Wave function

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% Author: Izaak Neutelings (December 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta} % for arrow size
\tikzset{>=latex} % for LaTeX arrow head
\colorlet{xcol}{blue!70!black}
\colorlet{vcol}{green!60!black}
\colorlet{myred}{red!70!black}
\tikzstyle{vvec}=[->,vcol,very thick,line cap=round]
\tikzstyle{myarr}=[-{Latex[length=3,width=2]},myred]
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
\def\xpeak#1{{(0.21+#1)*\xmax}}
\def\wave#1{
  \coordinate (F) at (\xpeak{#1},\ypeak);
  \draw[very thick,xcol]
    (-0.08*\xmax,0) -- ({(0.06+#1)*\xmax},0) to[out=0,in=180,looseness=0.5] (F)
    to[out=0,in=180,looseness=0.6]++ (0.25*\xmax,-\ypeak) -- (0.94*\xmax,0);
}
\begin{document}
% WAVE t = 0
\def\xmax{4.2}
\def\ymax{2.0}
\def\ypeak{0.80*\ymax}
\def\v{0.17*\xmax}
\begin{tikzpicture}
  \draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[right=4,below left=1] {$x$};
  \draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[left=1] {$y$};
  \wave{0.0}
  \node[above=4,right=5] at (F) {$y(x,0)=f(x)$};
  %\node[left] at (0.97*\xmax,0.65*\ymax) {$t=0$};
  \tick{\xpeak{0.0},0}{90} node[scale=0.9,below=-1] {$a$};
  \draw[vvec] (F)++(-64:0.35*\ymax) --++ (\v,0) node[above right=-2] {$v$};
\end{tikzpicture}
% WAVE t = Delta t
\begin{tikzpicture}
  \draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[right=4,below left=1] {$x$};
  \draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[left=1] {$y$};
 
 
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