ACOUSTIC RESEARCH
User’s Manual
UPTURNED T
series
ACOUSTIC RESEARCH
7
SOUND REINFORCEMENT
CONTROLLED RADIATION
4.3 Array effect
UT Active Stac
k systems fall under the loudspeakers array category.
However, they differ from the classical professional modular arrays in
the fact that they are compact, straight and strictly vertical; as such, they
produce a sound beam that is directed vertically with extreme precision.
Up to a certain distance depending on the frequency, these arrays
produce a sound decay of only 3 dB per doubled distance (
cylindrical
waves
) as against 6 dB for standard point sources (
spherical waves
). The
separation distance between the
near field
(
cylindrical waves
) and the
far
field
(
spherical waves
) can be calculated using the following formula:
where
L
is the length of the linear array,
λ
and
f
are the length of the wave
and frequency, and
c
is the speed of sound.
As already mentioned sound starts to spherically decay, just like a
punctual source, as the target distance is greater than
d
(6 dB per double
distance, in fact). However, the array effect still occurs, taking the form of
a pronounced vertical directivity, which also depends on the frequency.
When the frequency increases, the separation distance between the two
phenomena increases. Thus, the sound pressure decay decreases and the
beam of vertical dispersion in the far field is reduced.
To confirm this theory, the directivity balloons are shown below
(simulated in the far field starting from the directivity balloons measured
on the individual loudspeakers) for a PSUT8TE element at 250 and 1000
Hz frequencies: at 1000 Hz, the vertical array is much more directed (see
figures 13 and 14).
Note
: the resulting strong directivity requires a very accurate use of the active
stack systems that are highly suitable for any location with a limited vertical
beam (for example, flat-floor or slightly lowered audience stalls), but not for
traditional opera houses, for instance, where the stage layout requires a wide
vertical coverage. Listeners should always be in the “slice of space” edged by
the vertical extension of the array.
The debate on the border between near and far field shows how sound
pressure decay, on the axis of a linear array, becomes weaker when the
frequency increases (a longer near field - where sound decays by only 3 dB per
double the distance - occurs). This generally involves an excess of mid-high
frequencies at long distances from the audio systems, but also an excellent
intelligibility of speech and singing at a distance and a high ratio of the
direct-to-reverberant field due to strong vertical directivity.
4.4 High frequencies and spatial aliasing
The situation we described is merely a model of a continuous, linear sources
distribution, while in real conditions the PSUT8xx models, like any real array,
have discrete sources streaming by a certain
step
, or central distance, that in
this case is equal to 120 mm. Above a certain frequency, a deviation occurs
from the ideal behaviour of an array. This is represented by a “sound colour”
that is a function of the space, in the near field (due to mutual loudspeaker
cancellations in points where a destructive interference prevails) and by the
presence of undesired lobes in lateral directions (upward and downward), in
the far field.
The following formula shows the minimum frequency above which this
phenomenon occurs:
where
C
is the speed of sound,
Δx
is the value of the central distance and
sin φ
is the sine of the angle between the listener and the farthest loudspeaker;
this angle is 0° for listeners along the array axis at an infinite distance and
approximately 30° for listeners at 2 meters from the sound column, on axis.
In this case, the minimum
aliasing frequency
is of approximately
3 kHz
, at 2
meters, and rapidly increases as the distance scales up (thus narrowing the
frequency range affected by the aliasing).
The pronounced directivity of each loudspeaker at high frequencies further
reduces the spatial aliasing phenomenon. Furthermore, the orientation
of the mixed cone loudspeakers typical of the PSUT8xx models boosts this
benefit even more: a listener who moves on the horizontal plane, will always
approach the axis of a single loudspeaker at a time and at high frequencies
the individual contribution of the relevant loudspeaker is predominant, thus
limiting the interaction of loudspeakers and, consequently, the aliasing effect.
Therefore, the mixed orientation of the loudspeakers widens the horizontal
dispersion beam at high frequencies and lessens the problems of interaction
between the loudspeakers, but does not optimize the array effect in that area
of the spectrum which would be quite unrealistic, considering that, at high-
frequencies, transducers no longer have the precision phase they normally
display at midrange frequencies. This involves a deviation from the theoretical
behaviour of a line array.
Additionally, high frequencies are considerably “restrained” by the presence of
obstacles, the audience first and foremost. This is why, as already mentioned,
the audience in the last rows will hear the high frequencies especially from the
loudspeakers positioned in the top part of the column. This explains why, in
a real-life situation, high frequencies are subject to a strong attenuation over
distance - due to audience absorption and air dissipation -, while for an ideal
(continuous) array these frequencies would spread more efficiently in a free
field as compared to the rest of the spectrum.
The theory of arrays combined with the analysis of high frequency behaviours
leads to the validated assumption of a slight shortfall in low and very high
frequencies at considerable distances in response to active stack systems,
while the midrange frequencies are efficiently spread. For this reason the
default settings should be used (selecting between
short throw
and
long
throw
on the rear panel of the PSUTBASE/A), allowing the user to handle the
problem by deciding whether to optimize the near or far frequency response.
See more in the following paragraph.
Figure 13. Directivity balloon (simulated in the far field starting from the directivity
balloons measured on the individual loudspeakers) for a PSUT8TE element at 250 Hz.
The array is positioned vertically, i.e. directed along the blue axis
Figure 14. Directivity balloon (simulated in the far field starting from the directivity
balloons measured on the individual speakers) for an element at 1000 Hz.
The array is positioned vertically, i.e. directed along the blue axis
