Effective sound diffusion requires bumps sized between an eighth and half a wavelength.

Evidence

As well as absorption, it is essential that the sound be diffused when it strikes a surface. Ideally we want the acoustic equivalent of a matte surface. Unfortunately, most surfaces, including large areas of absorbing material, act like acoustic mirrors, with varying shades of darkness. In order to have a matte surface, one needs a “bumpy wall,” and many things can be used to provide this. Unfortunately, the bumps need to be at least an eighth and preferably a quarter of a wavelength in size to be effective. This results in the requirement for very large objects at low frequencies (1.25–2.5 m at 34 Hz) and very small objects at higher frequencies (1.25–2.5 cm at 3.4 kHz). If the objects are too small, that is, less than one eighth of a wavelength, they will not diffuse properly; if they are too big, that is, greater than about a half a wavelength, they will behave as acoustic mirrors in their own right and so will not diffuse effectively. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2071

Categorization

• SHARE: An acoustics-hobbyist friend who builds listening-room treatment panels would appreciate the precise bump-size rule and the 34 Hz vs 3.4 kHz scales.
• XREF: Connects to Schroeder diffusers, which reappear in the following paragraph.