File:Commutative diagram of harmonic wave properties.svg
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Summary
| Description |
English: 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:
Bahasa Indonesia: Diagram yang menggambarkan hubungan antara bilangan gelombang dan sifat-sifat lain dari gelombang harmonik.
Srpskohrvatski / српскохрватски: Dijagram međuodnosa talasne dužine i ostalih svojstava harmoničnih talasa. |
| Date | |
| Source | Own work |
| Author | Waldir Pimenta |
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}}
%\newcommand{\Tbar}{{\mkern0.75mu\mathchar '26\mkern -9.75mu T}}
\newcommand{\Tbar}{\raisebox{0.2ex}{--}\kern-0.6em T}
\begin{document}
\noindent
\pagestyle{empty}
\huge
\[
\xymatrix@C=0.5em@R+1em{
& \underset{_{\substack{\text{linear}\\\text{wavenumber}}}}{\tilde{\nu}}
\ar^-{_{\cdot 2\pi}}[rr]
\ar^>>>>>>>>>>>>>>>>>>>>{()^{-1}}@{<.>}[dd]
\ar_-{_{\cdot c}}[dl]
&
& \underset{_{\substack{\text{angular}\\\text{wavenumber}}}}{k}
\ar^-{_{\cdot c}}[dl]
\ar^-{()^{-1}}@{<->}[dd]
\\
\underset{_{\substack{\text{linear}\\\text{frequency}}}}{f}
\ar^{_{\qquad\;\; \cdot 2\pi}}[rr]
&
& \underset{_{\substack{\text{angular}\\\text{frequency}}}}{\omega}
\ar^>>>>>>>>>>>>>>>>>>>>{()^{-1}}@{<->}[dd]
\\
& \underset{_{\substack{\text{linear}\\\text{wavelength}}}}{\lambda}
\ar^-{_{\qquad\quad\cdot \frac{1}{2\pi}}}@{.>}[rr]
\ar^>>>>>>>>>>>>>>>{_{\cdot \frac{1}{c}}}@{.>}[dl]
&
& \underset{_{\substack{\text{angular}\\\text{wavelength}}}}{\lambdabar}
\ar^-{_{\cdot \frac{1}{c}}}[dl]
\\
\underset{_{\substack{\text{linear}\\\text{period}}}}{T}
\ar^-{()^{-1}}@{<->}[uu]
\ar^-{_{\cdot \frac{1}{2\pi}}}[rr]
&
& \underset{_{\substack{\text{angular}\\\text{period}}}}{\Tbar}
}
\]
\vspace{1em}
\Large
\noindent
$c =$ speed of wave propagation (phase velocity), from the Latin word "celeritas" (speed or swiftness).\\
%%%$x =$ generalized variable name\\
\end{document}
Licensing
I, the copyright holder of this work, hereby publish it under the following licence:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International licence.
- 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 licence, 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 licence as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:01, 5 November 2025 | | 689 × 864 (85 KB) | wikimediacommons>Waldyrious | use T-bar for angular period; use solid arrowheads |
File usage
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