Solution
= Solution
When $u_1=V/3$, the downstream speed in the shock frame is $2V/3$. Mass conservation gives
$$
\rho_0V=\rho_1\frac{2V}{3},
$$
so
$$
\boxed{\frac{\rho_1}{\rho_0}=\frac32}.
$$
= Solution
When $u_1=V/3$, the downstream speed in the shock frame is $2V/3$. Mass conservation gives
$$
\rho_0V=\rho_1\frac{2V}{3},
$$
so
$$
\boxed{\frac{\rho_1}{\rho_0}=\frac32}.
$$