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 |
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:
This file is licensed under the
Creative Commons
Attribution-Share Alike 4.0 International
license.
-
You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
-
Under the following conditions:
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- 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.