Should I use end fire or cardioid?

Should I use end fire or cardioid?

Q: Should I use end fire or cardioid?  Cardioid has better rear rejection, but at the expense of SPL and impact. Since we're almost always looking for max impact, we nearly always aim for end fire. Is this accurate?

A: That’s technically accurate, but the difference is both far less and far more in each direction than most people realize. It’s sometimes forgotten that there is SPL loss over distance, even if that distance is short. This is calculated based on the familiar inverse-square law. Most SPL specs and calculations are referenced to a 1 meter distance from the source. One additional meter incurs a 6dB loss relative to the measured output of the nearer source. That doesn’t account for any potential losses due to the obstruction of the waves/reflected energy from the back of the nearer cabinet. You’re not doubling the distance from the audience to the more distant cabinet, but the SPL added by the second cabinet at the reference 1 meter distance is not 6dB. Assuming coherent summation, it’s more like 1dB. And a third cabinet adds even less. If two cabinets are adjacent and effectively equidistant from the audience, they sum for an additional 6dB. 

Thus, 2 adjacent cabinets each producing 100dB @ 1 meter will provide 106dB at 1 meter from both, or 1 meter from the acoustical center of the two. 

If those 2 cabinets are not equidistant from the reference point, such that one is 1 meter from that point and the other is 2 meters from that point, and assuming the signal arrival at the reference point is coherent, the summation is as follows:

Box 1: 100dB @ 1 meter.

Box 2: 100dB @ 1 meter - 6db for the additional meter = 94dB

100db + 94dB (coherent) = ~101dB

If the offset is greater than 1 meter, the losses increase. 

If the SPL that reaches the audience is calculated from the SPL available at 1 meter from the nearest cabinet, there’s little advantage to the end-fire. If you move the cabinets nearer the audience, you can offset these losses. This may be possible in flown arrays, with downward orientation helping, but isn’t a benefit if the array puts the audience at a greater distance. 

The 2-box end-fire is capable of about 1dB more than a single cabinet and provides a limited amount of rearward rejection. 

The 2-box cardioid array (1 forward, 1 backward) would tend to deliver about 1dB less SPL to the audience but it offers far more effective rear energy rejection. (Many reasons for that, but that’s a different discussion.) A 3-box cardiod array would deliver at least 2.xdB more SPL to the audience and provide significantly better rearward rejection than a 3-box end-fire. It would also tend to be easier to deploy and take up a lot less audience space on the ground.

If you'd like to read more see our blog post on the subject:

Is there a point in cardioid for just 2 boxes? (bassboss.com)
One sub in cardioid mode? (bassboss.com)

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