Horn coverage angle doubles for every octave below the minimum directivity frequency.

Evidence

This is not small! You can have a smaller horn, but you must recognize that it will not have this coverage angle at 500 Hz. The sine of the −6 dB θ point is inversely proportional to the frequency below Fθmin; thus at an octave below Fθmin, θ will be approximately double that desired, and so on, until θ becomes greater than 90°, which implies the speaker is omnidirectional and has no directivity. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2507

Categorization

• DEFINE: Explains Fθmin — the lowest frequency at which a horn preserves its stated coverage angle — and its inverse-frequency behavior.