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These frequencies correspond to mode number n, and n was found to go from n=3,4,5,6. The second sound was then computed for each mode number and then the average of these were used for analysis. Figure 7 displays the data for the second sound velocity vs temperature. Again this is compared to the theoretical plot of figure 3 and it can be seen that the experimental data closely resembles that of the theoretical second sound vs temperature for temperatures greater than 1.3 K. Since the data was poor close to $T_{\lambda}$, the $T_{\lambda}$ line is not shown but the trend still matches the theoretical plot since the data for temperature for second stops at 2.12 K,just shy of 2.17 K. The theoretical plot and the experimental plot both show the speed decreasing as the temperature increases to $T_{\lambda}$.   \subsection{Error in $c_2$ and Temperaure}  Error in $c_2$ is found by the equation \[dc_2=\sqrt{\left(\frac{2c_2}{n}\right)^2 dL^2+\left(\frac{2L}{n}\right)^2 df^2} \]\\  The error here was calculated for each of the modes n-3,4,5,6 and then were averaged since that what was done for the $c_2$ values. dL=.0002 meters and df=1 Hz and the error in temperature used was .001 K. The error calculated for $c_2$ were very small and all fairly constant around 0.0236 and dont shup up very well in the plot.