The Low-Down on Subwoofer Placement, Part 1

(For the entire series, check out my system optimzation blog.)

There are two main variations of the “subwoofer question:”

1. Where is the best place to put my subwoofer(s)?
2. How should I time align my subwoofer(s) to the mains?

To answer the first question, we have to understand how subs interact with a room, which is just an extension of understanding how subs interact with each other. These are simple interactions but they’re not quick answers, so this post mostly examines those mechanisms. Due to the length, I’ll be handling the placement options and time alignment bits in Part 2.

The interaction between two sources is only up for discussion when the sources are close in level. If one is much louder, interactive effects are quite minimal. It’s possible to put numbers on this with vector summation math, but for the sake of simplicity let’s just put one pin in the map: at 10 dB level offset, the quieter source can only raise the combined level by 2.4 dB, and can only lower it (via cancellation) by 3.3 dB. It’s when the two sources are matched within a handful of dB that it’s meaningful to discuss their interactions. Remember that the level offset – and the distance offset – between the sources changes as we move around the space. A 10 dB level offset is a distance ratio of 3:1 (without walls to mess things up).

Wherever the multiple sources meet at similar level, the nature of their interaction is determined by the phase relationship between the arrivals. We can think about being in a room with two subwoofers, and let’s ignore the walls for the time being. If we stack the two subs on top of each other, the energy from both will reach us at the same time regardless of where we stand. There’s no time offset, and therefore no phase offset, and we get the full summation effects anywhere in the listening plane. Since they’re on top of each other, there’s no place we can stand that will cause the energy from one sub to reach us so much earlier than the other that we can accrue enough phase offset to break the summation.

The scales tip at a third of a wavelength (physical displacement) or 120° of phase shift (time offset). It’s important to realize that these are two different ways of talking about the same thing. It’s also important to realize that the highest frequencies will run into trouble first. Their shorter wavelengths and quicker cycles mean that they are proportionally more affected by a given physical spacing or time offset.

So let’s put two subs in a field (no walls) and see what happens:

This is pretty representative of a standard L/R sub configuration in a venue with a stage along the left wall. Down the center line of the venue – indicated by the dark red line – the subs are meeting at the same time at the same level and as such create a +6 dB summation over what the level would be with a single sub on. This is called Power Alley because it’s the only place in the venue that it happens for all frequencies. There are other peaks in the summation, visible as additional lobes, but they move with frequency. Right now we’re looking at the 60 Hz response, and we’ll see other frequencies soon.

This summation actually is a plane, not a line. Build a wall on that red line: that’s the true shape of Power Alley. It extends up to the roof and to the back wall (yep, passing through the lead singer and drum set positions as well). Our predictions are 2D but we have to remember that we’re dealing with a 3D phenomenon.

Power Alley is bordered by two narrow, deep cancellations in the response. These are the deepest cancellations in the room because they’re close to center line, which means the relative level offset is very small. Moving further off center means that one sub gains a level advantage, and so the cancellations become less severe.

The deep cancellations occur at locations for which the spacing offset is half a cycle. 60 Hz has a wavelength of about 18.9 feet and a period of about 16.7 ms. Standing anywhere in the deep, dark blue nulls puts you 9.45 feet closer (which is 8.35 ms closer) to one sub (or an odd multiple of that).

As we move off from center line, we come into another region of summation. Now the time / distance offset has reached a full cycle, and so we fall back into summation.

Viewing the same situation at 80 Hz:

Power alley hasn’t moved, but the subsequent peaks and dips in the spatial comb filter have. 80 Hz is about 14 feet long, so now it’s an offset of about 7 feet or 6.25 ms that causes the nulls.

At 30 Hz:

Power alley is much wider, since the longer wavelengths tolerate more spacing offset before they drop into cancellation (19 feet offset, or 16 ms for a half-cycle offset).

Now let’s have some fun. Let’s go back to 60 Hz and invert the polarity on one of the subs:

Notice that the room is not suddenly devoid of LF energy. Compare that to the first prediction in this post: All that happened is that we turned summations into cancellations, and vice versa. Power Alley is now power valley – meeting at equal level, but as exact opposites instead of exact matches. The previous cancellations are now summations, having accrued a half-cycle offset spatially and a half-cycle offset via the polarity inversion. A polarity inversion doesn’t remove acoustic energy from the room, it just distributes it differently.

Now let’s talk about walls. Remember earlier, when I suggested building a wall on the Power Alley line? Let’s actually do it, so we end up with a venue that’s half the width of the original.

Look familiar? Compare this against the original (shading added for emphasis):

So it turns out that we already know everything we need to know about walls, because a reflective wall (generally a safe assumption in the sub range) can be thought of as creating mirrored “virtual” sources on the other side of the wall. A sub 16 feet from a wall will behave just like two subs spaced 32 feet apart. (That’s actually how most prediction software does the math.) A partially absorptive wall is like turning the level down some on the virtual source.

Sorry – that’s only the effects of a single wall. That’s a luxury we don’t usually have, as rooms tend to have at least four, plus a floor and ceiling. Generally floor effects are minimal for ground-stacked subs because the boundary is within a third of a wavelength so we just get a nice SPL boost.

So the bad news first: When you have more than one sub, and they’re more than a few feet apart, you’ll have some comb filtering in the coverage. Even a single sub behaves as others are present once we put it in a room. That’s a fact of life. Sorry.

The good news is that this has never ruined a show. The response varies over the space but also over frequency, and the walls tend to even things out a bit, because there are multiple virtual sources all interacting with the real ones – and with each other. Here’s the first prediction from this post, but with four walls enabled:

The only notable trend here is that it’s louder in the front. This is not scary. Remember that this trippy little pattern is completely different at every frequency, and you can start to see that this is not as big of a problem in practice as people seem to think it is.

But let’s take the displacement mechanism and make it work for us.

Let’s create a long line of subs.

I turned the wall reflections off so it’s easier to see.

Out front, all the arrivals are pretty much in sync, so we see a nice summation. (This is also true behind the array on stage, and also up at the ceiling, so we actually have a donut-shaped coverage. Mmm. Donuts.)

On the sides of the array, we are a different distance from each sub, so we have staggered arrival times, and a bunch of different phase offsets, and the summation breaks down. So increasing the length of a line of sources will narrow the coverage in that dimension. Don’t have enough subs? Space out fewer.

The coverage angle stays the same as long as the line length isn’t changed:

This is a hugely important concept. As long as the individual boxes are spaced close enough to remain coupled (within 1/3 wavelength), the array’s coverage angle is determined by line length only. (As a neat rule of thumb, the coverage angle will be 72° for the frequency whose wavelength equals the line length. That won’t be on the test.)

So in a long narrow room with reflective side walls, a broadside array may be better than L/R. But the real, practical answer is that as long as we’re in a room with walls, your sub coverage will be somewhat inconsistent. This is not nearly as big of a problem as it seems unless your show consists of a single 60 Hz sine wave.

“But wait,” you may say. “We only have two subs! We can’t make a line!” True, you can’t. But all is not lost. In the follow-up, we’ll look at a couple different layout options and how to handle time alignment with the mains.

For more, please visit my system optimization blog: