Relaxation-time invariance of post-collision sonic velocity

Let $\tau$ be the relaxation time in the second-order macroscopic traffic model, and consider the jamiton produced by a collision. Sonic-velocity invariance conjecture. The sonic velocity of the jamiton resulting from a collision is independent of $\tau$. Numerical experiments for $\tau=1$, $5$, and $10$ support this claim because the relevant velocity functions depend only on the sonic density; no analytical proof is given.