Fourier Synthesis of a Series of Narrow Pulses Traveling in a Dispersive Medium

Above we see a handy dandy graph of a hundred term Fourier series representation of a train of pulses traveling through a dispersive medium. The superposition of cosine waves starts out as producing a series of single narrow pulses;we see two of them. As time evolves the longer wavelength components travel somewhat faster than the shorter wavelength components (the phase velocity is inversly proportional to the square root of the wavelength), and thus the pulses spread to form a wave packet. The group velocity of the pulse is less than the individual phases velocities and hence one sees the longer wavelength components moving toward the front of each wave packet. After a long time the pulses spread and overlap to produce a seemingly random collection of waves.

This page prepared by C.Hartley, Director of the Ernest B. Wright Observatory at the Department of Physics at Hartwick College in the City of Oneonta, NY. More things from C. Hartley at his home.

All text copyright ©2002 by C. Hartley.