On the method of lumens.

Parent and Allen [(2007). J. Acoust. Soc. Am. 122, 918-931] introduced the "method of lumens" to compute the plane-wave reflectance in a duct terminated with a nonuniform impedance. The method involves splitting the duct into multiple, fictitious subducts (lumens), solving for the reflectance in each subduct, and then combining the results. The method of lumens has considerable intuitive appeal and is easily implemented in the time domain. Previously applied only in a complex acoustical setting where proper evaluation is difficult (i.e., in a model of the ear canal and tympanic membrane), the method is tested here by using it to compute the reflectance from an area constriction in an infinite lossless duct considered in the long-wavelength limit. Neither the original formulation of the method-shown here to violate energy conservation except when the termination impedance is uniform-nor a reformulation consistent with basic physical constraints yields the correct solution to this textbook problem in acoustics. The results are generalized and the nature of the errors illuminated.