Below a horn’s minimum frequency, coverage angle widens with each lower octave.

Evidence

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. In practice, many commercially available directional speakers have to make some form of compromise in the frequency range of the desired directivity. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2507

Categorization

• QUESTION: Is Fθmin the horn mouth’s cutoff, and does this octave-doubling rule explain why small speakers ‘beam’ upward but lose bass directivity?
• XREF: Connects to the book’s earlier directivity/Q-factor material and to any home-studio monitor coverage claims.