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File:Commutative diagram of harmonic wave properties.svg

From Wikipedia, the free encyclopedia

Original file(SVG file, nominally 689 × 864 pixels, file size: 120 KB)

Summary

Description
This diagram describes the relationships between the various properties of harmonic waves: frequency, period, wavelength, angular frequency, and wavenumber.

The properties are organized in three axes:

  • linear properties on the left, and their angular equivalents on the right;
  • frequency properties on the top, and their periodic reciprocals on the bottom;
  • temporal properties at the front, and their spatial equivalents at the back.
Date
Source Own work
Author Waldir

LaTeX source code

The source code below was developed interactively using the ShareLaTeX online editor. It makes use of the xymatrix package, and uses a command definition from TeX.StackExchange do draw the barred lambda character.

To generate the SVG image, the LaTeX document was exported from ShareLaTeX as a PDF file, converted to SVG using Online-Convert.com, and cleaned-up (grouping related objects, tweaking positioning of some elements) using Inkscape.

\documentclass{article}
\usepackage[all]{xy}
\usepackage{amsmath,xcolor}
\newcommand{\lambdabar}{{\mkern0.75mu\mathchar '26\mkern -9.75mu\lambda}}
\begin{document}
\noindent
\pagestyle{empty}
\huge
\[
	\xymatrix@C=0.5em@R+1em{
	& \underset{_{\substack{\text{linear}\\\text{wavenumber}}}}{\tilde{\nu}}
	\ar^-{_{\color{gray}x \cdot \tau}}[rr]
	\ar^>>>>>>>>>>>>>>>>>>>>{\color{gray}\frac{1}{x}}@{<.>}[dd]
	\ar_-{_{\color{gray}x \cdot v_p}}[dl]
	&
	& \underset{_{\substack{\text{angular}\\\text{wavenumber}}}}{k}
	\ar^-{_{\color{gray}x \cdot v_p}}[dl]
	\ar^-{\color{gray}\frac{1}{x}}@{<->}[dd]
	\\
	\underset{_{\substack{\text{linear}\\\text{frequency}}}}{f}
	\ar^{_{\color{gray}\qquad\;\; x \cdot \tau}}[rr]
	&
	& \underset{_{\substack{\text{angular}\\\text{frequency}}}}{\omega}
	\ar^>>>>>>>>>>>>>>>>>>>>{\color{gray}\frac{1}{x}}@{<->}[dd]
	\\
	& \underset{_{\substack{\text{linear}\\\text{wavelength}}}}{\lambda}
	\ar^-{_{\qquad\quad\color{gray}x/\tau}}@{.>}[rr]
	\ar^>>>>>>>>>>>>>>>{_{\color{gray}x / v_p}}@{.>}[dl]
	&
	& \underset{_{\substack{\text{angular}\\\text{wavelength}}}}{\lambdabar}
	\ar^-{_{\color{gray}x / v_p}}[dl]
	\\
	\underset{_{\substack{\text{linear}\\\text{period}}}}{T}
	\ar^-{\color{gray}\frac{1}{x}}@{<->}[uu]
	\ar^-{_{\color{gray}x / \tau}}[rr]
	&
	& \underset{_{\substack{\text{angular}\\\text{period}}}}{?}
	}
\]

\vspace{1em}
\Large

$v_p =$ wave speed (phase velocity)

$\tau = 2\pi$
\end{document}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Captions

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Items portrayed in this file

depicts

1 October 2016

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current20:01, 14 November 2016Thumbnail for version as of 20:01, 14 November 2016689 × 864 (120 KB)Waldyrioustweak position of some elements
19:58, 14 November 2016Thumbnail for version as of 19:58, 14 November 2016689 × 864 (120 KB)Waldyriousupdated per request on talk page
12:57, 4 October 2016Thumbnail for version as of 12:57, 4 October 2016689 × 864 (55 KB)Offnfoptweird rendering issue in chrome, this one passes the test
12:40, 4 October 2016Thumbnail for version as of 12:40, 4 October 20161,049 × 1,337 (61 KB)Offnfoptadding white background, cropped some white space and increased height/width, revert if the changes are undesired
19:27, 1 October 2016Thumbnail for version as of 19:27, 1 October 2016564 × 626 (93 KB)WaldyriousUser created page with UploadWizard
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