Beamwidth halves each time the aperture spans twice as many wavelengths.

Evidence

For example, if exactly one wavelength fits across the speaker length, the −6 dB angle will be ±40° a beamwidth of 80°, and for two wavelengths the beamwidth will be 37° and so on, the beamwidth approximately halving for every doubling of frequency. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2937

Categorization

• CANDY: A memorizable rule of thumb: halve the beam every time you double the wavelengths across the source.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2937