Handbook for Sound Engineers

Computer Aided Sound System Design 1351

producing a high sound level at a large distance from

their point of installation, while minimally affecting

microphones located at close range to them. To have

this effect they must show a determined directional

characteristic and beaming. A radiator type suitable for

this purpose is the loudspeaker array consisting—in the

variant required—of a stacked arrangement of in-

phase-identical loudspeakers. In the plane orthogonal to

this arrangement, there occurs a pressure addition,

whereas in the areas above and below this plane, there is

a cancellation by interference because of the early-to-

late difference between the components stemming from

the different loudspeakers, Fig. 35-14. Each of the indi-

vidual loudspeakers radiates the sound spherically and

the sound waves get favorably superposed in the far

field, whereas the effect of the individual loudspeaker

prevails in the near field. For the far field the following

equation was given by Stenzel12,13 and Olson^14 for the

angular directivity ratio *, the so-called polars.

(35-22)

where,

n is the number of individual loudspeakers,

d is the spacing of the individual loudspeakers,

a is the radiation angle,

O is the wavelength of sound,

l is (n1) d, which is the length of the loudspeaker line.

This directional effect of a loudspeaker line
according to Fig. 35-15^15 is shown in Fig. 35-16A—a
balloon at 1 kHz, and in Fig. 35-16B—a balloon at
2 kHz. The line consists of nondirectional loudspeakers
arranged with a spacing of 25 cm. Secondary maxima

occur at frequencies above a critical frequency (wave-

length = spacing of the loudspeakers), that is above

1400 Hz in the example. Thus a desirable disc-shaped

radiation without secondary maxima can be observed at

1000 Hz, whereas at 2000 Hz lobes (secondary

maxima) are already utterly evident.

The drawback of an in-line loudspeaker arrange-

ment consists of the fact that

Figure 35-14. Operating principle of a classical sound

column.

*

nSd

O

sin ----------sina

n Sd

O

------sinsin a

= -----------------------------------

Figure 35-15. A line presentation with nine horns HP64 in

the simulation program EASE.

Figure 35-16. Balloon presentation of the line array

according Fig. 35-15 in a simulation.

A. 1000 Hz.

B. 2000 Hz.