Raising frequency narrows an array’s main lobe because the visible region expands

Evidence

As the visible region corresponds to the angles between ±90° of the normal direction, the effect of doubling the visible region also implies a narrowing of the main lobe if its shape does not change as the visible region increases, as in our examples. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2885

Categorization

• XREF: This matches the classic array/antenna result that directivity scales with frequency — also why ceiling-microphone arrays and line arrays behave differently across the spectrum.