Consider a shock$-$shock interaction problem generated by

compression corners with ${}_1=30$ and ${}_2=30($The same$).$ The Mach number ahead of the corners is $4\mathrm{.}0$; the flow pressure and temperature are $p_{}=100$kPa and $T_{}=300K.$

a$)$ Calculate the Mach number at $(2)$ and $(3).$

b$)$ Obtain the pressure, temperature, and Mach number at $(4)$ and $(4).$

c$)$ if ${}_1$ is lager than ${}_2,$ Discuss what happens at $(4)$ and $(4)$