Managing low frequencies is one of live audio’s constant challenges. We deal with room nodes, architectural resonances, uneven coverage and unwanted spill. The last two decades have brought about the ready availability of digital signal processing (DSP) and digital consoles. DSP is now in almost everyone’s arsenal, allowing the easy creation of cardioid arrays with everyday tools.
Low frequency arrays employ precisely controlled arrivals of multiple audio sources to provide “steering” of bass energy where we desire. You can gain this extra low frequency control without investing in anything other than the time you’ll need to understand the physics, reconfigure subwoofer placement, program a couple of outputs, and wire the enclosures accordingly.
In this article, we will leverage DSP to implement a cardioid array — named for the shape of its coverage pattern. This one of the most common directional low frequency arrays and easy to construct. We will show you how to quickly set up an array that projects low frequencies in front while providing cancellation behind. A cardioid array requires two outputs that are capable of producing the subwoofer high-pass, low-pass and delay.
Sub Array — Why?
The most treacherous enemy of quality sound reinforcement is often the space where the performance is heard. Whether it’s a band shell messing up monitor mixes, balconies creating reflections at FOH or arenas echoing for days, acoustics are problematic. For high frequencies, horns are successful in aiming sound onto the audience. Mid frequencies are typically moderately controlled for directivity, and most equalization tends to be applied in the midrange as a means to compromise between the direct and reflected sound. Extending control to low frequencies is then the next goal in managing room acoustics. Also, in many outdoor environments, the ability of limiting low frequency spill that drifts off the performance site (i.e., “angry neighbor” syndrome) is a value-added service any soundco can present to the promoters.
Even in a simple club or bar installation, creating directional low-frequency energy can go far in reducing the unappreciated bass thumping that inevitably leads to complaints by any neighboring business that happens to occupy the space on the opposite side of a backstage wall.
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 onstage subwoofer wash cleans up the mud that 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, subwoofer arrays have manifest benefits, and the costs and complexity are low compared to the many advantages they offer.
Sub Array — The How
Many papers and textbooks have been written on the science of using multiple sources in arrays to provide directional control of sound, and we won’t repeat that 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” simply 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.
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 something as basic as a typical double 15 subwoofer has one reverse-wired driver. When the cancellation is exact, the resultant pressure cancels to the baseline atmospheric pressure, and the sound volume is zero. Cancellation of high- and low-pressure regions is how directional arrays “remove” sound from specific locations.
The first mechanism at work in directional arrays is that sound sources are physically spaced to arrive at different locations at different times. This seems obvious, but it is an important concept. As 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 by physically spacing the sources apart. To create cancellation at a specific frequency, we require arrival times to be a half-wavelength apart at that frequency. A half-wavelength offset results in the maximum cancellation. This is also known as a 180-degree phase shift.
As subwoofers operate between 30 and 90 Hz, a center frequency of interest is 60 Hz, which has a wavelength of almost 19 feet, so a difference of 9.5 feet in arrival produces maximum cancellation. Note that if we place two subwoofers 9.5 feet apart, and look at their response at 60 Hz, we will see that the coverage pattern forms a figure 8, with output biased to the front and back, and almost none to the sides. This is not generally the coverage pattern we want from a subwoofer array.
Instead, we would like to “soften” the coverage pattern and give ourselves more coverage out front, and more cancellation in the back. An alternative way to cause cancellation is with a polarity reversal. Unlike the distance example above, a polarity reversal always causes the maximum cancellation at every frequency. Polarity reversal is not frequency dependent; it is like having exactly a half wavelength spacing at every frequency. Compare this to the distance case above, where you have maximum cancellation only when the distance between the speakers corresponds to a half wavelength at a specific frequency,
We can now combine the effects of polarity and physical distance to create a configuration that adds together up front, and cancels behind. As you will see below, we use a clever mix of physical spacing and digital delay to create a wider, softer front coverage pattern.
Building the Sub Array
Building a directional array begins with similar subwoofers, so that the relative phase of all of their baseline output is similar. Next, our two loudspeakers are separated in space. This can take several forms. One approach is to place the subwoofers one behind the other. This arrangement is a good option when stage height is low, but there is sufficient depth to the audience.
