conditions
can be schematically divided into two regions: the so-called near
field and the far field. In the first region of the acoustic field the
sound intensity can have a complex trend depending on the type
of source (see the following section about linear sources) and on
its dimensions, which does not necessarily follow a mo notonic
trend in relation to distance; moreover, the source directionality
characteristics should be carefully examined.
In the second re gion, from the near field to infinity in theoretical terms, the sound intensit y shows instead a linear trend and,
as is well-know, it is inversely proportional to the square of the
distance from the source; in other words, the sound inten-
sity level (defined as the quantit y of energy that flows, per time
unit, through a unitary surface area which is perpendicular to
the wave pro pagation direction. Unit of measurement: Watt per
square metre) decreases by 6 dB for each doubling of distance
(the so called “inverse-square” law). In addition to this, the
source directivity can be determined in an univocal and welldefined manner.
The far-field condition occurs when the values of the distance r from
the source meet all the following conditions:
r >>λ/2π , r >> L , r >> πL2/2λ,
13.5 MISITM and MLA: enclosure suspension rigging
14. Subwoofers
15. Tri-amplification system configuration
16. System configurations: standard examples
16.1 Linear Source Array
16.2 MISI
16.3 Mini Line Array
TM
where L is the largest linear dimension of the source, λ is the longest wavelength (therefore the lowest frequency) of the sound emit-
ted by the source (therefore λ is always ≤ 17.2 m - f ≥ 20 Hz) and the
“much higher” symbol means at least 3 times higher (Bies, Hansen
1988).
Note: a free-field variant is the so-called “free field on a reflect-
ing surface”, such as a large open space on a rigid and highly
reflecting surface (e.g. asphalt, ground) or a made-to-measure
special environment known as “semi-anechoic” chamber. An
omnidirectional source located near a reflecting surface acts as
if it was associated to an image source having the same sound
power: as a result, the intensity at every point of the acoustic
field is worth double the sound intensity generated by the same
source in a free field, therefore the intensity level will be 3 dB
higher.
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LINE ARRAYS
2. Sound power and pressure levels
At present, one of the most common and interesting problems to
face is the following: let the sound power (or the sound power level)
of a certain source be given, a magnitude that characterizes it intrinsically, determine the sound pressure (or the sound pressure level)
at any point of the space where the source works. In a free field
or in a free field on a reflecting surface, this problem can be easily
solved by calculating all the necessary elements with the following
simple formula:
Lp = Lw + ID
- 20 log(r) - 11 [dB].
θ,ϕ
Therefore this relationship, which is valid in far-field conditions (in fact,
in this case all the real acoustic sources smaller than the wavelength
of the sounds they produce can be approximated as pulsating point
spheres known as “monopoles”), enables the calculation of the sound
pressure level Lp produced by a source having a sound power level
Lw (=10 log W/Wo with Wo= 1 pW; e.g. if the acoustic power of a speaker system is 100 W its sound power level will be 140 dB), at a certain
distance r in a direction such that the di rectivity index of the source is
ID
(=10 log Q
θ,ϕ
with Q
θ,ϕ
being the direc tivity factor of the source in the
θ,ϕ
direction identified by angles θ and ϕ).
For example, a source with a sound power level of 120 dB (therefore with power W equal to 1 Watt) and a directivity index of 3
dB in the direction where the listener is positioned, produces a
sound pressure level of 84 dB in a 25 m far free-field, because:
Lp = 120 + 3 - 28 - 11 = 84 dB.
Furthermore, if we know the sound pressure level Lp1 at a certain
distance r1 from the source (for example, by measuring it through
a sound-level meter) and in a certain direction, the sound pressure
level Lp2 can be determined at another distance r2 in the same direction, without necessarily knowing the sound pressure level.
In fact, by using the equation above, we obtain:
Lp2 = Lp1 - 20 log(r2/ r1) [dB].
If, for example, a source produces a sound pressure level Lp1 =
92 dB at a distance r1 = 8 m, the sound pressure level at r2 =16 m,
in the same direction, will be 86 dB (as mentioned at the beginning, the sound pressure level decreases by 6 dB when distance
doubles).
Note: in a free-field on a reflecting surface, in the semi-space where
the source is forced to radiate, as previously mentioned, the sound
intensity is twice the intensity existing in a free field. Therefore, 3 dB
should be added to the sound pressure level calculated with the
formula above.
3. Physical-mathematical model: brief description
Most acoustic models are simplified solutions of a general equation
(wave equation) which are subject to certain “constraints”, such as
the environment’s volume or its known value at certain points in the
listening space. Therefore, in an acoustic study the used formulas
are a small set of specific solutions which is almost suitable for describing with sufficient approximation the acoustic field in a listening
environment. In general, these solutions are expressed in terms of
pressure in relation to space and time variables.
