音箱线阵列能否产生柱面波.doc

关于音箱的波束导向以及线阵列的指向性控制

对于线阵列，多个品牌都在介绍自己的独特技术，但从物理层面来讲，不少“技术”都有吹嘘之嫌。我在这里抛砖引玉，欢迎大家讨论。

扬声器不象手电筒，声音的特性也跟光线的特性不同，扬声器不能象手电筒一样对各频段的声音产生锐利的投射声束，而且声音也不象光束，不同的声音覆盖在同一块地方会因相位的关系相互抵消和出现梳状滤波（事实上，不同的光源发出的光线在同一处叠加也会相互抵消和产生梳状滤波，不过由于光速太快，波长太短，使得人眼不能分辨而已）。

虽然怎样处理扬声器波束导向的书和论文都很少。可是，在军事上很早就有两个领域应用了波束导向技术：天线阵（相控雷达）和水下天线阵（声纳），而且应用广泛。

相对于雷达和声纳，扬声器的波束导向是相当困难的，因为人耳的听域范围非常宽，从20Hz（低频）到20KHz（高频）。一个20Hz纯音的波长是15.25米，而一个20KHz纯音的波长仅0.013米。这11倍频程的频率范围使波束导向的变得非常困难。事实上，雷达和声纳的工作频率范围最多是单个倍频程，往往只是工作在单一频率。如果只需单个频率的声音进行导向，也很容易做到，但是，从20Hz（低频）到20KHz（高频）就很困难了。由于阵列的间隔和几何尺寸对波束的传播都有影响，通常，对不同的阵列进行优化处理用于不同的频率范围，而这对于专业音频领域的应用是不切实际的，它受扬声器单元尺寸和工艺的限制，波束导向在专业音频的应用只限制于某一频段。

为了使波束导向能够应用，阵列中的每一个扬声器单元的辐射区域必须和阵列中其它扬声器的辐射区域相叠加，如果从两个（或更多）的扬声器单元辐射出来的声音不能交叠，声音的导向跟本无从谈起，相关的理论可以查阅波动力学。

对于现在市场上的所有线阵列音箱，线阵列看上去象紧密排列的单元——看上去就象雷达理论书上所示的图形，也跟介绍波束导向理论中理想化的全指向单元所组成的图形相同。——但是它们的本质是非常不同的，现在的所有线阵列的本质都是－－－低频（有的包括中频）都是采用直接辐射的方式，而高频采用波导（Waveguides）方式。而也没有任何的一款线阵列音箱产生柱面波，详情请查阅《Can line Arrays Form Cylindrical Waves》一文（线阵列能否产生柱面波）。----（原文如下）。只是不同品牌采用了不同的波导方式而已。
Can Line Arrays form cylindrical Waves
Written by Meyer Sound
线阵列能否产生柱面波
What Is a Line Array?
A line array is a group of radiating elements arrayed in a straight line, closely spaced and operating with equal amplitude and in phase. Described by Olson in his 1957 classic text, Acoustical Engineering, line arrays are useful in applications where sound must be projected over long distances. This is because line arrays afford very directional vertical coverage and thus project sound effectively.
什么是线阵列?
线阵列是指一组排列在一条直线上的辐射元件，它们紧密的靠紧，工作时有着相同的振幅及相位。Olson于1957年在他的经典著作<<Acoustical Engineering>>中说过：线阵列在需要长距离声音传输的场合中是非常有用的。这是因为线阵列提供非常直接的垂直覆盖范围，因而有效地辐射出声音。

Fig. 1. Directional behavior of an eight meter long array of sixteen omni-directional sources
The MAPP plots of Figure 1 illustrate the directional characteristics of a line array composed of sixteen omni-directional sources uniformly spaced 0.5 meters apart. The array is highly directional to 500 Hz; above that, the directional characteristic begins to break down. Note the strong rear lobe at low frequencies; all conventional line arrays will exhibit this behavior because they are omnidirectional in this range. Note also the strong vertical lobes at 500 Hz. (The horizontal pattern of this system is independent of the vertical, and is omni-directional at all frequencies.)

