One-dimensional traveling wave pulses are defined and generalized to sinusoidal traveling waves. The mathematical description of sinusoidal waves is considered in depth. It is shown that any traveling wave can be considered the sum of standing waves, and vice versa. Longitudinal polarization is introduced and contrasted with the previous examples involving transverse polarization. The effects of dispersion, where the wave speed may depend on frequency, on wave propagation are briefly discussed.
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