In indoor acoustics, the space characteristics are modelled as
boundary conditions and they exert a remarkable influence on the
acoustic field. It is the physical dimension of the space that makes
the presence of waves with a certain length possible (or impossible). In mathematical terms this falls within the category of the
eigenvalue problems. The solutions will be strictly dependent on
frequency and will have periodical behaviours (in acoustical terms
this is the so-called modal theory).
On the contrary, in outdoor acoustics, the boundary conditions
imposed on the wave equation will commonly be radiation conditions, which are necessary to make the mathematical model coherent with the physical reality. The dependency on frequency is no
longer regular as it occurs in closed spaces and the modal theory
cannot be applied. Of course, the differences between open and
closed spaces affect sound reproduction and the ability of a speaker system to adjust to different reproduction contexts, especially if
we consider the wide range of problems arising in open spaces.
Line arrays can solve the various problems associated with
sound reproduction. In this short introduction we will analytically
describe a line array mathematical model and we will com ment
on a few important results deriving from this model. Finally we will
demonstrate that a simple theoretical model can suitably meet
the coherence requirements with real measurement. This short
introduction, having an analytical and general character, will not
deal with the problems concerning the technological features of
the models (waveguides, etc…) or with the electro-acoustics solutions that are nevertheless essential for designing and producing line arrays.
4. Linear sources: introduction
Generally speaking, real sound sources are very complex and it
is quite difficult to describe them in detail. Luckily, in most practical cases, we can resort to substantial simplifications. The most
drastic one, as previously mentioned, consists of considering a
real source as an infinitely small point source whose dimensions
are actually much smaller than the wavelength λ of the reproduced
sound and/or if the listener is at a great distance from the source
position. However, other more complex ideal sources can better
represent the properties of the real sources: it is the case of the
linear sources, namely point sources that are conveniently arranged along a straight line, which are used in the literature to
exemplify a stacked or flying vertical line array system. A row of
cars along a straight road is another more common example of a
real source which can be approximately represented as an infinite
length linear source.
Line source
b=step
n
...
W
0
3
W
0
2
W
0
1
90°
r
0
β
η
P
fig. 1
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User’s manual
4.1 Infinite length linear source
With reference to fig. 1, let’s imagine an infinite sequence of unrelated
sources, spaced out by a distance b and all having the same sound
power Wo. As a result, the intensity of each source adds up to that of
the other sources in determining the total intensity at the distance ro in
a normal direction towards the linear source. Working from this hypothesis, we can demonstrate (Beranek, 1988) that with a distance value
ro >= b/π
and therefore at a distance such that the individual sources cannot
be distinguished one from the other, the average sound intensity
can be simply approximated by the relationship:
〈I〉=Wo/4bro [W/m2].
In other words, at distances exceeding the distance between one
source and the next (these are exactly the listening conditions of the
vertical line array sound reinforcement systems, since the distance between the elements is generally one linear metre) the intensity no longer varies with the square of the distance as in the case of
the monopole sources, but is inversely proportional to the distance.
This means that these sound waves (often known as cylindrical)
decrease by just 3 dB for each doubling of the distance rather than
by 6 dB as it occurs in traditional systems (the previously mentioned
“inverse-square” law).
4.2 Finite length linear source
If the sources arranged on a line are in a finite number n (>=3) and
βn is the angle, in radians, below which the source line is seen from
the observation point (as indicated in fig. 1), always at sufficiently
large distances (ro >= b/π), the sound intensity can be determined
according to the following relationship:
〈I〉 = Wo·βn /4πbro [W/m2].
In this case too it is inversely proportional to the distance and,
obviously, it is directly proportional to the angle opening below
which the linear source is seen from the listening point. In conclusion, in this case, one can state that a reasonably accurate description of the ver tical line array behaviour has been reached,
which is approximated as a finite linear source in its near field.
In fact, owing to the di mensions of the magnitudes at issue, the
b/π limit beyond which the array can be approximated as a linear
source (and therefore it can be seen as a source of cylindrical
waves) is much smaller than the above-mentioned limit between
a far field and a near field (it should be recalled that this limit is
represented by the larger distance between the following ones:
r >>λ
/2π, r >> L , r >> πL2/2λ
max
max
).
5. Description of the sound field of a linear source
In order to analyse the sound field generated by a line array let’s
start from a simple and ideal model: the finite linear source (or
line source).
