AbstractWe study short wavelength solutions to then‐dimensional wave equationutt=(c(x))2Δu. We prove that the propagation of certain spatially localized pulses is determined by a time dependent analogue of geometrical optics up to an error whose energy tends to zero in the zero wavelength limit. Our method is very explicit, and no difficulties are incurred as the pulses propagate through caustics. Our goal is to study the physical question of where the energy propagates, rather than the more mathematical question of the propagation of singularities which has been studied in Fourier integral operato