Chris Spencer edited Theory 2.tex  almost 10 years ago

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\subsection{First Sound}  For first sound it can be seen from figure 3 that there is a slow decrease in $C_1$ from T=0 onward except at the $\lambda$ point where there is a acusp due to theromodynamic behovior close to a transition temperature [1]. First sound also experiences attenuation peaks at $T_\lambda$ and near 1 K.   \subsection{Second Sound}  The second sound mode is special to the superfluid state of helium 4 in that its a propagating temperature and entropy wave, different from normal liquids where waves are diffuse. Here the normal fluid and superfluid move in opposite directions so that $J=0$ so $v_s=-(\frac{\rho_n}{\rho_s})v_n$ Second sound can be detected using a transducer with small pores in it where only the superfluid component, having zero viscosity, can move through the pores. Again referencing figure 3, second sound starts with dashed lines that are not observed in practice. Above 1.2 K, $c_2$ has a max at about 20.4 m/s near 1.65 K and then falls to zero at $T_{\lambda}$.  \subsection{Fourth Sound}