$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\halfi}{{1/2}}
\newcommand{\xpoint}{\boldsymbol{x}}
\newcommand{\normalvec}{\boldsymbol{n}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\Ix}{\mathcal{I}_x}
\newcommand{\Iy}{\mathcal{I}_y}
\newcommand{\It}{\mathcal{I}_t}
\newcommand{\setb}[1]{#1^0} % set begin
\newcommand{\sete}[1]{#1^{-1}} % set end
\newcommand{\setl}[1]{#1^-}
\newcommand{\setr}[1]{#1^+}
\newcommand{\seti}[1]{#1^i}
\newcommand{\Real}{\mathbb{R}}
$$
Running a case
- Vibrations of a guitar string
- Triangular initial shape (at rest)
$$
\begin{equation}
I(x) = \left\lbrace
\begin{array}{ll}
ax/x_0, & x < x_0\\
a(L-x)/(L-x_0), & \hbox{otherwise}
\end{array}\right.
\tag{20}
\end{equation}
$$
Appropriate data:
- \( L=75 \) cm, \( x_0=0.8L \), \( a=5 \) mm, time frequency \( \nu = 440 \) Hz
