A local particle-like approach to wave propagation

Abstract

Waves and particles are the main constituents of nature, but waves are our main method of communication, whether biological or technological. Historically, the study of waves has been separated into the stationary (standing wave) and nonstationary (pulse) case. Pulses are of fundamental consideration in radar, sonar, acoustics, fiber optics, among many other areas. A pulse has been called by many terms—transient, wave group, progressive wave, wave packet, nonrecurrent wave, traveling wave, nonperiodic wave—all to describe basically the same thing. The fact that so many names exist is an indication that there is no full understanding of their behavior. We present a simple particle-like view of pulse propagation, which makes pulses easier to understand and deal with intuitively. We have derived exact expressions for many physical quantities such as the spreading of a pulse, the conditions as to when a pulse contracts, the contraction time, and other important physical quantities. What emerges from these considerations is not only a clearer view of how pulses propagate, but a practical means to obtain their propagation in a dispersive medium.