A normal shock is moving with a speed $550$ m$/$s into still air at $1$bar and $160$C$.$

$($a$)$Compute the pressure, temperature and velocity downstream of the shock wave.

$($b$)$Compute the stagnation pressure and temperature downstream of the shock. Are

they larger$/$smaller$/$equal to the stagnation pressure and temperature upstream of the

shock?

$($c$)$ Explain and resolve any inconsistencies that you find in $($b$)$ from your understanding

of the change of stagnation properties across a normal shock.