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Basics of Waves: One-Dimensional Wave Properties

This article explores the fundamental properties of one-dimensional waves, including phase measures, wavelength, wave number, period, frequency, and speed. It also covers specific cases of non-dispersive and dispersive waves, as well as the concept of group velocity.

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Basics of Waves: One-Dimensional Wave Properties

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  1. Basic properties of waves One-dimensional wave t t=0 phase measures the position of a wave feature, such as a wave peak or trough wavelength distance between repeating units of a propagating wave wave-number circular wave-number period T duration of one cycle in a repeating event frequency number of occurrences of a repeating event per unit time angular frequency phase speed

  2. Euler formula i: imaginary unit Harmonic wave : one amplitude and one frequency Right moving wave Left moving wave Waves superimpose together Example 1: standing wave

  3. Example 2: Non-dispersive and dispersive wave Specific case 1 Non-dispersive wave-packet Specific case 2 Dispersive wave-packet Non-dispersive wave: wave phase speed dos not depend on wave number. Dispersive wave: wave phase speed depends on wave number.

  4. Specific case 3 Specific case 4 Because of the reinforcement or cancellation of wave amplitude, the energy of wave group will be concentrated in regions where the wave amplitude is large, and those regions with small wave amplitude contain less energy. Thus, wave energy does not propagate at the phase speed of individual waves, but at the speed of wave envelope, called group velocity.

  5. Group velocity high frequency carrier wave slow moving envelope wave group velocity

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