IOA_Tonal_Balance_Variation_2012.pdf

Proceedings of the Institute of Acoustics

Vol. 34. Pt. 4. 2012

TONAL BALANCE VARIATION USING LINE SOURCE ARRAYS L-ACOUSTICS 1 INTRODUCTION

In the past, conventional horn-loaded speakers were grouped together to achieve greater sound pressure level. These clusters produced a coherent sound field for low and low-mid frequency ranges. However, within upper-mid and high frequency ranges, interferences would lead to severe comb filtering in the frequency response. Wavefront Sculpture Technology

solved these issues by

providing a perfect coupling for the entire frequency range. In addition to benefits in terms of directivity control, SPL and throw capability, the smooth and controlled frequency response of WST

line sources provide high intelligibility and sound quality. The tonal balance of a line source array is an approximation of the frequency response, defined by the relationships between different ranges of the frequency spectrum. Understanding how to adjust the tonal balance of a line source array in order to achieve the desired sonic signature allows end-users optimizing the benefits of such an advanced PA. This paper describes how the tonal balance of a line source may vary according to the listening distance, as well as the array length and curvature. 2 HISTORICAL PERSPECTIVE

In the 1970s, performance expectations of SPL and coverage consistency grew progressively. A popular rule of thumb was used to estimate how many watts were required to achieve a targeted SPL. As a result, the number of loudspeakers in the composition of sound systems increased, and the associate cost and bulk grew proportionally. From a purely musical perspective, the biggest challenge was the sound quality. More and more cabinets were stacked, but without a technology providing constructive acoustic coupling, position-dependent interferences led to a chaotic sound field and severe comb filtering in the frequency response.

Figure 1: Example of comb filtering produced by a traditional line array

To overcome these issues, the world of sound reinforcement had to wait for the introduction of the V-DOSC system from L-ACOUSTICS in 1993. The V-DOSC loudspeaker enclosure was designed according to the WST

criteria described by Christian Heil and Marcel Urban. It integrated the first

waveguide that produced a continuous and isophasic wavefront, thus allowing the perfect coupling of high-frequency drivers when setup in a line array: the patented DOSC (Generator of Cylindrical Sound Waves). At high frequencies, traditional line arrays are not much more than a collection of point sources that cannot produce coherent summation, while WST

defines the coupling conditions for the entire

hearing frequency range and enables the construction of a line source array that is the equivalent of a single line source segment (see [2]). This constructive acoustic coupling prevents comb-filtering effects. This also allows engineers to optimize the resources of the transducers in order to bring the

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

high frequency range to a higher SPL level. The resulting shape of the tonal balance is the standard for the sonic signature of L-ACOUSTICS WST

line sources. It corresponds to 12 V-DOSC at 40m

from the centre of the array, and is characterized by a slope of -3dB per octave from 80Hz up to 1kHz while remaining flat from 1kHz to 20kHz.

Figure 2: Reference tonal balance of WST

line sources

Figure 3: L-ACOUSTICS K1, large format WST

system

3 PROPAGATION MODES OF LINE SOURCE ARRAYS

3.1 Spherical and cylindrical propagation

It is essential to understand the concepts of point source and line source, two ideal sources that exist only theoretically, and can only be approximated by loudspeaker systems. The basic physics of line source versus point source radiation explains why line sources are so attractive. A perfect point source emits from an infinitely small point, equally in all directions. It is therefore characterized by a spherical wavefront at all frequencies. When the distance is doubled, the wavefront surface is multiplied by four so that the radiated energy is divided by four. This is the inverse square law: a decrease of 6dB SPL each time the distance is doubled. In reality, an infinitely small point does not exist. A sound source can generate spherical waves for a limited frequency

range, where its dimension is small relative to wavelength. This explains why, at listener scale, most of low-frequency loudspeakers can be considered as point sources in their operating frequency range.

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

A theoretical line source emits from an infinitely long straight line, with a dispersion of 360 around the line. It is therefore characterized by a cylindrical wavefront at all frequencies. When the distance is doubled, the wavefront surface is multiplied by two so that the radiated energy is divided by two. This is the inverse law: a decrease of 3dB SPL each time the distance is doubled. In reality, an infinitely long straight line does not exist. A line source array is a truncated linear sound source that can generate cylindrical waves for a limited frequency range, where its dimension is large relative to the other scales in the problem: wavelength and listening distance. If not, it will start to behave as a point source and produce a spherical wavefront.

Figure 3: Spherical wave propagation as opposed to cylindrical wave propagation

3.2 Border distance

The border distance is a key concept to understand line source arrays. It is the distance at which propagation moves from the near field, where cylindrical wavefront applies, to the far field, where spherical wavefront appears. A different border distance corresponds to each single frequency produced by the line source array: border is further away with a higher frequency. Moreover, all border distances increase in proportion to the array length squared.

Figure 4: Border distance definition For a specific array length, listening distance and frequency, the relative contribution of each propagation mode determines how much the acoustic energy has decreased along the path of the wave. The resulting SPL values for an extended range of frequencies gives the tonal balance of this line source array at this listening distance. To generalize, array length and listening distance are the two parameters that explain the variations in the tonal balance of straight line source arrays. When moving away from the sound source, SPL of low frequencies decrease faster than SPL of high frequencies. The same scale effect is at work when reducing the length of the array.

