Nonlinear generation and propagation of video-pulse signals produced as a result of the detection of high-frequency acoustic pulses in dry and water-saturated river sand is studied theoretically. The waveform of the video pulses, their amplitude against the amplitude of the primary wave, and the propagation velocity versus static pressure are determined. The theoretical results are contrasted with experimental data to determine the acoustic parameters of sand. These parameters are compared with the data on the nonlinear and dissipation properties of granular media described in the literature.