Sound Field Simulations
Griffin (2003) gives a comprehensive and comprehensible presentation of what is involved in designing practical line sources that approach the performance of full-height lines using less hardware. Smith (1997) describes a commercial realization and explains why it does what it does.
Keele culminates a series of papers on constant-beamwidth transducers (CBTs) in a collaboration with Button, in which they examine the performance of several variations of truncated lines: straight and curved, "shaded" (drive power reduced toward the end), and unshaded (all transducers driven equally), all standing on a plane-reflecting surface (Keele and Button, 2005). It is a masterpiece of predictions and measurements that provide many answers and suggest many more possibilities. Figure 18.3 shows a small sample of the informative sound field simulations in the paper.
It is rare to see such clear illustrations of what is right and wrong with certain aspects of sound reproduction. In Chapter 12, we looked at adjacent boundary interactions, pointing out that the immediate surroundings of loudspeakers affect how they function and that some of the effects are not subtle.
Figure 18.3a shows how just a single reflecting surface, the floor, disrupts an omnidirectional point source. Instead of tidy expanding circular contour plots, we see an example of gross acoustical interference with alternating lobes of high and low sound levels. The constant directivity of the source, indicated on the right, means that this problem exists at all frequencies, but the patterns will be different because of differing wavelengths.
FIGURE 18.3 Illustrations of the near-sound fields generated above a ground plane by several sound sources. The shading gets darker as sound levels drop; adjacent contour lines represent sound levels that differ by 3 dB. The original paper displays results for several frequencies; all of those shown are for 1 kHz. The words and graphics on the left explain the sources. On the right are far-field directivity indexes. Data from Keele and Button (2005).
Additional boundaries - ceiling, side walls - add more of the same, of course, and the merged combination usually ends up being more satisfactory than this single-dimensional perspective suggests. This is, after all, another perspective on comb filtering, discussed in Chapter 9.
Chapter 12 finished with examples of loudspeakers designed to interface with room boundaries. Illustration 18.3b and those that follow show how much better things can be if a boundary is considered as part of the loudspeaker design. Figure 18.3b shows that a simple truncated line seems to be an improvement over the elevated point source, but note that uniform directivity has been sacrificed. The directivity index has a sharply rising character, indicating high-frequency beaming.
Figure 18.3c shows that shading the output, reducing the drive delivered to the transducers closer to the top of the line according to a Hann contour, greatly simplifies the pattern, but it still beams at high frequencies. We are not there yet.
Curving the line, as shown in (d), seems to be a step in the right direction. The contour lines are not yet smooth, but there is an underlying desirable order to them. The constancy of the directivity index tells us that it applies over a wide bandwidth.
Shading the curved line using the Legendre contour yields a set of plots that have a sense of order and beauty, (e). The constant directivity index indicates that it will be similar at most frequencies. This is the kind of thing we like to see.
If the marketing department thinks that the customers might prefer a straight line, applying the right delays to the drive signals can, in effect, contour the line (f). When shaded, the result is very similar to (e) - and good.
Scanning from (a) to (e) and (f), it is easy to see that there are improvements that can be made in the delivery of sounds from loudspeakers, through rooms, to listeners. This is a two-dimensional example of what is possible. Interfacing the source with the floor benevolently uses that reflection, and directivity control reduces the effect of the ceiling reflection. Line sources, by their nature, have a narrow frontal aspect, so horizontal dispersion can be wide and uniform.
How did (e) and (f) sound? Excellent - at least that is the author's opinion from a biased, sighted test. It was distinctive in how little the sound level and timbre appeared to change with location in the room and how the loudspeaker did not get "loud" as one walked up to it. Note that the sound level contours around ear height (just under 2 m) are only gently sloped.
Any of these line radiators can be positioned at the ceiling interface - for example, as surround loudspeakers - or positioned between floor and ceiling. In the latter situation, they lose the boundary reflection and will need to be physically lengthened to regain comparable radiation performance. The shaded versions would have the lower half inverted so the acoustical output would decline toward both ends, top and bottom. So as we move into the detailed characterization of loudspeaker performance, it is important to keep in mind that directivity and propagation characteristics are important parts of the data set.
Beranek, L.L. (1986). Acoustics, Acoustical Society of America, New York.
Cox, T., and D'Antonio, P. (2004). Acoustic Absorbers and Diffusers, Spon Press, London & N.Y.
Griffin, J.R. (2003). "Design Guidelines for Practical Near Field Line Arrays," http://www.audiodiycentral.com/resource/pdf/nfl awp.pdf.
Keele, D.B., and Button, D.J. (2005). "Ground-Plane Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays," 119th Convention, Audio Eng. Soc., Preprint 6594.
Lipshitz, S., and Vanderkooy, J. (1986). "The Acoustic Radiation of Line Sources of Finite Length," 81st Convention, Audio Eng. Soc., Preprint 2417.
Smith, D.L. (1997). "Discrete-Element Line Arrays - Their Modeling and Optimization," J. Audio Eng. Soc., 45, pp. 949–964.
Printed with permission from Focal Press, a division of Elsevier. Copyright 2008. "Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms" edited by Floyd Toole. For more information about this title and other similar books, please visit www.elsevierdirect.com.
Acoustics and Psychoacoustics Applied - Part 1: Listening room design
Acoustics and Psychoacoustics: Introduction to Sound, Part 1: Pressure waves and sound transmission | Part 2: Sound intensity, power and pressure level | Part 3: Adding sounds together | Part 4: The inverse square law | Part 5: Sound Interactions | Part 6: Sound Interactions (cont.) | Part 7: Time and frequency domains
Using the Decibel - Part 1: Introduction and underlying concepts | Using the Decibel - Part 2: Expressing Power as an Audio Level