Line Source Array

CYLINDRICAL (near field)

SPHERICAL (far field)

Border distance

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

Figure 6: SPL decrease slopes according to listening distance

for different array lengths at 1kHz

Figure 7: SPL decrease slopes according to listening distance

for a 4m-array at different frequencies

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

3.3 Curved line source array

Straight line source arrays provide a long-throw due to a focused vertical coverage at high frequencies, which works well for listeners at greater distances. But in real applications it is necessary to cover the whole audience. That is why most of line array systems can be curved, by setting variable splay angles between the elements of the array. In fact, introducing a slight curvature within an array allows a better SPL distribution to reach listeners in close and far proximity. Regarding propagation modes, curvatures produce a smoother transition between the near field and the far field. Rather than starting with cylindrical propagation and the decrease of 3dB when the distance is doubled, a curved line source array radiates a toric wavefront with a higher attenuation pattern. In addition, the border distance that marks the beginning of spherical propagation moves further away. Nevertheless, like a straight line source array, the border distance changes with the array length and frequency.

Figure 8: SPL decrease slopes according to listening distance

for a 4m-array at 1kHz with different curvatures 3.4 Projection on the audience

It should be noted that what is commonly named listening distance in many documents, this article included, refers to the distance along the propagation path that is perpendicular to the line array. If one considers the actual projection of the sound field on the audience area, WST

defines

conditions for implementing a line source array that would produce an even SPL decrease along this area. That is the WST

criterion n4. As a matter of fact, a curved line source array, whose

propagation is in between cylindrical and spherical modes, can achieve pseudo-cylindrical effects when considering the audience perspective.

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

4 TONAL BALANCE VARIATION

In order to provide an optimum sound experience for the entire audience, sound engineers need to have appropriate tonal balance at their mixing desk. As much as possible it should represent the tonal balance given to the rest of the audience. For a system engineer, it is therefore important to understand how the tonal balance of variable-curvature line source arrays varies and how it can be adjusted. Studying the border distance has enabled us to understand its influence and to identify the critical parameters that can be modified: _ Listening distance _ Length of the line source array _ Curvature of the line source array The variations they imply will be illustrated through a few examples on the reference tonal balance of curved line source arrays: the shape of the frequency response given at 40m by 12 K1 loudspeakers arrayed with a slight progressive curvature. 4.1 Listening distance from the source

Lets consider a listener walking from the reference listening distance to the double of this distance. The lowest frequency that propagates in cylindrical propagation mode will double as well. For the frequencies that travelled in spherical mode from the reference listening point to the new listening point, the SPL level has decreased by 6dB. But for frequencies that are still in cylindrical mode at the listening point, the SPL level has decreased by only 3dB. By approximating the resulting frequency response, it can be observed that the -3dB/octave slope has shifted to a lower frequency range.

Figure 5: Shift in tonal balance when the listening distance is doubled

4.2 Length of the line source array

Suppose now that the length of the observed line source array, thus the number of cabinets, is divided by two, and the listener stands at the same reference location. The border distances will get closer to the source, so that frequencies will start to propagate earlier in spherical mode. For frequencies that are still in cylindrical mode at the listening point, the same line segment as with any longer array actively contributes to the energy of these frequencies, so that and their SPL remains unchanged. But a smaller line segment actively contributes to the energy of the frequencies that are in spherical mode, so that their SPL level gets lower. Considering the -3dB/octave slope, this has the same effect as increasing the listening distance: a shift towards the low-frequency range.

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

Figure 6: Shift in tonal balance when the array length is reduced by half

4.3 Curvature of the line source array

The last parameter to observe is the curvature of the array. Suppose that the reference curved line source array is flattened and the listener remains at the same reference listening distance. Again, the border distances will get closer to the source, so that frequencies will start to propagate in spherical mode earlier. But with the flattening of the array, the frequencies that are in cylindrical mode at the listening point will benefit from an increased energy summation proportional to the initial curvature. On the other hand, the lower frequencies that are in spherical mode will use the same array length, and therefore their SPL will remain unchanged. In terms of the -3dB/octave slope, a shift toward the low-frequency range can be observed once again, as when increasing the listening distance or shortening the array.

Figure 7: Shift in tonal balance when the array is flattened

Proceedings of the Institute of Acoustics

Vol. 33. Pt. 6. 2012

5 CONCLUSION

It has been explained that a line source array exhibits two different propagation modes: cylindrical and spherical. The near field is the region of cylindrical waves with SPL decreasing by the inverse of the listening distance. The far field is the region of spherical waves with SPL decreasing by the inverse of the listening distance squared. The position of the border between these two regions is proportional to the frequency and to the array length squared. Studying the influence of that border distance on the tonal balance allowed the identification of three critical parameters: listening distance, array length and array curvature. Of course this type of analysis does not provide the precise numerical results given by measurement or numerical simulation. However, this semi-qualitative approach gives us an intuitive understanding. Changing the array length, the listening distance, or the array curvature affects the tonal balance of line source arrays in the same way: a shift of the -3dB/octave slope. This shift is progressive and entirely predictable. It does not alter the general shape of the response, and thus preserves the sonic quality of line source arrays. Clarity and intelligibility remain homogeneous all over the audience, even at long throw distance. L-ACOUSTICS exploited this observation by providing a specific EQ tool for its systems, the array morphing tool. More specifically, the zoom factor function allows the tonal balance to be adjusted by shifting the -3dB/octave slope, as if the user was virtually changing the reference listening distance, array length, or array curvature. 6 REFERENCES

1. C. Heil and M. Urban, Sound Fields Radiated by Multiple Sound Source Arrays, presented at the 92

nd Convention of the Audio Engineering Society, J. Audio Eng. Soc. (Abstracts),

vol. 40, p. 440 (1992 May), preprint 3269 2. C. Heil, M. Urban, & P. Bauman, Wavefront Sculpture Technology, J. Audio Eng. Soc.,

vol. 51, No. 10, p 912 (2003 October)