General goal of the project. The main goal is to make available and introduce to experts and others interested in the industry an innovative way of tackling a show on a circular stage, one in which a high SPL could be achieved in the audience area while keeping the stage free of disturbances. To date, there is no record of any purely circular stage ever having existed where the subwoofers were placed at the foot of the stage and attendees could stand right next to a 360º stage.
For this reason, it seeks to introduce this array, along with the processes for building it and understanding it from its origins. It is interesting not only for the shape it creates, but also for how simple it is to configure on site. This is because it uses only 2 DSP processing channels, which would be enough to control the entire circumference.
Within the general goal, it is important to mention the possibility of bringing about a drastic change in the way events are conceived and produced, since the traditional stage is no longer necessary.
Specific goals
Eliminate the need to fly the subwoofers by placing them around the perimeter of the stage. This is possible because the array formed by the cabinets lets us keep the stage free of disturbances and very considerably reduces the weight borne by the stage structure
Reduce the number of calculations and DSP processors in order to save time. Since all the groups are built the same way, the delay processing is the same for all of them. This allows us to reduce the number of processing channels to two.
Graphically demonstrate sound propagation in the environment using this ring. As was done in the previous sections and will be done in the upcoming ones, acoustic predictions and images will be included to facilitate and illustrate the theoretical explanations.
Explain how to build this array and how to position it. Explain in detail how to build the array and how to obtain the position of each group of subwoofers.
Assess the response both inside and outside the ring. Provide estimates of the phase, frequency and SPL response in different situations within the area intended for the audience.
Gather the trigonometric calculations needed to position the cabinets. A mathematical explanation of the loudspeaker placement, as well as the reasons behind the results.
Technical outline of the tasks to be carried out
Before starting to explain how to place the loudspeaker cabinets, it is vitally important to clarify that there are two ways of understanding this array. One is to divide the circumference into sets of 5 cabinets. In this case they would behave like a gradient configuration. The other possibility is to analyze it by rings, that is, to analyze how the outer ring and the inner ring would each behave independently.
Loudspeaker placement
The loudspeaker cabinets are placed concentrically around the center of the stage. Keep in mind that whenever the loudspeakers are separated by more than 240° of the wavelength, alleys will be created, which is why a large number of groups must be used. Another option worth mentioning is to reduce the radius, which, as we will explain in the section devoted to it, can give us an increase in the control frequency as well as a decrease in the number of cabinets to be used.
Loudspeaker grouping
In this section we will focus on analyzing how the array behaves, both as a set and as a ring. It is important to understand its behavior as a set in order to get an idea of how the rings work.
A. As a set
When we refer to analysis as a set, we mean the group of five loudspeakers, that is, how the gradient array behaves in the strict sense. As we explained in the introduction, it consists of two rows, the first made up of three loudspeakers facing the audience. These loudspeakers have no delay or phase inversion. The second row contains two loudspeakers, which have a delay of 2.94 ms and a 360º phase inversion.
The explanation of this array lies in the fundamentals of the traditional gradient. In the original array (two cabinets separated in the same direction), the loudspeaker cabinet closest to the audience has no delay or phase inversion, just as in our array, where we place three cabinets instead of one. This gives us a less directional lobe and a wider cardioid, thus avoiding the creation of cancellation alleys between lobes.
The second row contains two cabinets responsible for producing the cancellation at the rear of the array. These cabinets are placed one meter away from the first row, because this array has a useful bandwidth of 1.5 octaves; we must therefore define the control frequency through the separation distance between the two rows. To do so, we need to know the maximum frequency to be controlled, which in our case is 85 Hz, whose wavelength (λ) is 4 m. Since the separation between cabinets must be λ/4,
we must keep a separation of one meter between the cabinets.
This gives us a physical delay of one meter between the wave from the first row and the one generated by the second. Since we use 1/4 of the wavelength, the phase difference between the two is 90°. If this delay is increased by a digital delay of the same value, we will achieve maximum acoustic summation at the rear of the array. This time is given by the time it takes sound to travel the space between the two cabinets.
If we know that the speed of sound is given by:
𝑐=𝑓∗λ
and that the f (frequency) of our array is 85 Hz, and that λ (wavelength) is 4 m, we can determine the speed of sound, that is:
𝑐 = 85 ∗ 4 so: 𝑐 = 340𝑚/𝑠
Another way to determine this value is to use the propagation speed equation:
𝑐 = 331.4 + 0.6𝑇
where T refers to the temperature of the medium.
