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How far apart can I space my subwoofers?

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We all know that pushing your subwoofers together gives you more SPL and less power alley. But what if you want to pull them apart to make the line longer for more narrow coverage?

Imagine a long, narrow room. You’ve got 4 subs. Each of those subs is 3.8 feet wide, giving you a line of 15.2 ft total. That’s going to give you directional control down to 74 Hz. Not bad. But what if you are crossing over at 80 Hz? You need more control.

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Prediction @ 30 Hz

In that case, you could push the subs apart 8 feet, giving you 24 extra feet of line length, for a total of 39.2 feet. That gives you directional control down to 30 Hz without breaking the pattern. Woot!

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Prediction @ 30 Hz with 8 ft spacing

How did I figure that out?

You will always have some amount of subtraction when two frequencies meet at equal level between 120º and 240º of phase offset. What you need to do is make sure that your speakers are within 2/3 wavelength of the highest frequency at which they could combine.

In our case, we are crossing over at 80 Hz, but to be safe I used 90 Hz for the calculation since the Sub and Main won’t be level isolated right at 80 Hz. Then I found the wavelength of 90 Hz, which is 12.5 feet. After that, all I needed was 2/3 of that, for 8.3 feet, which I rounded down to 8 feet.

Those steps again:

  1. F = the critical operational range of your subs
  2. max distance from center to center = (speed of sound / F) * (2/3)

Warning: the pattern will narrow as frequency rises. The tradeoff of pattern control down to 30 Hz is that you may now be too narrow at 80 Hz. The solution? Create a physical or delayed arc.

Further questions?

Click here to download my new eBook, 105 Questions about Sound System Tuning, free until Nov20th. It’s everything you wanted to know about live sound system setup, but were afraid to ask.

Dave Rat’s End-Fire Adjustable Arc Subwoofer Array Explained

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During my interview with Dave he explained a subwoofer array that he developed during a Blink182 tour. Here’s what it looks like.

Here’s where Dave explains it in the interview, starting at 45 minutes.

This came out of the sub testing that I did, primarily on the Blink 182 tour and then finished or got farther on the SoundGarden tour. I tried multiple arrays and out of it I came up with this fanned array.

The way to make it is, find your zero point, your rear sub location, the center of the grille. I would just have someone step on a tape measure there or put a road case on it. Then walk out 6.25ft for a 45Hz maximum rear cancellation. Then I draw an arc with the string.

Then you would place along that arc the front radiating points. One, two, three, however many you want. The 0ms point is your rear sub. Set your front ones at +6.25ft, which is about 5.8ms.

I see, so if you soloed up any of those front subs, they should be arriving at the same time as the rear subs.

Yeah, so the concept is the sound radiates from [the rear sub] and travels 6.25ft to sum with the subs in the front.

The closer these are together the beamier it gets. As you spread them out on the arc, the wider it covers.

[You have to put a sub stack in the back equal to the ones in the front. Each stack has three.] It’s making sound that will actually cancel out everywhere else and sum in the front.

The theory

Dave’s design is a combination of end-fire and physical arc. The end-fire takes care of the cancellation in the rear and the arc controls the coverage width.

End-fire array: an array of multiple subwoofers, placed in a line, one behind the other, with a specific spacing and delay strategy in a timed sequence that creates forward addition and rearward subtraction.

Bob McCarthy, Sound Systems: Design and Optimization

The array achieves summation in the front by delaying the front elements to the rear, causing everyone to arrive at the same time. It achieves cancellation in the rear through delay as well (output processing + distance offset), except in the rear everyone is arriving late causing a chaos of phase relationships.

Physical arced arrays exhibit a coverage angle equal to the segment of the arc segment of virtual circle whose origin lies behind the array.

Merlijn van Veen

A physical arced array turns a line source into a point source. Where all elements were arriving at equal level and time on-axis, they are now steered outward with a virtual origin from behind the array. As arc angle increases so does coverage width as the various spatial crossovers move away from on-axis.

The design

How did Dave come up with the 6.25ft spacing?

spacing = ¼λ

spacing = speed of sound / frequency * 0.25

6.2778 = 1130 / 45 * 0.25

Dave’s design breaks some rules, which is fun. Normally we avoid a two-element end-fire array because it is limited to a single cancellation in the rear and then comes back with a nasty peak an octave up.

It is for this reason that if you design this array in Merlijn van Veen’s Subwoofer Array Designer, it will recommend high and low-pass filters at 29 and 60Hz, respectively.

With preferred filters.

The model

Wide coverage

I haven’t tried this in the field, yet, but we can look at some models in MAPP XT.

I’ll start with the widest spacing to get the widest coverage.

Here’s a prediction at 44.2Hz showing an opening angle of 176º.

In the measurement viewer we have a nice F2B ratio of 50dB at 50Hz.

