From 248e906daad4b3242ba7da1ac965a847dc01e8e3 Mon Sep 17 00:00:00 2001 From: jannisp Date: Sun, 29 Aug 2021 17:10:27 +0200 Subject: [PATCH] Add Phasenlinien image and change babel to german --- Mathematik-V-ZF.tex | 13 +++++++++++-- img/phasenlinien.png | Bin 0 -> 128868 bytes 2 files changed, 11 insertions(+), 2 deletions(-) create mode 100644 img/phasenlinien.png diff --git a/Mathematik-V-ZF.tex b/Mathematik-V-ZF.tex index 05f6e0d..a77feeb 100644 --- a/Mathematik-V-ZF.tex +++ b/Mathematik-V-ZF.tex @@ -1,4 +1,5 @@ \documentclass[8pt,landscape]{article} +\usepackage[ngerman]{babel} \usepackage{multicol} \usepackage{calc} \usepackage{bookmark} @@ -313,13 +314,20 @@ Periode $\tau = \frac{2\pi}{\omega}$ \subsubsection{Wellenüberlagerung} Für die Gruppengeschwindigkeit zweier überlagerter Wellen mit $k_1 \neq k_2$ und $\omega_1 \neq \omega_2$ gilt -$$v_g = \frac{\Delta \omega}{\Delta k}$$ +$$v_g = \frac{d \omega}{d k} \approx \frac{\Delta \omega}{\Delta k}$$ Dispersion tritt auf, falls $v_g \neq v_p$ (in der Praxis meist der Fall) \subsection{2D-Welle} -Für eine Linie konstanter Phase +Für eine Linie konstanter Phase (Phasenlinie) $$kx + ly - \omega t = \mathrm{const.}$$ Die Ausbreitung verläuft senkrecht auf diese Linien, was entlang dem Wellenvektor $\vec{h}$ entspricht. \\ +\begin{figure}[H] + \centering + \includegraphics[width=.25\textwidth]{phasenlinien.png} + \caption{Phasenlinien einer 2D-Welle} + \label{fig:phasenlinien} +\end{figure} + \subsubsection{Kennzahlen} Für die Wellenlängen gilt @@ -445,6 +453,7 @@ Jannis Portmann, FS21 \begin{itemize} \item Abb. \ref{fig:geo-coordinates}: E\^(nix) \& ttog, \url{https://de.wikipedia.org/wiki/Geographische_Koordinaten#/media/Datei:Geographic_coordinates_sphere.svg} \item Abb. \ref{fig:sir}, \ref{fig:sir-2}: Vorlesungsunterlagen + \item Abb. \ref{fig:phasenlinien}: Jannis Portmann basierend auf Vorlesungsunterlagen, CC BY-SA 3.0 \end{itemize} \end{multicols*} diff --git a/img/phasenlinien.png b/img/phasenlinien.png new file mode 100644 index 0000000000000000000000000000000000000000..e43034e7a223c458635b613c335fcb238279a495 GIT binary patch literal 128868 zcmeFZcU03$v^Go$QUw%2k*YKiDGE}hiF5%4>0L#n_g+F#5Tz+1BGN>p_g({{MnQV7 z3DSG$0YdUlJVo!7^Zoy=b}NlFB5r9aAE!7=K|nxoTvg?UHUR+% zmVkhGj_ertO(4p29DE~m(^kGtP}sq|0RHEOm4WI54Gn^e;Ab)d!f+b`2>wsN*IDod z-kL^8Kn%VU;(wP$^v|m#*fipQekPv7{~_nyr(xh5v&{{yJK#GJ{&(PQTi~Aye|;z1 zBp^KT-LP`{EdhZXf$9zUJKluLiYj@>u+&)pvS3RF=Fi=Zz;R!{E zgTCU^Q#K)ApBl*BKBXxCp8UMZ3CL~Q6Ss`W8U|w@y)i@Jq%pg-s?{rFk~31BaXezX z9d9>NIuk9&5#N&|PBK7f

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