Talk:Wave vector

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[edit] Introductory section

Comments

• A wave vector is not a vector representation of a wave unless one introduces a function space, a set of orthonormal basis functions, and a way to describe any arbitrary wave as a vector in the function space using the basis functions. The author has clearly not explained any of the details to the reader. Furthermore, any such discussion does not belong in the introductory paragraph of the wave vector article.
• The author states that a single wave vector describes a family waves. What does the author mean? I offer the following different scenarios and comments. (a) The author means that any arbitrary wave is really a family of basis functions with the wave vector giving the appropriate coefficients. In this case, the meaning is totally lost. (b) The author means that a single point disturbance in time constitutes a wave and that a spatially extended collection of point disturbances in time constitutes a family of (presumably temporal) waves. This idea culminates with the confusing statement that a family of waves is exemplified by a plane wave in one spatial dimension. The author unsuccesfully tries to make a distinction between waves in time and space. Introducing such a distinction to explain the concept of a wave vector is unnecessary. Furthermore the distinction between temporal and spatial oscillations is already made in the waves article. Therefore the first section of the wave vector article should focus on the spatial characteristic of the wave. Then the more advanced section on four vectors etc. can discuss both the spatial and temporal characteristics of the wave. (c) The author confuses the ideas in points a and b. (d) I think I finally understand. The author means that a plane wave is a family of one dimensional waves. In other words one could imagine constructing an infinite plane by stacking an infinite number of lines. To get a plane wave the lines just need to have sinusoidal oscillations of the same wavenumber, frequency, and initial phase. Here a picture would be worth a thousand words. The meaning is totally lost.
• In any event a single wave vector describes a single plane wave.
• The introductory section needs a major rewrite.

Edits

• Remove the following statements.

The wave vector is a vector representation of a wave.

The wave vector is most useful for generalizing the equation of a single wave into a description of a family of waves. As long as the family of waves all travel in the same direction and with the same wavelength, a single wave vector is valid for the entire family. The most common case of a family of waves that meets these requirements is the plane wave, in which the family of waves is also coherent, i.e. all the waves have the same phase.

• Replace

That last step where it equals zero, is a result of the fact that, for light, k=ω/c

with

That last step where it equals zero, is a result of the fact that, for light, k⁰=k₀=ω/c