But why 50Hz? I expected to see it at 45Hz.

It turns out that I spread the subs out so far that the distance offset changed from 6.28ft to 3.77ft from the rear. This changed the combined phase of the front subs to 150º apart at 45Hz and 180º apart at 50Hz, compared to the rear sub.

I reset the placement and delay based on the outside subs instead of the center one and was able to shift the null down to 47Hz. Hurray!

Narrow coverage

Now let’s try the narrow coverage version.

Here’s the prediction at 44Hz. Looks like it’s 10º more narrow than the previous design.

Nice F2B rejection of 31dB at 44Hz.

An alternative?

Dave breaks some rules here, which is fun.

Never end-fire with just two elements. It’s a one-note-wonder on the back side. Use the gradient in-line instead (same physical, different settings).

Bob McCarthy

This make me wonder what an in-line gradient array would look like with the same design.

Gradient array: A cardioid configuration commonly used for subwoofer arrays with front and rear elements. The rear element is delayed and polarity reversed to effectively cancel behind the speakers.

Bob McCarthy

The gradient array has frequency dependent coupling in the front in exchange for broadband cancellation in the rear.

You can use the exact same speaker placement, with different output processing.

It looks very similar to the end-fire at 44Hz, but is quite different across its operating range.

Where we had a limited range of cancellation with the end-fire array, we now have broad-band cancellation with the gradient. You may be worried about the dip at 100Hz, but notice that that the expected response is already 20dB down, moving it into isolation if you are running a linear system.

What’s it for?

As we discussed on the podcast, Dave was looking for a way reduce LF interaction in the center of the audience and total LF energy behind the arrays.

Compare a traditional setup of left and right sub stacks…

To two of Dave’s end-fire arcs splayed 90º apart.

If you would like to play with these MAPP designs, you can download them here. Please let me know if you discover any improvements. 🙂

Have you tried something like this in the field. What were your results?

How to Estimate Delay and Level Offset Between Speakers in Your 3D Models

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Save time in the field by presetting your speaker output delay and level offsets.

Here’s a model from a recent show where I estimated the level and delay for a pair of relay speakers and line of front-fils.

If you know the difference in distance between two sources, you can accurately estimate their time offset, and therefore, the delay necessary to bring them into alignment. The challenge is finding the correct crossover point.

Drawing About Sound

Crossover (spatial): An acoustic crossover in a spatial domain, i.e. the location where elements combine at equal level.

Bob McCarthy, Sound Systems: Design and Optimization

Finding a spatial acoustic crossover point in the field is pretty simple. Once you have defined the on-axis (ONAX) point for source A and source B, match their levels, then walk in a line between the two points until they sound equal. Place our measurement microphone at this point, then use the audio analyzer for verification.

You can simulate the process in a modeling and prediction software like MAPP XT, but I have been practicing a quick offline method of drawing speaker coverage shapes and estimating their crossover points that you can do on a plane (or even with pencil and paper in 2D).

Here’s a recent show that I worked on using JBL VRX 932 speakers on stands. The distance from the speaker to the end of coverage is 61.66ft. I can divide this distance by the forward aspect ratio of this 100º speaker to find the coverage width.

61.66ft / 1.31 = 47.1ft

For more on forward aspect ratio, please read One Simple Tool to Find the Right Size Speaker for Any Space. These topics are also covered in detail inside of Pro Audio Workshop: Seeing Sound.

This gives me a quick sketch of the coverage shape.

For comparison, here’s a similar speaker’s prediction at 4kHz.

The Steps

Here’s how you would do this in the field with the audio analyzer:

  1. Match solo ONAX levels B1 to A1.
  2. Find XAB (the acoustic crossover between A and B) between ONAXA and ONAXB where A1 and B1 match in level .
  3. Set delay.

Now let’s do those steps in our model with distance measurements.

Set Level

B1 level = 20 * Log10((distance from ONAXB to B) / (distance from ONAXA to A))

In our model that would be -2.4dB.

20 * Log(22.59 / 29.78)

You can drop that formula into google to verify it.

Find XOVR.

Find XAB at the center of their coverage pattern overlap.

Set Delay

B1 delay = (distance to A1 – distance to B1) * 0.9

In our example model that would be 24.17ms.

(48.01 - 21.16) * 0.9

Field results

Once we got into the room the coverage shape of B1 changed due to an obstruction. This changed the level offset, but the delay was very close to my estimate.

Much of the front-fill processing changed because we replaced two of the 928 speakers with 932 models and were able to level set and delay them independently.

Will this work for subs?

Yes for delay. If you have followed Merlijn van Veen’s Relative/Absolute Method, then you already have a preset for the relative relationship of the spectral crossover alignment of your main and sub. Use your 3D model for the absolute step.

