Diffuse sound field synthesis: Ideal source layers

Abstract

Can uncorrelated surrounding sound sources be used to generate extended diffuse sound fields? By definition, targets are a constant sound pressure level, a vanishing active sound intensity, and uncorrelated sound waves arriving isotropically from all directions. Are there ideal source layouts to synthesize a maximum diffuse sound field within? As methods, we employ numeric simulations and undertake a series of considerations based on uncorrelated source layouts at a finite radius. Statistically expected active sound intensity and sound energy density are insightful and highlight the relation of active sound intensity to potential theory. Correspondingly, both Gauß’ divergence and Newton’s spherical shell theorem apply, and they provide valuable insights. In a circular layout, uncorrelated elementary point-source fields decaying by 1/√r ideally compose an extended sound field of vanishing active sound intensity; in spherical layouts this is the case with a 1/r decay. None of the layouts synthesizes a perfectly constant sound energy density inside. Theory and simulation offer a broad basis for understanding the synthesis of diffuse sound fields with uncorrelated sources in the free sound field.

Keywords

• sound field synthesis
• diffuse sound fields
• gauß’ divergence theorem
• newton’s spherical shell theorem
• potential theory