Once we know this figure, we can go on to calculate the delay we need to apply to our cabinets. So, how long does it take to travel one meter?
This is why a 2.94 ms delay is applied to the subwoofers in the second row. As a result, the wave from the first loudspeaker and the wave from the second loudspeaker arrive in acoustic summation, producing total acoustic summation at the center of the stage and cancellation at the front, where the audience is.
As can be seen in the prediction, this effect is completely undesirable, since the audience does not perceive low frequencies and the stage would be completely immersed in them. To solve this, a phase inversion is applied to the two rear loudspeakers, thereby swapping the locations of summation and cancellation.
B. As rings
Once we have understood the configuration as a set, it is simpler to understand the configuration by rings. In the previous section we explained how each group works individually, but once we place a succession of them along the circumference, we see that they also interact with each other; that is, all the groups work together to create a main system. This main system can be understood as two subsystems: the outer ring, which houses the three-loudspeaker groups of the first rows, and the inner ring, where the second row of each group is located. This is a very important point, since it explains how the entire array can be controlled with only two DSP processing channels.
B.a. Outer ring
This is the ring closest to the audience. It is located 8 m from the center of the stage because, using a frequency of 85 Hz, whose wavelength is 4 m, the distance between the farthest-apart loudspeakers is 16 m, that is, four times the wavelength of that frequency.
As can be seen in the images, if only the outer ring existed, several rings would appear on the stage as a result of acoustic summations and cancellations.
If we look at the prediction, we can see how, for each grid cell (2 m), there is one total summation and one total cancellation.
B.b. Inner ring
This is the ring closest to the stage. It is located one meter behind the outer ring, it is made up of two-loudspeaker groups, and it is responsible for creating the cardioid itself. To build this array, these loudspeakers have a physical delay provided by the separation between the two circumferences and a digital delay which, as explained earlier, has a value of 2.94 ms. In order to achieve acoustic summation in the audience area and cancellation at the rear (the stage), a phase inversion must be applied.
Having explained the array as a set and as a ring, it becomes much easier to understand how it works, and this will also help us understand the use of trigonometry to build it.
Mathematical placement calculations (formulas)
Having explained what the array consists of, it is important to mention and explain how we can arrive at this placement. In other words, the mathematical formulas that lead us to the position coordinates of each group. So as not to go on too long, we will explain how to find the position of the central cabinet of the outer ring, since the two remaining cabinets are placed one on each side of it. We will also explain how to find the central position of the two loudspeakers of the inner ring, since once that point is known, all that is needed is to place one loudspeaker on each side of the line formed by that point and the center of the ring.
It is important that we explain the terms we are going to use in this section. We decided to write this introduction mainly to set the scene and to be able to 
better understand the upcoming explanations lobes between the two sources. First of all, in the attached image we can see a circumference that simulates one of the rings of our array. Points A and B represent the position of the groups, and the line segment AB represents the shortest distance between A and B.
As we explained earlier, the maximum distance by which two sound sources can be separated is 270° or 3/4 of the wavelength. This is because with greater separation, cancellation alleys would appear and would begin to generate
As we explained in previous sections, we have used a frequency of 85 Hz, whose wavelength would be 4 meters, so the distance between one group and the next should be at most 3/4 of 4 meters, which is the same as 3 meters.
Therefore, the maximum distance between point A and point B must be 3 meters, represented by the line segment AB. It is important to mention that if we wanted control over higher frequencies, we would have to reduce this distance. Knowing this value of 3 meters, we can determine the maximum angle of separation between groups as a function of the radius. This calculation is done using the trigonometric chord equation, given by the following formula:
𝑐 = 2 ∗ 𝑅 ∗ sin α/2
c = distance A ----> B
R = radius of the circumference (the ring we want to calculate)
α = angle between groups
Knowing that C equals 3 meters and that the radius (R) is 8 meters, we find that the angle formed between group A and group B is 22.5º. This is the formula that lets us determine the angle at which we must orient the cabinets in our array or, depending on the unknown, lets us determine the maximum control frequency of the array.
To better explain this section, we are going to carry out the calculations needed to position the first group. To calculate the placement of the subwoofers, we must turn to the fundamental formulas of trigonometry and rely on an XY Cartesian plane, which will give us the coordinates needed to position the array more easily.
In the images accompanying this heading, I considered it appropriate to include group 0 as a visual aid.
