Dear Wayne,[1] Geddes, E., R.: "Acoustic Waveguide Theory revisited." JAES., vol. 41, pp. 452-461 (June 1993). See Section 3.5. The equation introduced there and its implication are treated in:
[2] Geddes, E., R.: "Sound Radiation from Acoustic Apertures." JAES., vol. 41, pp. 214-23 (April 1993). See in particular Section 6; the conclusion in the first paragraph.
M