\documentclass{standalone}
\usepackage{tikz}


\begin{document}
\begin{tikzpicture}
\draw[thin,->] (0,0)--(9.5,0) node[below]{$x$};
\draw[thin,->] (0,0)--(0,4.2) node[left]{$t$};



\draw (8.25,3)--(4.5,0)--(.75,3);

\fill[fill=yellow] (8.25,3)--(4.5,0)--(.75,3)..controls (3,4.5) and (5,2.5).. (8.25,3) ;


\fill (4.5,0) circle (.04) node[below] {$(\bar{x},0)$};

 
\node[rotate=38.6598082540901] at (6.7,1.5)  {$x=\bar{x}+ct$};
\node[rotate=-38.6598082540901] at (2.2,1.5)  {$x=\bar{x}-ct$};

\node at (4.5,2) {$\Delta^+(\bar{x},0)$};

\end{tikzpicture}
\end{document}