1st: knowing the radius of the outer circumference, we calculate the X-axis position of the central loudspeaker. To do so, we will use the cosine formula.
cos α = adjacent side / hypotenuse
If α equals the 22.5º we obtained earlier with the chord formula:
cos 22.5 = 0.9238
So for a circumference with a radius of 1 m, the cosine would have a value of 0.9238 m. To make the value match that of our circumference, all we need to do is use the initial equation and substitute the data:
cos α = adjacent side / hypotenuse
we substitute the values of the angle and the radius of the circumference:
cos 22.5 = value on X axis / hypotenuse
We substitute the value of the cosine and rearrange the equation as follows:
0.92388 ∗ 8 = 𝑋
We solve the equation for X:
𝑋 = 7.3910 𝑚
Having found the value on the x-axis (abscissa), we move on to the y-axis (ordinate).
2nd: knowing the radius of the outer circumference, we calculate the Y-axis position of the central loudspeaker. To do so, we will use the sine formula.
sin α = opposite side / hypotenuse
This value gives us the information needed to place our central cabinet on the radius of the circumference. First, knowing that α has an angle of 22.5°, we calculate the sine:
sin 22.5 = 0.3826
So for a circumference with a radius of 1 m, the sine would have a value of 0.3826 m. To make the value match that of our circumference, all we need to do is use the initial equation and substitute the data:
sin α = opposite side / hypotenuse
we substitute the values of the angle and the radius of the circumference:
sin 22.5 = value on the Y axis / 8
We substitute the value of the sine and rearrange the equation as follows:
0.38268 ∗ 8 = 𝑌
We solve the equation for Y:
𝑌 = 3.0615 𝑚
We now know the coordinates of our central loudspeaker, which determines the placement of the two adjacent loudspeakers.
coordinates = 7.3910, 3.0615
As can be seen in the images, this simple calculation makes placing the rings enormously easier. Once we know the splay angle between groups, we only need to repeat the previous trigonometric calculation while varying the angle α, which in each step is the previous one plus 22.5°.
To place the inner ring, we carry out the same calculations as in the previous process. That is, we find the sine and cosine values for a circumference of radius 1, and once we have obtained that value, we multiply it by the inner radius. It is important to mention that the inner radius equals the outer radius minus one meter. This meter does not change, regardless of the radius, since the separation between rings is determined by the maximum control frequency.
𝑟=𝑅−1
r = inner radius
R = outer radius
1 = distance set by the cardioid
so, to find the coordinates, we repeat the calculations but with the smaller radius:
cos α = adjacent side / 𝑟
sin α = opposite side / 𝑟
once the calculations are done, we get:
𝑋 = 0.92388 ∗ 7 𝑌 = 0.38268 ∗ 7
which is the same as:
coordinates = (6.46716, 2.67876)
Having obtained this value, it should be made clear that the reference point we use is the center of the subwoofer. That is, all measurements are taken to the loudspeaker's central axis. It is important to always use the same reference point, because if we took the front for one ring and the center for the other, the separation distance would be different and the cardioid would not form correctly. In this second ring, the point obtained lies right on the straight line separating the two subwoofers, level with their centers.
In fact, the coordinates give us a specific point located right under the cross that represents the center of the rear loudspeaker of group 1.
To place two loudspeakers, that loudspeaker must be shifted by half its width so that the ring's second subwoofer can be placed next to it, which allows us to achieve maximum cancellation at the rear.
5.3 Radius
This section is intended to explain, and help readers better understand, the influence of the circumference's radius on our array. As we have explained repeatedly, we used a radius of 8 meters because it equals twice the wavelength of our maximum control frequency. Now, what would happen if we decided to change our radius? In fact, as long as the 270° rule was maintained, we would not notice any difference. This means that if we double the radius, we must double the number of groups so that they are not separated by more than 3 meters along the chords formed between groups.
Therefore, using the formula for the length of a circumference, we can obtain the length of our ring:
𝑙 = 2𝜋 ∗ 𝑅
l = length of the circumference
R = radius of the circumference
If we substitute the values:
𝑙 = 2𝜋 ∗ 8
Then
𝑙 = 50.2654
This figure is important for the following reason:
If we know the length of our circumference and find the length of the arc separating our cabinets, we can determine the number of groups needed to build our array. To find the arc length, we will use the following formula:
arc length = (𝛼/360) ∗ (2𝜋𝑟)
we substitute our data:
length = (22.5/360) ∗ (2𝜋 ∗ 8)
Solving our equation gives us the length of the arc formed between groups:
length = 3.141592
mysteriously, the value of the arc length matches the number 𝜋
If we divide the 50.2654 meters of our circumference by the arc length we obtained, we can see that it comes out to exactly 16, which is the number of groups in our array.
