A mechanism is presented by which the observed acoustic intensity is made to vary due to changes in the acoustic path that are caused by internal-tide vertical fluid displacements. The position in range and depth of large-scale caustic structure is determined by the background sound-speed profile. Internal tides cause a deformation of the background profile, changing the positions of the caustic structures-which can introduce intensity changes at a distant receiver. Gradual fades in the acoustic intensity occurring over timescales similar to those of the tides were measured during a low-frequency (284-Hz) acoustic scattering experiment in the Philippine Sea in 2009 [White et al., J. Acoust. Soc. Am. 134(4), 3347-3358 (2013)]. Parabolic equation and Hamiltonian ray-tracing calculations of acoustic propagation through a plane-wave internal tide environmental model employing sound-speed profiles taken during the experiment indicate that internal tides could cause significant gradual changes in the received intensity. Furthermore, the calculations demonstrate how large-scale perturbations to the index of refraction can result in variation in the received intensity.