**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%.

Rafa says

Eso quiere decir que tenemos que implementar filtros fir?

Nathan Lively says

Not necessarily. They just another tool in the toolbox. 🙂

Soddy Wu says

Dear Nathan

Thank you very much for your guidance. I am a loyal reader of Taiwan. Through your technical article, I have improved my understanding of the coverage of bass in the audience area.

In the learning video, I saw the calculation table you made,

Can I ask for a copy with you? I want to further study and understand through the form.

Glad the live performance technology has your wisdom to pay for everyone, thank you

Best regards

Soddy Wu form Taipei ^ _ ^

Nathan Lively says

Hi Soddy! You’re welcome.

Sure – https://my.pcloud.com/publink/show?code=XZVdP9kZYilbWmzAm3m2qlacbrcaSSeDMPck