Now, if instead of using this radius we decide to change it, we can see that the length of our arc always remains constant. That is, if we use half the radius of the circumference, the number of groups is halved. This is because with a radius of 4 meters, the angle must be doubled to achieve the distance of 3.141592. In other words, to achieve a separation of π along the arc formed by the groups, each sector must be angled at 45 degrees, so we would need half as many groups.
In the opposite case, say we double the radius (simply because doubling makes the calculations easier), we find that for a radius of 16 meters we would need an angle of 11.25 degrees between sectors, and the number of them would be:
so:
𝑙 = 2𝜋 ∗ 𝑅
𝑙 = 2𝜋 ∗ 16 = 100.53096 𝑚
then
length = (11.5 /360)∗ (2𝜋 ∗ 16)
length = 3.141592
(100.53096 / 3.141592) = 32 groups
Once again the constant π has appeared in the length of the arc formed between groups, so the maximum arc separation between cabinets is π meters.
From this we understand that:
no. of groups = (2𝜋 ∗ 𝑅 ) / [𝛼 ∗ (2𝜋 ∗ 𝑅)] / 360
This equation relates the number of groups we need to the distance between them along the entire circumference, which makes the calculations easier, since we know the exact number needed to cover the whole surface.
Cancellation alleys
One of the main features is the coverage of this array, and it is true that we have only mentioned the 85 Hz frequency. Not because it only works at that frequency, but because it is the highest frequency before cancellation alleys appear.
Like any array, it has a useful frequency bandwidth, and in this case it extends up to 85 Hz, the frequency we have chosen as the cutoff frequency.
Now, what happens if we reproduce higher frequencies?
As we raise the frequency, we can see how the array becomes more directional and the lobe of each group begins to narrow. For example, at a frequency of 91 Hz, subtractions begin to appear in the audience area; that is, the separation exceeds 270°, and this is why acoustic subtractions appear. The interesting thing is that no matter how much we raise the frequency, the stage will not be flooded with sound.
As can be seen in the images, new cancellation alleys are generated as the frequency rises. This is the reason for using 85 Hz as the cutoff frequency, since it is more than enough for low-frequency loudspeakers. If this frequency had to be raised, all the previous calculations would need to be redone with a different frequency, which would result in an increase in the number of groups or a decrease in the radius with the same existing groups.
DSP channels
As we anticipated in the introduction and throughout our project, only two DSP channels are needed. Such a low number of channels is possible thanks to the use of rings. One way to understand this process is as follows:
If our processor has two channels (channel A and channel B), we will assign one of them to each ring. This way, channel A would control the outer ring and channel B the inner ring, so that:
Outer ring ---> channel A -----> no processing
Inner ring ---> channel B ---> 2.94 ms delay + phase inversion
If the array needed to be delayed to align it with the PA, an additional equal delay would be added to both channels.
Stage area
Within the stage, it is important to mention a disturbance generated at its center. This is because at that point all the cardioids arrive in phase. As a result, even though there is a very large decrease in energy due to the distance and the use of groups, a considerable SPL summation is still generated. Even so, we would be talking about a summation within the usual margins of any stage, so it does not create any significant problem.
It is important to mention that, depending on the frequency, it ranges between 1.5 m and 50 cm in radius and can be considered insignificant, although it is good to know it exists. As can be seen in the image, there are two rings inside that vary with frequency but never reach 75 dB, so they are not a problem. In addition, these rings change size depending on the frequency. Even at their maximum sound pressure, they do not cause any problems in a sound reinforcement setup.
The center, however, does reach a higher SPL, but it would be located under the stage, or, if it did pose a problem (something very unlikely with today's miking methods), it would be as simple as avoiding it or using it to route the cabling needed on the stage.
Phase measurements
This section is devoted to the phase measurements of our ring. Since we were not able to build it, we simulated it with MAPP XT. The phase graphs would be as follows:
Human resources
As with any other large-scale event, a large team of people is needed to carry it out. This is where we will list the people in charge of building the ring, as well as all staff involved with the array. Since event timeframes are generally tight, the sound engineer in charge of system tuning should plan the placement of the cabinets in advance.