Far field
Line source
L/2
dl
x
dl sin(α)
fig. 2
The sound pressure generated by a linear source can be obtained analytically as a special solution of the wave equation,
in relation to space and time coordinates. Moreover, it is also
assumed that the source can only emit a sinusoidal signal. From
a mathematical viewpoint, this simplification allows us to use a
notation (known as phasorial) which simplifies calculations and
ensures completeness without losing its general character. The
Fourier theory shows that, within some hypotheses (which have
been widely verified in the case of musical signals), any periodical
signal can be modelled as the sum of individual sinusoids.
Having said this, we can therefore express the sound pressure generated from a linear source as:
where L is the line length, k is the wave number, A(l) and ϕ (l) are
the signal amplitude and phase respectively on a point of the line (or
rather on an infinitesimal segment dl) at a distance r(l) from a generic
observation point or, rather, from a listening point P.
In order to analytically verify the line array properties, a few additional hypotheses are required. For example, it can be easily noticed that, beyond a certain observation (or ‘listening’) distance,
one will have:
Note: some empirical formulas can be found (Smith, Heil and
others) in which the border distance from the near to the far
field depends on variables such as the array length or the
reproduced frequency. However, it is better not to use them
as they lack any general validity!
In the far field, on the contrary, it is right to apply the considerations
mentioned just few lines earlier about the “inverse-square” law. In
particular, in the case of linear sources, since the sound power of a
single source Wo is known, the formula used to calculate the sound
pressure level in the free-field conditions on a reflecting surface will
be:
Lp = Lwo + 10 log(βn /r) – 8 [dB],
where βn is the angle below which the sources are seen from the
listening point.
This further condition is precisely that of the far field, as previously
mentioned.
Thanks to the far field hypothesis we can rewrite the final expression
of pressure in a form that we will use to evaluate the source directivity (see paragraph 5.1):
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LINE ARRAYS
5.1 Directivity analysis
The directivity function enables us to evaluate the pressure distribution in relation to a definite emission direction. By using again the
formulas of fig. 2, the directivity function R(α) can be defined as:
where
p
is the pressure in the maximum emission direction, in
which from a mathematical viewpoint the exponential function below the integral sign assumes the maximum value (= 1). Following
what has been stated above, one can obtain:
In order to have a qualitative representation of the linear source
directivity, take into account the simplest situation (the so-called
uniform linear source) with a constant amplitude (A(l)=A) and null
phase deviation (ϕ=0). One will have:
max
5.2 In-axis response analysis
Similarly to the directivity analysis, and referring to fig. 2, we force the
(observation or “listening”) point P to lie on the axis x. Now let’s go
back to the general case, thereby excluding the far-field hypothesis.
The pressure form will therefore be of the following kind:
where r
The corresponding directivity function on the x axis is often expressed in a logarithmical form:
(x,l) is the distance traced in fig. 4
mid
Line source
r
dl
L
mid
fig. 4
(x,l)
P
mid
(x)
x
p
whose solution is:
rendering the wavelength λ explicit from the expression of the wave
number k.
fig. 3
Figure 3 shows the polar diagrams of function RU(α).
Let’s consider the L/λ ratio (0.5, 1, 2, 8, 16), i.e. the ratio between
the line length and the wavelength. It can be easily noticed that a
very high directivity is obtained in wavelengths that are much shorter (1/8, 1/16) than the line length (in the specific case of a few metre
long line arrays, this leads to mid-high frequencies). In other words,
in the case of a linear source, the narrower the main emission lobe
is, the better the sound energy transmission can be forced into a
narrow and orientable corner of the sound front.
Where x
Note that R(x
case of a 4 m long uniform linear source (as already seen in A(l)=A and
ϕ= 0), will have a qualitative trend of the type shown in fig. 5
Each curve refers to a certain sinusoid frequency. A double slope is
observed for each curve: as the distance from the source grows, at the
beginning there is a decrease of 3 dB for each doubling of the distance,
then there is a decrease of 6 dB for each doubling of the distance.
The (theoretical) point in which the curve changes its slope is called
transition distance and it is a function of both the fre quency and the
dimension of the line source (L). The branch with a -3 dB slope is the
near field, that with a -6dB slope is the far field.
is a reference distance, generally 1 m.
ref
)=0. The double logarithmic graph of r(x), in the specific
ref
fig. 5
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Therefore, in a linear source the in-axis response decreases by 3
dB for each doubling of the length instead of 6 dB as it occurs in a
con ventional speaker system (point source) until the transition distance is reached, which at medium-high frequencies can be dozens
of metres for sources just a few metres long.
6. Arc, J and progressive sources
In a real configuration the wavefronts generated by the line array
should be adjustable to the variables of the listening space (number
and position of the listeners, listening space morphology, stage
dimensions) to reach, in theory, the maximum listening uniformity
from different positions.