Fig. 2. Directional behavior of an eight meter long array of thirty-two omni-directional sources
Figure 2 shows a line of thirty-two sources spaced 0.25 meters apart. Notice that this array maintains its directional characteristic to 1 kHz, where the strong vertical lobe appears. This illustrates the fact that directionality at high frequencies requires progressively more closely spaced elements.
How Do Line Arrays Work?
Line arrays achieve directivity through constructive and destructive interference. A simple thought experiment illustrates how this occurs.
Consider a speaker comprising a single twelve-inch cone radiator in an enclosure. We know from experience that this speaker’s directivity varies with frequency: at low frequencies, it is omni-directional; as the sound wavelength grows shorter, its directivity narrows; and above about 2 kHz, it becomes too beamy for most applications. This is why practical system designs employ crossovers and multiple elements to achieve more or less consistent directivity across the audio band.
Stacking two of these speakers one atop the other and driving both with the same signal results in a different radiation pattern. At points on-axis of the two there is constructive interference, and the sound pressure increases by 6 dB relative to a single unit. At other points off-axis, path length differences produce cancellation, resulting in a lower sound pressure level. In fact, if you drive both units with a sine wave, there will be points where the cancellation is complete (this is best demonstrated in an anechoic chamber). This is destructive interference, which is often referred to as combing.
A line array is a line of woofers carefully spaced so that constructive interference occurs on-axis of the array and destructive interference (combing) is aimed to the sides. While combing has traditionally been considered undesirable, line arrays use combing to work: without combing, there would be no directivity.
Can a Line Array Form Cylindrical Waves?
In a word, no.
The common misconception regarding line arrays is that they somehow magically enable sound waves to combine, forming a single "cylindrical wave" with special propagation characteristics. Under linear acoustic theory, however, this is impossible: the claim is not science but a marketing ploy.
Unlike shallow water waves, which are non-linear and can combine to form new waves, sound waves at the pressures common in sound reinforcement cannot join together: rather, they pass through one another linearly. Even at the high levels present in the throat of compression drivers, sound waves conform to linear theory and pass through one another transparently. Even at pressure levels of 130 dB nonlinear distortion is less than 1%.
The MAPP plot of Figure 3, which shows a cross-fired pair of Meyer MSL-4 loudspeakers, illustrates this point. At the area labeled A, in the crossfire region, there is significant destructive interference in the dark areas. At the area labeled B, however, the output of the corresponding MSL-4 is completely unaffected by the cross-firing unit. Though the waves interfere at A, the interference is local to that area in space, and they still pass through one another unaffected. In fact, you could turn off the cross-firing unit and hear virtually no change whatsoever at B.

Fig. 3. Cross-fired MSL-4 loudspeakers
This experiment is best done in an anechoic chamber or outdoors in an open field, away from reflecting surfaces. It’s also advisable to apply a low-cut filter to remove information below about 500 Hz, where the MSL-4 starts to lose directionality. 
But don’t line arrays produce waves that only drop 3dB with every doubling of the distance from the array?
This simplistic marketing claim appears to be a misapplication of classical line array theory to practical systems. Classical line array mathematics assumes a line of infinitely small, perfectly omni-directional sources that is very large compared with the wavelength of the emitted energy. Obviously, practical systems cannot approach these conditions, and their behavior is far more complex than some audio company marketers suggest.
Modeling the behavior of a fifteen-inch woofer with Bessel functions (which describe a piston), Meyer Sound has written custom computer code to model line arrays with various numbers of loudspeakers at various spacings. This computation shows that it is theoretically possible to construct an audio line array that follows the theory at low frequencies, but it requires more than 1,000 fifteen-inch drivers, spaced twenty inches center-to-center, to do it!
A truncated continuous line array will produce waves that drop 3 dB per doubling of distance in the near field, but the extent of the near field depends on the frequency and the length of the array. Some would have us believe that, for a hybrid cone/wave guide system, the near field extends hundreds of meters at high frequencies. It can be shown mathematically that this is true for a line of 100 small omni-directional sources spaced an inch apart, but that is hardly a practical system for sound reinforcement and is not a model for the behavior of wave guides.
Nor does the purely theoretical computation reflect the reality of air absorption and its effects at high frequencies. The table below shows the attenuation at various distances from an array of 100 one-inch pistons spaced one inch apart, as modeled using a Bessel function. At 500 Hz and above, it also shows the total attenuation when air absorption is included using the calculation given in ANSI Standard S1.26-1995 (the conditions for this table are 20° C ambient temperature and 11% relative humidity). Note that, while at 16 kHz the array as modeled by the Bessel function is approaching 3 dB attenuation per doubling of distance, air absorption makes its actual behavior closer to 6 dB per distance doubling.

2 meters
4 meters
8 meters
16 meters
32 meters
64 meters
128 meters
256 meters
125 Hz
0
5.5
11
17
23
29
35
41
250 Hz
0
5
11
17
23
29
35
41
500 Hz
0
2.3
7.2
13
19
25
31
37
w/air absorption

