Handbook for Sound Engineers

Loudspeaker Cluster Design 649

Fig. 18-6 shows why there will always be interfer-
ence with conventional horn arrays (whether they are
enclosed in arrayable cabinets with trapezoidal sides or
mounted in free air). As the wavefronts radiate from
points of origin that are separated in space, they will
always create some interference at the coverage bound-
aries.

18.4 Conventional Array Shortcoming Analysis

For an array in far field, dependence on angle is

(18-1)

For a distance to the listening area very much larger

than the array dimensions, let the sound pressure P be

the real part of

(18-2)

where,

P is the sound pressure,

Z is the angular frequency,

Ai(T) is a function of the angle between the array longi-

tudinal axis and the direction of the distant listening

point. It gives the ratio of the sound pressure due to

the source as a ratio of its on-axis value at the same

distance.

For the ith source shown in Fig. 18-7, assuming

identical sources, the pressure contribution is given by:

(18-3)

where,

k is 2SeO = 2 Ofc,

O is the wavelength,

g is the frequency,

c is the speed of sound,

Si is the distance by which the path length from the ith

source to the distant point exceeds the distance from

the origin to that point.

For an array of n sources, the total pressure P is given

by:

Figure 18-5. ALS-1 interference predictions for a wider
splay show reduced interference, but the three horns are
clearly apparent at higher frequencies.

Figure 18-6. The acoustic pressure wave expands as a
sphere, and multiple spherical sections will always overlap
unless they originate from a common center.

SPL T = 10 logP 02 dB Figure 18-7. For a circular arc array, the additional path

length Sj is as shown.

P T =Ai Tj^ ZW–kSi

Pi=Ai Tj^ ZW–kSi