Handbook for Sound Engineers

650 Chapter 18

(18-4)

The square of the pressure amplitude is given by:

(18-5)

where,
Ai(T) is Ai(T - Di

For a circular arc array, the additional path length Si
as shown in Fig. 18-7, for the ith source at radius R and
angle D is given by:

(18-6)

Therefore, the smaller Ri is, the smaller the Si differ-
ences, and the less the interference between sources.
Ideally, R = 0 for all sources. As R approaches 0, the
interference will become less audible and frequency
response across the array’s intended coverage area will
become more uniform.

18.5 Coincident Acoustical Centers: A Practical
Approach

Clearly, the ideal solution is to collocate all the acoustic
points of origin, as shown in Fig. 18-8. We could
achieve this by stacking the horns vertically, but this
would solve the problem in the horizontal plane by
creating a worse situation in the vertical (front to back)
direction. Fig. 18-9 shows a more realistic approxima-
tion that takes into account the physical constraints of
loudspeaker design (the dimensions of the transducers,
horns, enclosure walls, etc.). Because the acoustic
sources are real physical objects, we cannot reduce Ri to

0. But we can get close enough to make measurable,
   audible improvements in the performance of the
   multi-enclosure array.

18.5.1 TRAP Horns: A New Approach

Fig. 18-9 implies that the way to minimize Ri—and the
resultant interference—is to move the acoustic centers as
far to the rear of the enclosure as possible. We can

attempt to minimize the size of the drivers, for instance

by using high-output magnetic materials such as

neodymium. But the biggest obstacle to coincident

acoustic centers is the horn itself. This is because typical

constant directivity horns exhibit astigmatism: their

apparent points of origin are different in the horizontal

and vertical planes. In order to create a wider coverage

pattern in the horizontal plane, the apparent apex is

moved forward, while the vertical apex is farther to the

rear because its coverage pattern is usually narrower.

This is certainly the case with the most popular horn

patterns in use today: 60° × 40° and 90° × 40°. One

approach to a solution, then, is to rotate the horn and use

the vertical apex of the horn in the horizontal plane. By

doing so, we are effectively moving the acoustic center

as far to the rear of the cabinet as possible. This tech-

nique when combined with cabinet design that mini-

mizes the space between adjacent drivers in an array,

P T AiqejZW–kSi

i 1=

n

= ¦

HjZW AHT jZWkSi

i 1=

= ¦

P 02 T AiTkSi

i 1=

n

¦

2

= +>@Ai qTsin kSi^2

• Si T =Ricos TD– i

Figure 18-8. The acoustic ideal—colocating the acoustic

centers of all horns is not a practical possibility.

Figure 18-9. Because drivers and enclosures are physical

objects, the acoustic centers of TRAP horns are not per-

fectly coincidentbut they are close enough to achieve

measurable and audible reductions in interference.