Directivity depends on wavelengths fitting across the radiating aperture

Evidence

This appendix has presented the basic Fourier relationship between the far-field polar response and the near-field illumination of the aperture. It has demonstrated its utility in a variety of electroacoustic applications. In particular, it is possible to derive some useful relationships between the size of the speaker, with respect to wavelength, and its directivity performance versus frequency—in particular that for directivity, size really does matter! — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2946 (#expands, via linked claim)

Categorization

• XREF: connects to: A piston’s radiation efficiency depends on size relative to wavelength, not absolute size; Shorter wavelengths scatter more strongly from small objects than longer ones do.; Short wavelengths escape open pipe ends while long wavelengths reflect back (+6 more)

Related

• Radiation directivity depends on wavelength relative to source size (similarity 0.95)
• Acoustic wavelength size relative to objects governs how sound interacts with them (similarity 0.93)
• Larger speaker size relative to wavelength enables higher directivity (similarity 0.90)
• At low frequencies only drivers and ports define a loudspeaker’s effective source size (similarity 0.88)
• A piston’s radiation efficiency depends on size relative to wavelength, not absolute size (similarity 0.86)
• A speaker’s coverage angle roughly doubles for each octave below its minimum directivity frequency. (similarity 0.86)
• Reflection and diffraction of sound both depend on object size relative to wavelength (similarity 0.83)
• Small loudspeakers radiate omnidirectionally because they are small relative to wavelength (similarity 0.82)
• Increasing speaker directivity reduces the reverberant field like a tone control does (similarity 0.82)
• Large radiating surfaces become highly directional at high frequencies (similarity 0.81)
• Sound-radiation efficiency depends on piston size relative to wavelength, not absolute size (similarity 0.81)
• Speaker drivers’ directivity at high frequencies causes spectral dips in the reverberant field (similarity 0.80)
• Digital signal processing made constant-directivity array loudspeakers practical and popular (similarity 0.80)
• Low frequencies radiate omnidirectionally while high frequencies become directional (similarity 0.80)
• Sound diffracts strongly only when wavelengths exceed opening size (similarity 0.79)

Broader Connections

• Larger speaker size relative to wavelength enables higher directivity #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2946
• Reflection and diffraction of sound both depend on object size relative to wavelength #expands (0.80)
• Stringed instruments radiate low frequencies omnidirectionally but high frequencies directionally #exemplifies (0.80)
• Array spacing beyond half a wavelength causes spatial aliasing with multiple lobes #exemplifies (0.78) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2890
• Standing waves arise when wall spacing equals half-wavelength multiples #qualifies (0.75)