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I am working on a small home audio project which I think contains an interesting and challenging physics/audio engineering problem which I have zero knowledge of how to solve.

The speaker driver is facing downwards, and I want to design a cone which points upwards towards the driver so that the sound is redirected as efficiently as possible in all radial directions. I also would like to minimise the space between the cone of the driver and the base of the "redirection" cone as much as possible.

I suspect that this may be a complex set of calculations and may not be possible, in which case I'll try various designs. But having even a ballpark estimate of the required dimensions and spacings would be extremely useful.

The driver I am using is a Dayton Audio RS100-4. It is being mounted on a panel of radius 100mm.

I realise this question is likely to be marked as too broad and I am happy to add further details as required. Fact of the matter is that I don't know what information is required to tackle the problem and/or aid comprehension.

Thank you.

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Aside from downward facing subwoofers, where there is not really a need for a diffuser, the only "audiophile-ready" loudspeaker that is similar to what you ask is the Citation X by Harman Kardon.

It didn't use a parabolic diffuser attached to the surround, but has this strange shape attached to the speaker cone - part of the profile is rather close to a parabola:

enter image description here

Full article that picture is taken from is on Roger-Russell.com - which also talks about the specific requirements and some of the tech decisions made.

As reflection from a surround based diffuser will depend on the cone you use, the frequencies etc in use, I don't think you can get a perfect design, so you may be best off assuming a paraboloid coin is a reasonable simple fit and avoid the challenge of trying to create a "best" fit. In my experience, even a normal cone will probably do the job sufficiently well.

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