No for level. Low-frequency energy will enjoy room gain and I’m less confident that a distance measurement will help you estimate the level. If you try it, let me know.

Have you tried presetting your DSP using distance measurements from a model? How did it go?

Console Prep: Simplicity is Key (FREE lesson from Guerrilla Mixing on Digital Consoles)

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Learn more about Guerrilla Mixing on Digital Consoles.

Quick notes:

  • Start with system output setup, so you can later focus on input
  • Only setup inputs that you need + 1 (minimal with spare lead vocal)
  • Use shortest signal path from input to output (if building from scratch) – get the signal to the listener
  • Make sure you have all the channels you need (consider recording, intro, playback, communication, pink noise, DCA setup, etc)
  • 1:1 patch is usually simplest and most logical (avoid complexity!)
  • Convenient patch is sometimes dictated by the console (only even and odd channels can be linked for stereo, fader bank layout)
  • Have DCAs ready for controlling more channels

Should audience depth influence crossover frequency between main and sub?

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Hypothesis: By choosing a lower crossover frequency I can expand the coupling zone between main and sub.

Conclusion: While lowering the crossover frequency does expand the coupling zone between main and sub and this fact may influence the system design, its advantages are secondary to the efficient functionality and cooperation of both drivers.

Coupling zone: The summation zone where the combination of signals is additive only. Phase offset must be <120º to prevent subtraction.

Bob McCarthy, Sound Systems: Design and Optimization

While working on a recent article about crossover slopes I started thinking about main+sub alignment and its expiration. If we know that ⅔ of the phase wheel gives us summation and ⅓ of it gives us cancellation and we know the point in space where the two sources are aligned, then we should be able to predict the expiration date of the alignment, compare it to the audience plane, and consider whether lowering the area of interaction will benefit coverage.

If two sources are aligned at 100Hz and the wavelength of 100Hz is 11.3ft, then a 3.8ft distance offset will create a ⅓ λ (wavelength) phase shift (120º). If we have two sources at opposite ends of a room and they are aligned in the center, then we have a 7.6ft coupling zone. From one edge of the coupling zone to the other is ⅔ λ (240º).

80Hz has a λ of 14.13ft and would give us a coupling zone of 9.4ft, an expansion of 1.8ft.

Lowering the crossover frequency to expand the coupling zone

Here’s a section view of a main+sub alignment where you can clearly see a cancellation at 24ft. The coupling zone is 29ft, which is 65% of the audience plane.

I can lower the crossover frequency and expand the coupling zone by 4ft, which is 71% of the audience plane.

This process can be sped up using Merlijn van Veen’s Sub Align calculator. Here’s the same system design observing the relative level difference at 100Hz.

And here it is at 80Hz. Notice that the checkered pattern indicating the coupling zone has expanded.

Instead of putting every design through every potential crossover frequency, I made a new calculator that shows the percentage of audience within the coupling zone by frequency.

I am now able to quickly compare the potential benefit of selecting one crossover frequency over another by how much the coupling zone will expand or contract. Using the example from above we can see that changing the crossover frequency from 100Hz to 80Hz only provides a 7% improvement. This doesn’t seem significant enough to make a system design decision, but it could be included in other factors in the decision making processes.

Let’s look at another example. In this case the vertical distance offset is reduced and the audience depth is increased.

The calculator reveals that a 120Hz crossover would include 58% of the audience in the coupling zone, but a 75Hz crossover gives us a 13% improvement.

Should I use this calculator to pick my crossover frequency?

No. When it comes to choosing a crossover frequency there are other more important factors to consider like mechanical and electrical limitations. If your design only puts a small portion of the audience in the coupling zone, changing the crossover frequency is not going to save you.

Instead, start by observing the manufacturer’s recommendations, then the native response of each speaker, and the content of the show and its power requirements over frequency.

All that being said, knowing more about the expected performance of a sound system is powerful. I might make design changes based on the calculator’s predictions. I might I do nothing. Either wa,y I walk into the room with fewer surprises during the listening and optimization steps.

If lowering the crossover frequency increases the coupling zone, why not just always make it as low as possible?

I don’t have a great answer for this question. As I mentioned already, there are limitations to how low you can go. One major tradeoff is that your main speaker will need to handle more and more power as the crossover frequency lowers, making it less efficient.

One clear benefit I can see is estimating the viability of an overlap crossover. If you are planning a system with an overlap crossover that goes all the way up to 120Hz and you look at the calculator and see that 120Hz will only be coupling through 50% of the audience, you might decide on a unity crossover to limit the main+sub interaction into those higher frequencies, making it more stable over distance.

What about aligning at 3/4 depth?

Right! I included a phase offset option to test this and it makes a big difference. In the most recent example, if I use a ⅓ λ offset (120º), the portion of the audience in the coupling zone goes up to 88%.