ARCHIVES OF ACOUSTICS Vol. 40, No. 1, pp. 33–40 (2015) Copyright c  2015 by PAN – IPPT DOI: 10.1515/aoa-2015-0005 A Revised Sound Energy Theory Based on a New Formula for the Reverberation Radius in Rooms with Non-Diffuse Sound Field Higini ARAU-PUCHADES (1) , Umberto BERARDI (2) (1) ArauAcustica Barcelona, Spain (2) Department of Architectural Science, Ryerson University Toronto, Canada; e-mail: uberardi@ryerson.ca (received November 9, 2014; accepted November 20, 2014 ) This paper discusses the concept of the reverberation radius, also known as critical distance, in rooms with non-uniformly distributed sound absorption. The reverberation radius is the distance from a sound source at which the direct sound level equals the reflected sound level. The currently used formulas to calculate the reverberation radius have been derived by the classic theories of Sabine or Eyring. However, these theories are only valid in perfectly diffused sound fields; thus, only when the energy density is constant throughout a room. Nevertheless, the generally used formulas for the reverberation radius have been used in any circumstance. Starting from theories for determining the reverberation time in non- diffuse sound fields, this paper firstly proposes a new formula to calculate the reverberation radius in rooms with non-uniformly distributed sound absorption. Then, a comparison between the classic formulas and the new one is performed in some rectangular rooms with non-uniformly distributed sound absorption. Finally, this paper introduces a new interpretation of the reverberation radius in non-diffuse sound fields. According to this interpretation, the time corresponding to the sound to travel a reverberation radius should be assumed as the lower limit of integration of the diffuse sound energy. Keywords: reverberation radius, critical distance, non-diffuse sound field, sound energy, revised sound decay theory. 1. Introduction The reverberation radius in a room, or critical dis- tance as it is often called in audio engineering, is the distance from a sound source at which the level of di- rect sound equals the level of reflected sound (Fig. 1). This distance is an important parameter for the sound perception as by knowing the distance of the listener from a source and the reverberation radius of the room, it is then possible to assess if the direct or diffused sound filed prevails. The reverberation radius is hence highly useful in assessing the reverberance of a room. Generally, a room is defined as “live” when a prepon- derance of reflected sounds produces a reverberant feel- ing; on the other hand, if the direct sound is dominant, the room is considered “dry” or “dead”. Attempts have been made to express liveness as the ratio of the direct and diffuse energy density, often using the reverbera- tion radius concept. In this way, the comparison of the reverberation radius with the room dimensions allows an easy estimation. Fig. 1. Sound energy decay and reverberation radius rep- resentation.