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If a horn is
too small for the frequency it is operating at (an acoustic
mouth circumference much less than about 1 wl), then placing
it next to an identical unit will normally extend the low
cutoff.
When the area
ratio between the mouth and throat is not large, the low
cutoff of the horn is set by the ¼ wavelength resonance and
in this situation the resonance is roughly set by the length
of the horn path.
While a horn
is not at maximum efficiency until it is ½ wl long or
longer, it can provide usable output (significant gain over
the same driver not horn loaded) down to about the ¼ wl
resonance and at much lower frequencies, only has the output
of a sealed box (the driver, its compliance and back volume).
The quarter
wavelength resonance is the lowest mode a pipe closed at one
end and open at the other resonates at, for a pipe to resonate
at the same frequency with both ends open (½ wave length
resonance) it has to be about twice as long.
In
a horn, as the mouth area becomes larger, some of the air out
in front of the horn is still governed by (highly coupled to)
the pressure gradient at the mouth and so is an acoustic
length added to the horn path length. How much it adds to the
length depends on its shape with round or square (including
the mirror image) being the best and typically adding about .6
to .8 times the horn mouth radius. A large mouth can add
significantly to the path length and can have a significant
effect on the low cutoff.
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