Chris Spencer edited data and analysis c4.tex  almost 10 years ago

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\subsection{Fourth Sound}  Fourth sound is now calculated in the same fashion as above by the equation \[c_4=f2L\] for n=1 and L=.0495 meters as before. This time though there is a scattering factor,n, that is caused by the powder in the fourth sound cell that results in a lower measured velocity for fourth sound. This scattering can be determined by the equations \[ c_4=nc_{4 exp}=\sqrt{\frac{\rho_s}{\rho}}c_1 \] coupled with the equations \[ \frac{\rho_s}{\rho_n}=\frac{\frac{\rho_s}{\rho}}{1-\frac{\rho_s}{\rho}} \] the scattering factor can be solved for. The maynard tables give a value for $\frac{\rho_n}{\rho}$ at for our lowest temperature. The lowest temperature measured was 1.34 K for fourth sound so ,rounding up to 1.35 K , the value for $\frac{\rho_n}{\rho}=.0598$. solving for $\frac{\rho_s}{\rho}$ and utilizing the value for $\frac{\rho_n}{\rho}$ , it is found that $\frac{\rho_s}{\rho}=1-.0598=0.9402. Then to find n, use the values for $c_1$ and $c_4$ for 1.34 K.\[n=\sqrt{0.9408}\frac{236.511 K}{185.229 K}=1.2385\]