Reciprocal of the Mean Free Path

The geometry of a rectangular enclosure is examined from the viewpoint of the absorption of reverberant energy. For diffuse sound, the significant quantity is not what is implied by the term mean free path but rather the mean reciprocal of the pathlengths. For particular modes, the reciprocal of the pathlengths can vary widely from its mean value and introduce a corresponding uncertainty in the relation of decay rate to absorption coefficient. Although no simple expressions have been found for enclosures of general shape, the range of variation from mode to mode seems to be nearly as great as for rectangular enclosures. This paper was written independently of a related one by F. V. Hunt [J. Acoust. Soc. Am. 36, 556‐564 (1964)] and their simultaneous appearance is purely a coincidence. Hunt's paper is concerned primarily with reconciling the various formulations of the mean free path, whereas this paper stresses the variation of mean free path and the inversely related collision frequency for isolated normal modes.