% Bernd Berg sep 9 2017.
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\centerline{\bf Special and General Relativity (PHZ 4601) Fall 2017 
Solutions} \medskip

{\bf Set 2:} \medskip

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% \end{figure} \centerline{Potential as function of $z$.}

\begin{description} 
\item{\bf 6. M\"ossbauer precision for measuring a gravitational
frequency shift (Rindler 1.9).}
\end{description} \smallskip

Let a $22\,[m]$ long cabin fall freely in the gravitational field $g$
and send a light signal from the top to the bottom. We need to show 
that when the light signal reaches the bottom, the cabin will already
move with velocity $v>10^{-5}\,[cm/s]$, so that the frequency shift
can be detected. This is easily calculated.

Duration of the signal: 
$$t = \frac{22\,[m]}{3\times 10^8\,[m/s]}=7.33\times 10^{-8}\,[s]\,.$$

Velocity reached:
$$ v = g\,t = (980\,[cm/s])\times(7.22\times 10^{-8}\,[s])
     = 7.2\times 10^{-5}\,[cm/s]\,.$$

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