We could say that the staffing chain begins at the transport stage, so we will need loading and unloading staff as well as a person qualified to transport the equipment. At the event venue, the loading and unloading team will be needed again, along with someone in charge of giving orders and supervising the operation.
Once the equipment has been unloaded, a sound technician or sound engineer who knows the cabinet layout must be present to position them, with the help of a tool that allows the subwoofers to be moved correctly.
Once the two rings are in place, a qualified team or person will again be needed to connect and configure the equipment. Once all the sound equipment has been set up, a system technician will be needed to properly align the ring with the main PA. When the show is over, a loading and unloading team will be needed again, as well as someone in charge of moving the equipment.
Loading and unloading team® 4 people
Driver: 1 or 2 people
Rigging technician: 1 person
Senior sound technician or sound engineer: 1 person
Technician who will do the sound mixing: 1 person
Material resources
Material resources cover a very wide range of things that may be necessary for the success of one event and yet may not be needed at another. The items that are vitally important are:
Subwoofers, the number of which will depend on: no. = (2𝜋 ∗ 𝑅 ) / [𝛼 ∗ (2𝜋 ∗ 𝑅)] / 360
Cables to connect all the equipment, plus spares in case something fails.
2 DSP processors
Power amplifiers to drive the loudspeakers if they are passive.
* These would be the minimum materials needed to carry it out. In addition, equipment for moving the gear might be needed.
* It is not possible to talk about money, since it depends on the number of subwoofers as well as the brand, model and power.
Working methodology
To explain the working methodology for building our array more conveniently, we will describe in detail each of the steps needed to successfully achieve our configuration, starting with the simulations and going all the way to the event itself.
Simulation
First, a plan of the venue must be drawn up. As we explained earlier, it is advisable to know the venue where the event will take place, as well as the stage data (radius, height...). It is also worth finding out whether there are nearby elements that could interfere with the sound, such as a glass facade, or whether the venue is an arena with metal surfaces. Once we have gathered as much information as possible, we proceed to design and simulate the event and the array in prediction software (possibly chosen by the production company or depending on the equipment used). This phase is important because it will give us an initial idea and show us the possible problems we will encounter at the venue, allowing us to anticipate and solve them from the initial phase.
Another important factor to mention is time: it takes a long time to move loudspeaker cabinets, whereas in a simulation the change is instantaneous. It is also worth noting that in this phase there is much more time to resolve any conflict, since during the event and its setup everything is timed down to the last detail.
Once the simulation is finished and the reliability of the array for the event has been verified, we move on to the second phase.
Production
The second phase corresponds to the production work, which is responsible for obtaining the various sound equipment and managing its transport.
This phase is really what is commonly known as paperwork, and it is where prices and budgets are decided. Possible conflicts such as schedules and work teams are also addressed, and possible solutions are proposed for problems that may have arisen in the first phase of the work. It does not really affect the tuning itself, but it is worth keeping in mind because, if any item were later missing, this section could be reviewed to find the source of the problem.
Transport
This is where the event itself begins to take shape. Once the data is known and the budgets have been agreed, the setup process begins. It may take place several days before the event, but it is vitally important that everyone knows their task and that they do not get in each other's way. The chain begins with the loading and unloading teams, qualified staff responsible for moving the equipment to the truck and positioning it inside. It is important that the gear is not damaged, because if any system fails, the entire array could be ruined. Once it has been loaded onto the truck or other means of transport, it is taken to the event venue, where another loading and unloading team, or the same one, will unload the equipment from the truck.
Building the ring
In this phase the rings begin to take shape. It is advisable for the stage to be fully positioned and assembled, because this reduces the possibility of conflict between work teams and minimizes the risk to the equipment.
A sound technician or engineer who understands the essence of the double ring must be present, because they will be in charge of positioning the cabinets. Everything needed to position the cabinets is defined in the previous sections. It is advisable to use some tool that allows the subwoofers to be moved comfortably and effortlessly.
Once the groups are in place, it is important not to mix up the circuits of the outer ring and the inner ring, because the entire array could be ruined. For that reason, it is recommended to cable one of the rings first and then the second. If power amplifiers are used because self-powered units could not be used, it is recommended that each group have its amplifiers close by, so that if a failure occurs during the event they can be accessed quickly and it can be identified which loudspeaker they correspond to. None of this process is mandatory, although it is advisable simply because it makes things easier in the event of a possible failure. It is also advisable to place the DSPs near the front-of-house position, because depending on the ambient temperature it may be necessary to readjust a general delay in order to align the double ring with the main PA.