With one subwoofer placed behind the other, an appropriate spacing distance between them is close to a quarter-wavelength, or about 5 feet from the front of one cabinet front to the next. Another way to create this distance is to stack up the subwoofers and turn the bottom one around backwards. The spacing here is then the total distance the sound must travel around the cabinets.
The second cabinet, placed either behind or below the main subwoofer, can be thought of as providing the cancellation, as shown in Fig. 1. We invert the polarity of this second enclosure. The polarity reversal causes it to create pressure opposite the main subwoofer at all frequencies, with the result being a directional cardioid pattern, such as that in Fig. 2. Opposite pressure is required for sound cancellation behind the array. For convenience, we will call this cabinet the “cancellation sub.”
Now we have spaced sources about one-quarter of a wavelength apart, and a cancellation sub with reversed polarity. But we need the output of the cancellation sub to add with the main sub in the audience. Therefore we must adjust its arrival time to line up with the main subwoofer facing the audience. Since we know that a half-wavelength offset produces maximum cancellation, half-wavelength spacing coupled with a polarity inversion produces maximum addition. It is almost like having a full 360-degree phase rotation over a narrow band of frequencies.
We therefore need to add about a quarter-wavelength of delay to the cancellation sub to create the desired offset. Half of the offset is physical distance, and the other half is digital delay. Adding 4 to 5 milliseconds (ms) of delay to the cancellation sub gives the desired result.
To recap:
• In front of both subs, the rear cancellation sub arrives a quarter-wavelength late and is also electronically delayed by a quarter-wavelength totaling a half-wavelength difference in arrival.
• This would normally create cancellation, but as the rear sub has its polarity inverted, it sums constructively in front of the pair out in the audience area.
• Behind the two subs, the main sub arrives a quarter-wavelength late due to physical offset, but because the rear sub is electronically delayed by a quarter-wavelength, they appear to arrive at the same time behind the array.
• The polarity reversal then causes cancellation behind.
Finally, we turn the level of the cancellation sub down by about 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 similar subwoofers, we perform the following four steps:
1. Place one sub about a quarter-wavelength behind the main sub.
2. Reverse the polarity of this rear “cancellation” sub.
3. Delay the cancellation sub by about a quarter wavelength (4 to 5 ms)
4. Turn down the cancellation sub by about 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 Bottom Line
With small digital consoles routinely used at even simple events, the live sound professional will have the DSP readily at hand to direct low frequencies with cardioid arrays of two or more subs. Obviously, the subwoofers also require separate drive amplifiers, but this has become more common as speakers (particularly subwoofers) evolve more into self-powered designs. Otherwise, some reconfiguring of amplifier racks will usually facilitate the two distinct subwoofer processing channels.
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, stacked shipping cases or the venue’s wall. This will enable the array to work effectively and makes sure that the sound can either add or cancel before interacting with a solid boundary.
The details of this basic cardioid array are simple enough for almost anyone to utilize at their events. Try the cardioid array, and hear for yourself how effective the rear cancellation can be. From a big festival to a wedding in a ballroom, less boom outside the room is close at hand.
Phil Graham is FRONT of HOUSE’s regular technical contributor and resident scientist.
Calculating Wavelengths
One key factor in creating cardioid low-frequency arrays is the ability to determine the half-, quarter- or full-wavelength of sound at any frequency. Although the speed of sound can vary due to temperature or atmospheric conditions, a good starting point to know is that the speed of sound in dry air at 68° Fahrenheit is 1,126 feet per second. Under such conditions, a 20 Hz (20 cycles per second) wave is 56.3 feet long, determined by:
Using basic algebra, the seconds cancel out and we are left with the length of a single wave cycle — 56.3 feet in this case. Determining the half- or quarter-wavelength is simply dividing that length of a single wave by two or four.
In broadband audio cases, such as determining the amount of delay necessary to align the sound from the stage P.A. with delay speakers, a figure based around the length of a 1 kHz wave usually does the trick (1,126 feet/sec divided by 1,000 Hz = 1.126 feet). As a rough approximation in such cases, you can often guesstimate longer distance delay times as about a millisecond of delay for each foot of separation between the main and rear speakers. This gives you a good starting point and from there, you can slightly tweak the amount of delay applied to the main system to achieve a more precise delay time.
—George Petersen
