Managing low frequencies is one of live audio’s constant challenges. We deal with room nodes, architectural resonances, uneven coverage and unwanted spill. Today’s line arrays provide fairly uniform horizontal coverage with adjustable vertical splay. However, an equivalent vertical subwoofer array that provides low-frequency directivity is enormous. The last decade has brought about the ready availability of digital signal processing (DSP) and with the advent of digital consoles, modest DSP is included in every mixer’s outputs, allowing the easy creation of cardioid arrays with everyday means.
Powered loudspeakers are a logical extension of our evolution towards improved control and precision. With amplifiers and processing integrated into each enclosure, powered loudspeakers provide protection, flexibility and ease of use. Powered subwoofers, like those in this month’s Buyers Guide, can be used with stereo system processors’ dual subwoofer outputs, but even the DSP in digital consoles can create a simple directional low frequency array.
Low frequency arrays employ precisely controlled cancellation to provide “steering” of bass energy where we desire. This extra low frequency control is nearly free, except for the time it takes to understand the physics, reconfigure subwoofer placement and program some DSP with polarity inversion, a few milliseconds of delay and a slight gain reduction.
In this article, we will leverage simple DSP to implement a particular type of directional subwoofer configuration known as a cardioid array — named for the shape of its coverage pattern — one of the most common directional low frequency arrays1 and easiest to construct. We will show you how to quickly set up an array that projects low frequencies in front, while providing cancellation behind. The cardioid array requires two channels of DSP and is easily implemented with two self-powered subwoofers.
Steering Sound: Why
The most treacherous enemy of quality sound reinforcement is usually the space where the performance is heard! Whether it’s a band shell messing up monitor mixes, balconies causing reflections at FOH, or arenas echoing for days, room acoustics are our nemesis. We already battle the room in several common ways: system equalization to reduce excitation of troublesome acoustical problems; directional microphones used to isolate performers and instruments from the room and from each other; and mid and high frequency horns that aim sound onto the audience, but off the walls. Extending control to low frequencies is the next frontier in managing room acoustics. And as subwoofers have grown more powerful to keep up with line arrays, the need to control the subs has grown.
In addition to wrestling with room acoustics, it is often beneficial to reduce low frequency energy for the performers on stage, or for event considerations. Reducing subwoofer stage wash cleans up the “mud” that normally clouds monitor mixes and has musicians asking for more level on stage. Whether indoors or out, when we keep low frequencies out of adjacent areas, event organizers have one less frustrated entity to pacify. Whether for acoustics, performers or logistics, the benefits of steering low frequency sound are substantial.
Steering Sound: How
Many papers and articles have been written on the science of using multiple sources in arrays to provide directional control of sound, and we won’t repeat that excellent work here. Instead, we mention the key mechanisms that these arrays employ, and then move directly to the practical details of setting one up.
The first factor for grasping the function of directional arrays is that sound waves combine in varying amounts depending on the time when they arrive at a specific location. Sound is merely regions of high- and low-pressure air that move through space. “High-pressure” means that the air is compressed above atmospheric pressure, and “low-pressure” means the air has a pressure below atmospheric. If two high-pressure regions arrive at the same location at the same time, then they combine to produce an even higher pressure, and greater sound volume. Two, four or eight subwoofers stacked together become louder and louder.
Conversely, if a region of high pressure and a region of low pressure arrive at the same place at the same time, the combination results in cancellation. For example, this can happen accidentally if a double-eighteen subwoofer has a reverse-wired driver, or if one of two banana plugs was inserted backwards in its amp’s binding post. When the cancellation is exact, the resultant pressure cancels to atmospheric pressure, and the sound volume is zero. Cancellation of high- and low-pressure regions is how directional arrays “remove” sound from specific locations.
One mechanism at work in directional arrays is that sound sources can be physically spaced to arrive at different locations at different times. This seems obvious, but it is an important concept. Since the speed of sound is constant, a sound source that is farther away arrives later. We can utilize different arrivals to control sound’s cancellation, so the sound sources must be physically spaced apart.
As subwoofers operate mostly between 40 and 120 Hz, a center frequency of interest is 80 Hz, which has a wavelength of 14 feet, so a difference of 7 feet in arrival — a half-wavelength — produces cancellation. Another mechanism for producing cancellation is polarity reversal of one of two sources with the same arrival, as in the case of our dual-eighteen with one driver miss-wired.
Combining these factors allows us to employ spaced, delayed and polarity-reversed sound sources to produce locations where pressures either combine to increase sound volume, or cancel to reduce SPL.
