%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\schrift{11pt}
\input format

\def\baselinestretch{1.1}

\begin{document}

\pagestyle{empty}

\Blatt{4}{WS 2003/2004, 17.11.2003}
         {Mechanik der Kontinua}
         {Prof. J.~L.~van~Hemmen}

\begin{deflist}{20.}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\item[10.]
{\bf Schallwellen}
\par\smallskip

\begin{enumerate}
\item Linearisieren Sie die Eulergleichungen
  \begin{eqnarray*}
    \partial_t \varrho + \div (\varrho\, \vek{v}) & = & 0 \\
    \partial_t v_i + \sum_{j=1}^3 ( \partial_j v_i ) v_j & = & - \frac{1}{\varrho} \partial_i p \,,
  \end{eqnarray*}
um $\varrho=\varrho_0$, $p=p_0$ und $\vek{v}=\vek{0}$, indem Sie
$\varrho=\varrho_0+\Delta\varrho$, und $p=p_0 + \Delta p$ setzen und
Terme zweiter Ordnung in $\Delta \varrho$, $\Delta p$ und $\vek{v}$
vernachlässigen. Beachten Sie, dass für Schallwellen in Gasen die
adiabatische Zustandsgleichung
\begin{displaymath}
  \frac{p}{p_0} = \left( \frac{\varrho}{\varrho_0} \right)^\gamma
\end{displaymath}
gilt und für Flüssigkeiten und Festkörper
\begin{displaymath}
  \varrho = \varrho_0 (1 + \varkappa \, \Delta p ) \,.
\end{displaymath}
\item Wie erhält man eine Wellengleichung für $\Delta \varrho$?
\item Berechnen Sie die Schallgeschwindigkeit in Luft und in Wasser
  (die Kompressibilität von Wasser beträgt $\varkappa = 50 \cdot 10^{-6}
  \mathrm{bar}^{-1}$).
\end{enumerate}



\par\smallskip
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{deflist}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vfill 

\footnotesize
\rule[.5mm]{\textwidth}{0.1mm}\\
Besprechung der "Ubungen am 24.11.2003 um 14.15 Uhr im Raum PH 127
(Garching).\\
"Ubungsleitung: Moritz Franosch, mail@Franosch.org, http://www.physik.tu-muenchen.de/lehrstuehle/T35/.

\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