The general formulation of the directivity function, in case of N dif-
ferent sources, sums up the effects of these N (linear or not) sources
— the resulting function is as follows:
Given the freedom levels, this type of model can de scribe some
real situations in a simplified way, such as those in fig. 6, relating to
the measurement of a typical musical event with a line array sound
reinforcement system.
fig. 7
The formal calculation of the expressions relating to the J source,
despite having been substantially simplified, requires superfluous
complex steps. On the contrary, the qualitative analysis of the contribution to directivity given by the lower semi-arc is quite interesting.
Similarly to the considerations made for the linear source, an ideal
arc source model can be created and the pressure expression can
be analysed.
fig. 6
The directivity diagram as shown in fig. 6 can be used to approximately represent a specific case of the suggested general for mula,
where the sum has been reduced to two terms. The mathematical sum of these two terms represents the overlapping of half an
arc source (which will be analytically described later) and a linear
source. The resulting model is an important one, called J source.
Fig. 7 provides a further explanation of the link between the model
we are trying to improve with the analytical description and the line
arrays.
fig. 8
Skipping the mathematical steps required to replace the variables
below the integral sign, we can write down directly the expression
of the acoustic pressure as:
from which the directivity function is obtained.
A qualitative analysis of the polar diagrams of the arc source,
indicated in fig. 9, reveals the same dependency between the lobe
distribution and the frequency/arc length ratio noticed in the case of
the linear sources. As far as linear sources are concerned, however,
a greater width of the main lobe is observed as one can clearly see
from the polar pattern chart in the following figure.
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LINE ARRAYS
fig. 9
As a result of this property of arc sources, taking into account the
lower semi-arc only and adding a linear source, one can see (fig.
10) that the J source model is suitable to describe the sound field
represented in fig. 6.
Line source Arc source
J source
7. Line arrays: “the state-of-the-art”
The term “line array” (also called “sound columns”) applies to a
sound reproduction system made up of a variable number of vertically arranged units (also called modules), which can achieve the
effect of a single acoustic source having the dimen sions of all the
component units and whose performance provides a coherent reproduction, that is the result of the sum of its various compo nents.
The vertical alignment allows narrowing of the reception zone to be
achived as well as greater directivity and sound pressure compared
to traditional systems.
The idea is to create columns made up of low, middle and high frequency speakers; the systems consist of small, light modules joined
into a wide acoustic source - the “line array”. The main advantage of
this type of system is the energy saving deriving from narrowing the
vertical directivity and a higher directivity of the sources which can
also produce sound waves decreasing by 3 dB only for each doubling of distance instead of 6 dB as happens in traditional systems.
These types of waves are defined as cylindrical and are generated
while respecting certain parameters relating to the elements making
up the array within a certain distance from the source (near field ),
which depends on the frequency of the reproduced wave and on
the lenght of the source itself. Having only two dispersion dimensions instead of three as in traditional spherical waves, the sound
transmitted by the cylindrical waves decreases much more gradually in relation to the distance from the source. As a result, the listening experience does not change significantly in terms of sound level
from a position far from the line array source to a position very near
to it. Moreover, the vertical radiation for this type of system decays
rapidly above and below the line array. As a result, less reverberation is generated in case of indoor use because no wave is radiated towards any reflecting surfaces existing in the upper part of the
room. Consequently, clarity and sound intelligibility are remarkably
improved.
fig. 10
The J source model can be generalized in the progressive source
(fig. 11), where the curvature is no longer null (or, better, infinite) and
then constant such as in the J source, but it is parametrized in relation to a coefficient σ. The analytical formulation is even more complex than the arc source but it is clear that a progres sive source can
achieve complete control of the emission lobes.
8. X-Treme Vertical Line Array: product range
Created in 2001, the X-Treme brand identifies all the products man-
ufactured by the Sound Corporation group business unit which
produces “concert, touring and portable sound systems”, that is
professional audio systems for concer ts, open air “live” events or
any other indoor installation where music is played live.
The X-Treme SBU (Strategic Business Unit) catalogue presents 3
different lines of vertical line array (VLA), all consisting of a 3-way
module (the bi or tri-amplification mode can be selected by switching the high current handling terminals in the crossover) and its corresponding stacked or flying subwoofer, available in both active and
passive versions.
The Linear Source Array (LSA) system is the top solution of the
range: in particular, the XTLSA module features high performances
in terms of acoustic pressure as well as an innovative horn-loaded
midrange configuration; the
system has been designed to achieve an acoustic pressure similar
to that of the above-mentioned “big” system, but with a higher response speed. Finally, the Mini Line Array (MLA) system stands
out for its exceptional sonic accuracy with extremely reduced bulk
and weight.
MISITM (Middle-Sized Line Array)
fig. 11
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