November 01, 2013, by Steve Bush
Directional subwoofers are one more tool that can be used by sound system designers in their quest to achieve consistent sound throughout the intended listening area.
When using traditional, more or less omni-directional bass reflex (a.k.a., “vented,” “ported,” or “front-loaded”) subs arranged left and right of a stage, there is a build-up or “power alley” created in the center, where the energy from each source location shows up at the same time, with no phase difference, and sums quite nicely.
Moving left and right off of the center line, this area of addition is followed by alleys of cancellation.
Wavelengths of 40 to 100 Hz are roughly 11 to 23 feet long. At any frequency in this range, as you move away from the center line and change the path length difference between the two sources by half a wavelength (about 5.5 to 11.5 feet) there will be a cancellation, with higher frequency “nulls” encountered first.
To alleviate this there are three methods that have been employed: line arrays of subs, end-fired sub arrays, and cardioid subs, which are sometimes combined.
Lines of subwoofers are one application of what Harry Olson discussed in the 1957 text Harry F. Olson, Acoustical Engineering, when he described a straight line source; using omni-directional elements, in a line, all reproducing the same signal, with relative close spacing compared to the wavelength, pattern control can be achieved.
Imagine a row of subs is assembled across the front of a stage. If it’s longer than the wavelength of the lowest frequency for which pattern control is desired (25 Hz is about 45 feet) and if the elements are close enough to one another, within two-thirds of a wavelength of the highest frequency produced (100 Hz is about 11 feet, so 2/3 is about 7 feet), cancellation at the ends of the line and addition in front of the array (and behind the array!) will be achieved.
Observed from the audience area, from one end of the line to the other, enough of the energy from each of the elements of the array arrives within +/- 120 degrees, at about the same level and sums.
Observed from the end of the array, enough energy from each of the elements arrives enough out of time but at similar enough level, causing destructive interference and level loss.
The use of a line array (yep, that’s what it is) of subwoofers can avoid horizontal differences in frequency response and deliver more energy to the audience area, while avoiding those nasty side wall reflections at lower frequencies.
Further, maximizing spacing can reduce the level differences from the front to back. In the interest of making sound where the audience is and not making noise where they are not, this is one option.
Remember, though, that the energy is the same in front and behind the array.
These arrays can also be assembled vertically, though space between the elements is not easily achieved with most rigging systems, so they are generally closely spaced arrays.
In amphitheater and arena situations where coverage to the sides is desirable, incrementally delay-tapering the horizontal array - so that moving away from center, each sub is slightly later than the one before it - can spread the coverage out towards the sides.
The end-fired array can be made up of two or more subs, spaced closely together, one facing the rear of the next, in a row along the “z-axis,” facing the audience and the direction of coverage.
Yes folks; it looks like it won’t sound “right.” Each cabinet needs its own drive line because we are going to incrementally delay all but the rear-most.
The rear, upstage, sub is delay time zero.
Moving towards the audience, each sub needs delay added corresponding to its distance from “sub zero.”
Let’s say the spacing is 3.5 feet: the delay time would be 3.1 ms (speed of sound = 0.9 ms/ft) for the next element.
The end-fired array produces gain in front of the array because the energy from each of the elements arrives in time at all frequencies being reproduced.
Cancellation behind the array is the summation of the energy produced by each source that is out of time and arrives at almost the same level.
There are a number of dips in frequency response based on the number of signals that have 180 degrees of phase difference. The level difference between front and rear is about 18 dB with a four-element array.
A few manufactures make multi-driver, single-cabinet cardioid enclosures, but they can be created with simple arrays of two or more cabinets.
The physical arrangement can be one of two options, both speakers facing the audience, one upstage of the other, lined up on the ‘z-axis,’ or one sub oriented facing backwards next to one or more facing forward. Again, people will question the appearance.
When both subs are facing the audience, one upstage of the other, delay and a polarity flip are applied to the signal going to the rear speaker.
In the rear, the energy from both loudspeakers arrives in time, at almost the same level, but with reversed polarity, resulting in broadband destructive interference and reduced level. In front of the array, the two signals arrive with polarity different and out of time.
This is a little tricky, but the first dip in the comb filter in this example is going to be at 160 Hz, out of band of the sub. If the spacing between the subs is 3.5 feet and the delay time is 3.1 ms, the two signals arrive 7 feet apart in front.
