On 2014-07-01, umashankar manthravadi wrote:
I have a completely untested theory that if the loudspeakers are mounted flush to room boundaries, reflections will not be an issue. a 1st order system might then work with Omni (in this case hemispherical) speaker directivity.
Once you mount anything and everything at all that way, in the far field it will radiate more or less as an Airy disc and/or the second spherical harmonic subtracted from your thingy. The first two spherical harmonics cut onto the plane, in the radiative solutions, in the far fied, pretty much cover that field. The second versus first spherical harmonic of prime order then pretty much reflects back as impedance matching, as far as the acoustic impedance ("acoustical radiation resistance") goes.
As always, Filippo Fazi is the guy who gets his partial differential equations right with this stuff.
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