Constant directivity horn for 5" woofer

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Is it possible to construct a midband waveguid that can be used from 250Hz to 9KHz? the driver skhould be a 5" cone speaker. Constant directivity horns have been populare for compression drivers for a while, but can something similar be made for a cone driver. Forexample useing an opening angle of 90 degrees.
For impedance matching horns with gain, 3 octave max...
Yeah, no arguments there.

Straight sided horn for directivity purposes only: Far as I
know, a cone is a cone is a cone no matter the size, why
should a three octave rule limit this application?

You need to narrow speaker down to a slot no more than
1/2 wavewidth at 9Khz, and preferably 1/4 wave or less.
Getting the whole cone to arrive at such a slot on phase
will be an issue.

If you treat majority cone as a ring radiator and ignore the
smaller surface area at the center as an acceptable loss,
you can copy JBL slot tweeter... Also look Selenium ST324
for inspiration how such a slot transition might be shaped.

After slot, its straight sided pyramid cone, no rocket science.

I really doubt you gonna get to 9K without a rough response,
but maybe half that isn't asking too much... You will need to
eliminate as much resonant cavity as possible, but this also
risks cone hitting the plug at lower end of the spectrum.


On re-read, seems I havn't been clear when cone means
a 5" speaker cone, and when cone means a straight sided
conical horn.... Sorry I didn't think ahead to use a different
word for each. And far too lazy to fix my mistakes...
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Thanks for all the inputs. I guess I should also mention that gaining sensitivity or sound pressure level is not needed. I just need the waveguid funktion to control dispersion.
Do you really belive a phaseplug is needed, wouldnt it be enough to kind of extend the cone shape, so the cone in it self is the first part of the waveguid side.
A little bit like when a dome tweeter is loaded with a flat horn/waveguid, then there is no phaseplug used.
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