Mathematics can be used to determine where and how addition or cancellation occurs at any point in space. Software can calculate these values and display them graphically. Fig. 1 shows the relative sound pressure level (SPL) from a typical two-box cardioid array looking down from above.
Steering Sound: Build It
Building a directional array begins with identical subwoofers, because while any closely matched sources can combine, it takes identical sources out of phase to maximize cancellation. First, our two loudspeakers are separated in space, one behind the other. This arrangement is a good option when stage height is low, but there is sufficient depth. With one subwoofer placed behind the other, a good spacing distance between them is a quarter-wavelength, or about 3.5 feet from the front of one cabinet front to the next.
Thus, if the subwoofers are 30 inches deep, there will be a foot between the back of the first enclosure and the front of the second. The second cabinet, placed behind the main subwoofer, will be used to cancel sound behind the pair, while reinforcing the sound in front of them both. Next we invert the polarity of the second, “upstage” enclosure. The polarity reversal causes it to create pressure opposite the main subwoofer at all frequencies. Opposite pressure is required for sound cancellation behind the array. For the rest of the article, we’ll call this rear cabinet the “cancellation sub.”
Now that we have spaced sources, with the cancellation sub polarity-reversed, we must adjust its arrival time to that of the main subwoofer in front. We want the inverted sub to add with the main subwoofer out in the audience, in front. Since we know that a half-wavelength offset produces maximum cancellation, half-wavelength spacing coupled with a polarity inversion produces maximum addition. We therefore need to a add quarter-wavelength of delay to the cancellation sub’s quarter-wavelength of physical spacing to create the full half-wavelength of offset. Adding 3.1 milliseconds (ms) of delay to the inverted sub provides an extra quarter-wavelength offset, but you may find that 4 ms will provide a more desirable result.
In front of both subs the rear cancellation sub arrives a quarter-wavelength late and is electronically delayed by a quarter-wavelength totaling a half-wavelength difference in arrival. This would normally create cancellation, but because the rear sub has its polarity inverted, it sums constructively in front of the pair in the audience area.
Behind the two subs, the front, primary sub arrives a quarter-wavelength late due to the offset, but because the rear sub is electronically delayed by a quarter-wavelength, they arrive at the same time. The rear sub’s polarity reversal causes the two to cancel behind them.
Finally, we need to turn the level of the cancellation enclosure down by 3 dB. This is because the sound level behind the main subwoofer is slightly lower than it is out front. We want to closely match the level of the rear cancellation subwoofer to the level of the main subwoofer to produce the best cancellation.
Quickly summarizing our creation of a directional subwoofer array from two identical subwoofers, we perform the following four steps:
1) Place one sub a quarter-wavelength (3.5 ft) behind the main sub.
2) Reverse the polarity of this rear “cancellation” sub.
3) Delay the cancellation sub by a quarter wavelength (3 to 4 ms).
4) Turn down the cancellation sub by 3 dB.
Two subwoofers, a little DSP, and four simple steps produce directional bass response to the benefit of your audience, musicians, and management. The details of this basic low frequency array are simple enough for anyone to utilize at their gigs!
Conclusion
In describing the steps above we have, of course, simplified the mathematical subtleties that give the cardioid array its special sauce. We feel this a worthy tradeoff to provide a simple process you can set up in your shop today. Try the cardioid array and hear for yourself how effective the rear cancellation can be. Your experiment can be as simple as feeding two matching subwoofers with the stereo outputs of a digital console reversing the polarity of one channel, delaying it a few milliseconds and turning it down 3 dB.
One important final factor when creating cardioid arrays is that there must be some space around the sides and back of the array. A good rule of thumb is to allow at least three feet from any solid boundary near the array, whether a stage or the venue’s proscenium wall. This will enable the array to work effectively.
With small digital consoles routinely used at even simple events, the live sound professional will often have the DSP readily at hand to direct low frequencies with cardioid arrays of two or more subs. The self-contained nature of powered subwoofers makes this even simpler. Small gigs, weddings, ballroom talking heads and other such events can now utilize the low frequency tricks of the “big boy” production houses. Control of low frequency energy ultimately improves your customer’s sonic experience, adding value to your services.
1http://en.wikipedia.org/wiki/Cardioid
Phil Graham is a principal of PASSBAND, llc in Atlanta, GA, a professional audio consultancy, and started building subwoofer arrays more than a decade ago. Email him at: [email protected].