The wavelength of 160 Hz is 7 feet. With the polarity flip, the first dip of the comb filter will be at 160 Hz, not 80 Hz. The two signals in front are also at about the same level, so the dip will be significant.
The cardioid arrangement using forward and rearward facing subs can be assembled vertically or horizontally, subs stacked one on top of another or laid side by side, in a line, some facing the audience and one or more facing backwards.
Talk about looking like it won’t sound good. Behind the array, the output of the front and rear facing elements of the array need to match in time and be very close in level, but polarity backward to create cancellation behind the array.
A polarity flip and delay of the rear facing loudspeakers achieves this.
Determining the number of forward and rearward facing elements depends on model and how much energy needs to be created behind the array to cancel the energy from the forward facing subs.
The delay time will vary too, depending on model, and dimensions of the array, both vertically and horizontally.
Measurement is needed to determine level and time relationships between the front and rear subs.
An FFT transfer function can quantify this accurately. In front of the array, the summation of the rear facing loudspeakers is out of time and polarity different from the energy being produced by the forward facing subs.
The problem in frequency response, that first dip in the comb filter, must be kept out-of-band, higher in frequency than the operational range of the subs.
A hybrid approach, combining cardioid pairs, arranged in a line across the front of the stage, results in cancellation left, right, and to the rear. Alternatively, combining end-fired arrays and line-arrays also achieves additional directional control.
Using a directional array left and right affords the opportunity to join -6 dB down points in the middle of the audience and minimize the interaction between the arrays by minimizing the area where they are level similar, moving quickly into isolation of one or the other arrays. This would lend itself to very wide audience areas, such as amphitheaters and festival sites.
Directional arrays are often misconceived, mis-assembled, or are faulty in their operation. They require a knowledgeable operator, good equipment, and proper implementation.
The benefits can be substantial and are sometimes worth the risks. Avoiding some reflections in rooms, decreasing the amount of low-frequency energy on the stage (turn the floor monitors down, folks), and making the coverage smoother in amplitude and frequency response in the audience area are the substantial benefits when considering the use of directional low-frequency arrays.
There are several critical factors of performance that must be considered when assembling these types of arrays. Control of low frequency directivity is only possible when using exceptionally linear systems, precision-manufactured to perform identically.
The relationship between individual components must be consistent. What is sent electrically to the array elements needs to be turned into acoustic energy, without distortion or changes in frequency response as signal level changes.
Historically, directional low-frequency loudspeakers have been in existence for some time.
Meyer Sound developed the first commercially available design, the PSW-6, a dozen years ago.
The PSW-6 uses a four-channel amplifier and signal processing built-into an enclosure that houses dual 18- and 15-inch drivers facing the audience, plus two more 15-inch drivers mounted in its rear.
This self-powered subwoofer provided cardioid vertical and horizontal polar response, serving as a new tool in the challenge of designing sound systems.
It eliminated 15 to 20 dB of the energy from the rear that would have bounced around and arrived in the audience area late.
Another advantage was the ability to place these loudspeakers in front of large walls without having to consider boundary reflections.
These and others continue to be advantages over omni-directional designs.
The PSW-6 design was a result of field experiments using the SIM (Source Independent Measurement) FFT measurement platform, along with prediction results from Meyer Sound’s then new MAPP Online (Multipurpose Acoustical Prediction Program).
MAPP, among its many uses, has become a tool that many practitioners use to design low-frequency directional arrays. Users are able to apply signal processing, arrange elements, and observe the results graphically as a narrow-band pressure plots or as broad-band Virtual SIM transfer functions, all predicted from the interaction of measured data sets of real loudspeakers.
“Measure twice and pile it up once.” Let’s face it, moving subs around in a parking lot is a lot of work and requires a substantial investment of time and effort, plus there’s tinkering with signal processing and measurement, as well as additional DSP and multiple drive lines.
On the other hand, moving subwoofers around on a computer screen is a two-finger event, and without the need for real subs, signal processing, and measurement platforms, a real time and money saver.
Not having to build and measure subwoofer arrays in the physical world as a first step has allowed users to design arrays that they might not have spent the time to experiment with in real life.
Steve Bush is a technical support representative for Meyer Sound.