Sistemas Line Array

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Audio Engineering Society

Convention Paper
Presented at the 110th Convention 2001 May 12–15 Amsterdam, The Netherlands
This convention paper has been reproduced from the author's advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained bysending request and remittance to Audio Engineering Society, 60 East 42nd Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society.

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Line Arrays: Theory and Applications
Mark S. Ureda JBLProfessional Northridge, CA USA
ABSTRACT

Line arrays of loudspeakers are often employed to provide increased directivity, generally in the vertical plane. For improved performance, contemporary line arrays employ specially designed loudspeaker elements to provide a nearly continuous line source. However, even these may have “imperfections” relative to a perfect line source. This paper providesmathematical models to evaluate the directivity response of line sources and to quantify the effects of certain imperfections.
INTRODUCTION Line arrays of loudspeakers are used by sound system designers to obtain a narrow directivity response, generally in the vertical plane. This narrow response provides increased gain that is useful in venues requiring long throw or improved direct/reverberantratios. In the past, these line arrays were constructed out of closely stacked direct radiators or horns and worked quite well where the wavelength was large compared to the length (height) of the array. At shorter wavelengths the array elements cast their individual directional characteristics into the response of the array, resulting in deviations from the expected response of a “perfect” linearray. Recently, certain loudspeaker systems have been designed specifically for use in line arrays. These produce a directivity response much closer to that of a perfect line source than earlier designs. Nonetheless, they are not perfect either. This paper provides a mathematical analysis of certain of these discrepancies. Nearly all analyses of line arrays reference several seminal works fromthe late 1920’s to the 1960’s. This paper is no exception. We will begin with a derivation of the general form of the directivity function of a continuous line source and discuss important assumptions made to express it in closed form. The resulting directivity function provides the mathematical basis for several important topics related to line arrays including the quarter-power angle, the off-axislobe/null structure, the distance to the far field and the on-axis pressure response. Each of these is discussed in the following sections. In practice, even with specially designed loudspeaker systems, large line arrays are not perfectly continuous line sources at all frequencies. They have gaps between the boxes which are essentially non-radiating portions of the line. Also, certain radiatingelements in the systems may produce radial wave fronts instead of pure, flat ribbons. These effects are particularly important at high frequency, where the deviations from a perfect line source are a material fraction of the wavelength. This paper closes with an analysis of how these imperfections affect the directivity response. LINE ARRAYS – CONTINUOUS MODEL The first step in deriving thedirectivity function of a line array is to develop an expression for the radiated pressure. A line sourcea can be modeled as a continuum of infinitely small line segments

a

Line array and line source are used interchangeably. Line arrays generally refer to an array of acoustical sources such as loudspeakers arranged in a line. A line source is a mathematical representation of a large number of...