The averaged impulse response for sound transmission in a shallow‐water channel is estimated by a theory based on ray acoustics with lossy specular reflection from the boundaries. Averaging is introduced primarily by strict averaging in depth of the square of the received pressure. Rays need be traced over but a single cycle of their paths. The impulse response contains useful and readily accessible information about environmental loss parameters. The rate of decay of the reverberant tail, which is characteristic of channels with only moderate variations in sound speed, appears to be a particularly valuable measure. Theoretical and experimental data are compared.