Superposition of waves on a string

waves_superposition-001.pngwaves_superposition-002.pngwaves_superposition-003.pngwaves_superposition-004.pngwaves_superposition-005.pngwaves_superposition-006.png

Edit and compile if you like:

% Author: Izaak Neutelings (December 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{physics}
\usepackage{tikz}
\usetikzlibrary{calc} % for pic
\usetikzlibrary{angles,quotes} % for pic
\tikzset{>=latex} % for LaTeX arrow head

\colorlet{xcol}{blue!70!black}
\colorlet{vcol}{green!60!black}
\tikzstyle{vvec}=[->,vcol,very thick,line cap=round]
\tikzstyle{rope}=[brown!20!black,double=brown!70!black,double distance=1,line width=0.3] %very thick
\def\wave#1#2{
  ({(#1-0.22)*\xmax},0) to[out=0,in=180,looseness=0.6] (#1*\xmax,#2*\ymax)
  to[out=0,in=180,looseness=0.6]++ (0.22*\xmax,#2*-\ymax)
}
%\def\waveR#1{
%  ({(#1-0.22)*\xmax},0) to[out=0,in=180,looseness=0.6] (#1*\xmax,-\ymax)
%  to[out=0,in=180,looseness=0.6]++ (0.22*\xmax,\ymax)
%}

\begin{document}

% SUPERPOSITION, CONSTRUCTIVE - t = 0
\def\xmax{3.0}
\def\ymax{0.8}
\begin{tikzpicture}
  \def\xL{-0.5}
  \def\xR{0.5}
  \coordinate (L) at (\xL*\xmax,\ymax);
  \coordinate (R) at (\xR*\xmax,\ymax);
  \node[above=-2] at (L) {$f(x-vt)$};
  \node[above=-2] at (R) {$f(x+vt)$};
  \draw[rope] %very thick,xcol]
    (-\xmax,0) -- \wave{\xL}{1} -- \wave{\xR}{1} -- (\xmax,0);
  \draw[vvec] (L)++(-65:0.5*\ymax) --++ (0.17*\xmax,0) node[right=-2] {$v$};
  \draw[vvec] (R)++(-115:0.5*\ymax) --++ (-0.17*\xmax,0) node[left=-2] {$v$};
  \node[right,scale=0.9] at (-1.35*\xmax,0.6*\ymax) {$t=0$};
\end{tikzpicture}

% SUPERPOSITION, CONSTRUCTIVE - t = Dt
\begin{tikzpicture}
  \coordinate (T) at (0,\ymax);
  \draw[dashed] \wave{0}{1};
  \draw[rope] %very thick,xcol]
    (-\xmax,0) -- (-0.22*\xmax,0) to[out=0,in=180,looseness=0.4] (0,2*\ymax)
    to[out=0,in=180,looseness=0.4] (0.22*\xmax,0) -- (\xmax,0);
  \draw[vvec] (T)++(-60:0.5*\ymax) --++ (0.17*\xmax,0) node[right=-2] {$v$};
  \draw[vvec] (T)++(-120:0.5*\ymax) --++ (-0.17*\xmax,0) node[left=-2] {$v$};
  \node[right,scale=0.9] at (-1.35*\xmax,0.6*\ymax) {$t=\Delta t$};
\end{tikzpicture}

% SUPERPOSITION, CONSTRUCTIVE - t = 2*Dt
\begin{tikzpicture}
  \def\xL{-0.5}
  \def\xR{0.5}
  \coordinate (L) at (\xL*\xmax,\ymax);
  \coordinate (R) at (\xR*\xmax,\ymax);
  \draw[rope] %very thick,xcol]
    (-\xmax,0) -- \wave{\xL}{1} -- \wave{\xR}{1} -- (\xmax,0);
  \draw[vvec] (R)++(-65:0.5*\ymax) --++ (0.17*\xmax,0) node[right=-2] {$v$};
  \draw[vvec] (L)++(-115:0.5*\ymax) --++ (-0.17*\xmax,0) node[left=-2] {$v$};
  \node[right,scale=0.9] at (-1.35*\xmax,0.6*\ymax) {$t=2\Delta t$};
\end{tikzpicture}

% SUPERPOSITION, DESTRUCTIVE - t = 0
\begin{tikzpicture}
  \def\xL{-0.5}
  \def\xR{0.5}
  \coordinate (L) at (\xL*\xmax,\ymax);
  \coordinate (R) at (\xR*\xmax,-\ymax);
  \node[above=0,right=7] at (L) {$f(x-vt)$};
  \node[below=0,left=7] at (R) {$-f(x+vt)$};
  \draw[rope] %very thick,xcol]
    (-\xmax,0) -- \wave{\xL}{1} -- \wave{\xR}{-1} -- (\xmax,0);
  \draw[vvec] (L)++(-65:0.5*\ymax) --++ (0.17*\xmax,0) node[right=-2] {$v$};
  \draw[vvec] (R)++(115:0.5*\ymax) --++ (-0.17*\xmax,0) node[left=-2] {$v$};
  \node[right,scale=0.9] at (-1.35*\xmax,0.5*\ymax) {$t=0$};
\end{tikzpicture}

% SUPERPOSITION, DESTRUCTIVE - t = Dt
\begin{tikzpicture}
  \coordinate (L) at (0,\ymax);
  \coordinate (R) at (0,-\ymax);
  %\node[above=0,right=7] at (L) {$f(x-vt)$};
  %\node[below=0,left=7] at (R) {$-f(x+vt)$};
  \draw[dashed] \wave{0}{1};
  \draw[dashed] \wave{0}{-1};
  \draw[rope] %very thick,xcol]
    (-\xmax,0) -- (\xmax,0);
  \draw[vvec] (L)++(-65:0.5*\ymax) --++ (0.17*\xmax,0) node[right=-2] {$v$};
  \draw[vvec] (R)++(115:0.5*\ymax) --++ (-0.17*\xmax,0) node[left=-2] {$v$};
  \node[right,scale=0.9] at (-1.35*\xmax,0.5*\ymax) {$t=\Delta t$};
\end{tikzpicture}

% SUPERPOSITION, DESTRUCTIVE - t = 2 * Dt
\begin{tikzpicture}
  \def\xL{0.5}
  \def\xR{-0.5}
  \coordinate (L) at (\xL*\xmax,\ymax);
  \coordinate (R) at (\xR*\xmax,-\ymax);
  %\node[above=0,right=7] at (L) {$f(x-vt)$};
  %\node[below=0,left=7] at (R) {$-f(x+vt)$};
  \draw[rope] %very thick,xcol]
    (-\xmax,0) -- \wave{\xR}{-1} -- \wave{\xL}{1} -- (\xmax,0);
  \draw[vvec] (L)++(-65:0.5*\ymax) --++ (0.17*\xmax,0) node[right=-2] {$v$};
  \draw[vvec] (R)++(115:0.5*\ymax) --++ (-0.17*\xmax,0) node[left=-2] {$v$};
  \node[right,scale=0.9] at (-1.35*\xmax,0.5*\ymax) {$t=2\Delta t$};
\end{tikzpicture}


\end{document}

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