What constant directivity can 3 sources produce?

[wonderfulaudio]

What directivity can 3 sources produce?

Hi,

A single source gives 360 degrees radiation pattern.

Two sources, in a cardioid give radiation in one direction only. The total directivity angle is 180 degrees.

So, adding more sources produce narrow directivity.

If 3 sources are used, how narrow does the directivity get and how should the drivers be positioned/delayed/tracked(and attenuated, if needed), assuming sources are omni on their own?

I would like to simulate.

Thanks and Regards,
WA

 

[wonderfulaudio]

Here is the 180 degrees radiation of a cardioid between 100Hz to 1Khz for reference.