Cardioid vs. Di-pole

Had a bit of free time today so started paying with some woofers in a box with a bit of DSP. Aim was to trying to create a cardioid response.

Got me wondering; which has more total sound power output for a given on-axis level, cardioid or di-pole?

I always thought cardioid bass systems made more sense than di-pole in an ideal world because it would closer match the midrange / tweeter polar pattern on a baffle. However today I realised if you have a box with woofers in the front and back some distance apart, say 30cm, the rear woofer needs attenuating more the closer you go to the speaker box due to proximity gain - you (or the mic) is closer to the rear woofer. Conversely, as you go further away from the box the front and back drivers need to be more equal in level.

Di-pole however always has near ideal cancellation on the side axis' because the distance to each woofer is equal regardless of distance.

Kii do a cardioid polar pattern by having the 'cardioid' woofers on each side of the cabinet rather than the back and I now realise that is to get them as close as possible to the front woofer enabling a polar pattern in tighter proximity to the speaker box.

Now I'm thinking mm.. do I add an extra woofer and put them on the sides to go cardioid or go di-pole. Which arrangement actually outputs more sound in to a room for a given on-axis SPL? That is the question that will determine which arrangement has the tightest highest quality bass, I think.

20220203_171957.jpg




20220203_172000.jpg


FYI if I had the mic about 30cm from the rear woofer, that rear woofer needed about -14dB attenuation to get cancellation working.
Yellow - front woofer only.

Cardioid in Garden 1.png


When I put the mic at 1.5m distance the rear woofer only needed -2dB attenuation to achieve cancellation.

Cardioid in Garden 1 1500mm distance.png


(Note did this in my garden. Wind, distant car noise etc probably messing up <30hz results).