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In vibration theory, the group speed is the response of a wave’s group of sinusoidal components, and is different from phase velocity. Group speed is important; the interaction of all the wave components in terms of wave number, amplitude, and frequency causes the appearance of a carrier wave of some wave number, amplitude, and frequency. This carrier wave is modulated by group waves that propagate at group speeds. In a nondispersing wave, the group speeds are the same as the phase velocity of the wave components. In a dispersing wave, however, these group speeds can be different. If the group speeds are greater than the phase velocities, it will appear that a carrier wave originates at the back of the wave, propagates forward until it reaches the front of the wave, vanishes, and reappears at the back of the wave. If the group speeds are less than the phase velocities, it will appear that a carrier wave originates at the front of the wave, propagates backward until it reaches the back of the wave, vanishes, and reappears at the front of the wave. This can be visualized by thinking of a caterpillar’s motion. The caterpillar’s ripples appear to move backward, yet the caterpillar moves forward. This is one reason the analysis of dispersing waves can be very complicated.