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Chris Spencer edited Data and Analysis.tex
almost 10 years ago
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\subsection{First Sound}
First to plot $c_1$,frequencies were found from the recorded data at various pressures. The frequencies and the sound speed are related by $f=\frac{c_1n}{2L}$ and solving for results in \[c_1=\frac{f2L}{n}\] where L=0.0495 meters and choose n=1.
Pressure data was taken from in torr and converted into temperatures in kelvin using a Maynard Table.
Temperatures were taken then from 1.3 K to 2.0 kelvin in .02 K temeperature steps then 2.0 to 2.18 Kelvin in .01 K temperature steps. Figure 6 shows the experimental $c_1$ vs T. In comparison to figure 3, it can be seen that the data matches very closely to the theoretical prediction of figure 3. What is reassuring is that even the at $T_{\lambda}\approx1.7$, the same "dent" is seen in the experimental graph of $c_1$ vs Temperature is in agreement with the
theoretica theoretical plot of first sound in figure 3.
\subsection{Error in $c_1$ and Temperaure}
The error in speed is found by the equation \[dc_1=\sqrt{(2f)^2 dL^2+(2L)^2 (df)^2}\]
where dL=.0002 meters and df=1 Hz. The error in temperature used was .001 K.