Convex Loudspeaker Arrays

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Recently we were discussing the Keele CBT design*, and the fact that it's directivity control is in one dimension. (That's why the array is curved like that; the curvature dictates the beamwidth of the array. If it was flat it would have a beamwidth of zero degrees.)

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While it's not immediately obvious, the face of the Beolab 90 is convex

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The face of the Beolab 50 is also curved.

So...

I wanted to figure out if this is done for cosmetic reasons, or acoustic reasons? My 'hunch' is that the convex baffle may be there to control the directivity. Let's find out!


* CBT24 line array speakers
 
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In order to simulate how the convex array behaves, I'm using Hornresp as usual.
In this sim, we have three 10cm midranges and they're arranged in a convex cap. (Same as a Beolab 50 or 90.)

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Here's what the wavefronts of the convex cap look like at 500hz. This uses no shading. You can also observe the wavfronts of a CONCAVE cap by looking at the left side of the baffle. (output on the left is from a concave cap, from the right it's a convex cap.)

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Here's what things look like if you add some shading. In this sim, the top and the bottom woofer are attenuated by 3dB, the center is receiving full power. Not a huge difference at 500Hz, the difference may be more apparent at higher frequency...
 
Here's the exact same sim as post #2, but this time at 2000Hz instead of 500Hz. To me, it looks like the shading is more important at high frequency than low. (Because the wavelengths are shorter.)

These sims seem to illustrate a couple of things:

1) a loudspeaker array arranged in a convex cap exhibits the benefits of a curved array. Except it works in two dimensions not one.
2) Shading an array is more important at high frequency than low. This would seem to make an argument for having independent channels of amplification and processing for each element in the array.

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without shading

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with shading. Note the reduction in lobes and the narrower beamwidth
 
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