38
1 kHz
0
1.3
3.2
8.2
14
20
26
32
w/air absorption

15
21
28
35
2 kHz
0
3
5.2
7
12
18
24
30
w/air absorption

8
13
21
29
41
4 kHz
0
2.7
6.3
9
11
16
21
27
w/air absorption

3.1
7.1
11
14
23
35
59
8 kHz
0
2.8
5
8.6
11
13
18
24
w/air absorption

3.5
6
12
17
25
42
72
16 kHz
0
3.1
6.6
8.2
12
14
16
21
w/air absorption

4.1
8.6
12
20
33
49
88

3 dB per doubling
0
3
6
9
12
15
18
21
6 dB per doubling
0
6
12
18
24
30
36
42

Table 1. Attenuation in decibels for octave frequency bands at various distances
from a line array of 100 one-inch pistons spaced one inch apart
With a practical, real line array of sixteen cabinets (each using fifteen-inch low frequency cones), a slight "cylindrical wave" effect can be measured at about 350 Hz, where there is a 3 dB drop between two and four meters from the array. More than four meters from the array, however, the sound spreads spherically, losing 6 dB per distance doubling. This behavior can be confirmed with MAPP using the measured directionality of real loudspeakers.
At frequencies below 100 Hz, the drivers in a practical line array will be omni-directional but the array length will be small compared with the sound wavelength, so the system will not conform to line array theory. Above about 400 Hz the low-frequency cones become directional, again violating the theory’s assumptions. And at high frequencies, all practical systems use directional wave guides whose behavior cannot be described using line array theory.
In short, the geometry of real audio line arrays is far too complicated to be modeled accurately by antenna theory. They can only be accurately modeled by a computational code that uses a high-resolution measurement of the complex directionality of actual loudspeakers, such as MAPP.
That said, practical line array systems remain very useful tools, regardless of whether the continuous line array equation applies. They still achieve effective directional control, and skilled designers can make them behave very well in long-throw applications. 
How Do Practical Line Array Systems Handle High Frequencies?
Figures 1 and 2 show that line array theory works best for low frequencies. As the sound wavelength decreases, more and more drivers, smaller in size and spaced more closely, are required to maintain directivity. This is why some line array systems cross over to eight-inch drivers for the midrange. Eventually, however, it becomes impractical to use, for example, hundreds of closely spaced one-inch cones.
Practical line array systems therefore act as line arrays only in the low and mid frequencies. For the high frequencies, some other method must be employed to attain directional characteristics that match those of the lows and mids. The most practical method for reinforcement systems is to use wave guides (horns) coupled to compression drivers.
Rather than using constructive and destructive interference, horns achieve directionality by reflecting sound into a specified coverage pattern. In a properly designed line array system, that pattern should closely match the low-frequency directional characteristic of the array: very narrow vertical coverage and wide horizontal coverage. (Narrow vertical coverage has the benefit that it minimizes multiple arrivals, which would harm intelligibility.) If this is achieved, then the wave guide elements can be integrated into the line array and, with proper equalization and crossovers, the beam from the high frequencies and the constructive interference of the low frequencies can be made to align so that the resulting arrayed system provides consistent coverage. 
Can Line Array Loudspeakers Be Used Singly?
No, the cone drivers in a line array loudspeaker need the other cones in the array to create directionality. The cones in a single cabinet have the same directional characteristics as comparable cone drivers in other types of loudspeakers. In other words, each cabinet in a line array is not producing a "slice of a cylindrical wave." That is a marketing concept, not a scientific one. 
Can You Curve a Line Array to Get Wider Coverage?
In practice, gently curving a line array (no more than five degrees of splay among cabinets) can aid in covering a broader area. Radically curving line arrays, however, introduces problems.
First, if the high-frequency section has the narrow vertical pattern that’s required to make a straight array work, curving the array can produce hot spots and areas of poor high-frequency coverage. Second, while the curvature can spread high frequencies over a larger area, it does nothing to the low frequencies, which remain directional because the curvature is trivial at long wavelengths.
Figure 4 illustrates these points. On the left is a series of MAPP plots for a curved array, and on the right are plots of a straight array. Both arrays are constructed of identical loudspeakers having a 12-inch cone low-frequency driver and a high-frequency horn with a 45-degree vertical pattern.
Notable in the left-hand plots is that, while the wider horn aids in spreading the high frequencies, it also introduces pronounced lobing due to interference. At 1 kHz and below, the array remains highly directional, following line array theory. In practice, this behavior would produce very uneven coverage, with the frequency response varying substantially across the coverage area and a large proportion of that area receiving almost no low-frequency energy.
The right-hand series of plots reveals that a loudspeaker with a moderately wide-coverage horn designed for curved arrays behaves poorly in a straight array. While the array is highly directional, pronounced vertical lobing occurs at 1 kHz and above. These strong side lobes divert energy from the intended coverage area and would excite the reverberant field excessively, reducing intelligibility.

Fig. 4. Directional characteristics of a curved (left) and straight (right) line array using a high-frequency horn with a 45-degree vertical pattern
Can You Combine Line Arrays With Other Types of Speakers?
Yes, since linear waves pass through one another regardless of whether they are created by a direct radiator or a wave guide, it is possible to combine line array systems with other types of loudspeakers as long as their phase response matches that of the line array speakers.