Configuration
Once the ring has been built and connected, it is time to proceed with the DSP settings. As you may recall, we said that the outer ring has no delay, while the inner ring has a 2.94 ms delay and a 180° phase inversion. These settings must be entered into the processor, and if it is possible to protect it with a password, that should be done. The reason is that if the phase were inverted by mistake or returned to its original state, the acoustic summation would occur in the stage area instead of the audience, creating a very unpleasant situation for both the musicians and the staff. Once this adjustment has been made and the ring is formed, it is aligned with the main PA system. Another recommendation is to use crowd barriers, or "anti-panic" barriers as they are known, because, as at any other concert, the presence of the subwoofers could make it easier for people to climb onto the stage.
The event
Throughout the event, it is advisable to measure humidity and temperature. This will help us keep all the existing parameters in our processors under control. During the event, it would be advisable to have two qualified people, one at front of house and another on stage, so they can communicate if any failure occurs.
Teardown
This would be the last phase of our event. It involves dismantling the equipment and loading it back onto the truck. It is important to check that all the previously inventoried equipment is returned to where it came from, in the best possible condition.
All the cabling is coiled up properly, and any faulty cable should be marked for future repair.
Results and conclusions
This project aims to inform about and introduce a new way of staging shows: the typical flat front facing the audience is no longer necessary. It is now possible to have an entire stage surrounded by people and to provide coverage to all of them in the same way.
I consider this project a success, since all the proposed sections have been covered, and it has been possible to verify, both theoretically and in practice, how all the groups work independently and together. It is true that a large amount of resources is needed to carry it out, but it can be one hundred percent reliable and could be put into practice without any drawbacks.
In conclusion, I can say that it has once again been shown that system tuning is not dead; rather, it keeps evolving and is more alive and present than ever, and there are many configurations still to be discovered that may be viable depending on the needs of the moment. Because, as one might well think, a large number of loudspeakers is required, but that does not stop it from being perfectly feasible.
Among the observations made throughout our project, we again emphasize the disturbance generated on the stage, which, as we have already mentioned, does not cause problems, but it is worth knowing it exists because that specific area could be used to "pass" cabling between the stage and the area beneath it.
Regarding the project, one possibility for reducing the number of groups is worth highlighting. It lies in using subwoofers with their own cardioid configuration; that is, there are loudspeaker cabinets made up of two or more drivers that radiate in a cardioid pattern. If a single cabinet could achieve the coverage radiated by a group, a single cabinet could be used instead of the five elements used so far. As can be seen, the number of parameters, cabinets and configurations that can be used is infinite, and each of them is ideal for a particular venue or event.
Appendix
To make this project easier to understand, we have decided to create a short glossary of terms we have used that may be worth clarifying.
- Loudspeaker, loudspeaker cabinet, subwoofer: all refer to the same thing.
- Ring: each of the concentric circumferences along which the loudspeaker cabinets are placed.
- Array: a configuration of loudspeakers with digital and spatial delays that allow us to control sound propagation.
- Cardioid: a subwoofer array that cancels the energy radiated toward the rear and increases radiation toward the front.
- Delay: the time offset of a signal with respect to another signal or to itself.
- DSP: (Digital Signal Processor) processors that allow us to modify the parameters of a signal; in this array, only phase inversion and delay are used.
- End Fired: a set of four cabinets placed one behind the other, each with its own delay, in order to achieve directivity in sound propagation.
- Cutoff frequency: the frequency identified by the transition between a passband and an adjacent stopband of a system or transducer.
- Gradient: a two-element array that adds polarity to its configuration.
- Lobe: an acoustic summation that appears between cancellation alleys.
- Octave: in communications, the interval between two frequencies in a 2:1 ratio.
- Cancellation alley: a place in space where the interaction between loudspeakers produces a negative sum, that is, a place located between two lobes.
- Sound pressure: the variation in pressure produced by a sound relative to the atmospheric pressure at that point in the absence of any disturbance.
- Bass boost: the accentuation of the lowest frequencies in the amplitude-frequency response of a system or transducer.
- Phase delay: the ratio between the total phase change experienced by a sinusoidal signal when transmitted through a system or transducer and the frequency of the signal.
- Signal: a wave, in a communication system, that carries information.
- Simulation: a software-based prediction that shows us how our array will behave
