A precise statistical analysis has been carried out for the steady‐state response of a general one‐dimensional wave‐bearing system formed of two identical subsystems coupled together at an end. The statistics correspond approximately to averaging in frequency. Cross correlation between the wave fields incident on the coupling from the two subsystems (neglected in most statistical analyses) strongly affects the magnitude of the coupling power and, for dissipative couplings, the dissipative power. Asymmetry of the wave field in each subsystem (also usually neglected) can have a significant additional effect even when the dissipative loss factor is small. These results from a scattering analysis are compared with prior results [T. D. Scharton and R. H. Lyon, J. Acoust. Soc. Am.43,1332–1343 (1968)] from a modal analysis of a particular system.