Horizontal ducting of sound between short-wavelength nonlinear internal gravity waves in coastal environments has been reported in many theoretical and experimental studies. Important consequences arising at the open end of an internal wave duct (the termination) are examined in this paper with three-dimensional normal mode theory and parabolic approximation modeling. For an acoustic source located in such a duct and sufficiently far from the termination, some of the propagating sound may exit the duct by penetrating the waves at high grazing angles, but a fair amount of the sound energy is still trapped in the duct and propagates toward the termination. Analysis here shows that the across-duct sound energy distribution at the termination is unique for each acoustic vertical mode, and as a result the sound radiating from the termination of the duct forms horizontal beams that are different for each mode. In addition to narrowband analysis, a broadband simulation is made for water depths of order 80 m and propagation distances of 24 km. Situations occur with one or more modes absent in the radiated field and with mode multipath in the impulse response. These are both consistent with field observations.