Longitudinal waves are waves where the motion of the material in the wave is back and forth in the same direction that the wave moves. Longitudinal waves are sometimes called compressional waves. Soun...Longitudinal waves are waves where the motion of the material in the wave is back and forth in the same direction that the wave moves. Longitudinal waves are sometimes called compressional waves. Sound waves (in air and in solids) are examples of longitudinal waves.