Consider an incident normal shock wave that reflects from the endwall of a shock tube. The air in the driven section of the shock tube (ahead of the incident wave) is at \(p_{1}=0.01 \mathrm{~atm}\) and \(T_{1}=300 \mathrm{~K}\). The pressure ratio across the incident shock is 1050. With the use of Eq. (7.23), calculate

a. The reflected shock wave velocity relative to the tube

b. The pressure and temperature behind the reflected shock

\[\begin{equation*}
\frac{M_{R}}{M_{R}^{2}-1}=\frac{M_{s}}{M_{s}^{2}-1} \sqrt{1+\frac{2(\gamma-1)}{(\gamma+1)^{2}}\left(M_{s}^{2}-1\right)\left(\gamma+\frac{1}{M_{s}^{2}}\right)} \tag{7.23}
\end{equation*}\]