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.