Hi budney -
I think you may be confusing the roll-off frequency of the acoustic low-pass filter, with the cut-off frequency of the horn. They are not one in the same. A typical roll-off frequency would be approximately 3 to 3 1/2 octaves above the horn cut-off frequency.
A low-pass filter is just that. The driver, chamber, and throat parameters dictate at which frequency where no higher frequencies will pass through the horn. Essentially, an acoustic 1st order cross over. It is at the roll-off frequency when the cone front will be acoustically in phase with the bass horn as long as the total length of the horn, not including the chamber, is multiples of half wavelengths of the roll-off frequency. Instead of the typical -3dB drop in amplitude that is found with a passive crossover network, think of the cone and horn acting in tandem, behaving as a single diaphragm. Otherwise called mutual coupling.
As for the discontinuity, allow me to quote Leo Beranek from his book, 'Acoustics' page 141 Part XIII under Acoustic Elements;
"An exponential connector....acts as a simple discontinuity when its length is short compared to a wavelength, and as a transformer for acoustic impedances when its length is greater than half a wavelength". In this section he describes an exponential connector as a transition between two pipes of different areas. A horn is in fact, an acoustical transformer. A transformer that serves to transition the very high impedance at the horn throat, to a lower impedance at the horn mouth. The ideal condition being a transition to the impedance of air which is 407 Acoustic ohms. Easy enough to accomplish for high frequency horns, but not so for low frequency horns. In order for a 30 cycle horn in free air, or 4 x Pi for example, to achieve an acoustic impedance of 407 ohms at the mouth, would be so immense it would be cost prohibitive to build it. All commercial bass horns are a compromise. Mutually coupling an array of small bass horns is a more practical approach to reach and impedance of 407 ohms.
This is why horn loaded speakers are more efficient than direct radiator speakers. The acoustic impedance of a cone is considerably greater than the acoustic impedance of air.
As per my previous example, a 22.5" long bass horn lacks the length and mouth area to allow support of very low frequencies. Ergo, a short horn would behave more like a horn loaded port, than a horn.
Regards,
H.F.