What happens when 2 shock waves collide?

[pyroknife]

If I have 2 shock waves propagating at different speeds in a tube, let's say to the right.
Let's say initially one of the shocks (shock 1) is ahead of the other (shock 2), but shock 2 is faster than shock 1, so eventually shock 2 will catch up to #1. What happens when they catch up? Do they become one shock?

 

[Danger]

Hi. Here's some stuff that should give you a decent start:
http://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves

(My apologies for the advertising.)

 

[CWatters]

Is it possible to get two shockwaves to propagate at different velocities in the same tube? Just curious as to how you might do that.

 

[boneh3ad]

It is definitely possible to get two shock waves to propagate and different velocities in the same tube. Consider a tube with three regions of different pressure separated by two diaphragms arranged in order of decreasing pressure. Let's say they are arranged from left to right as $p_3$, $p_2$, $p_1$ and $p_3>p_2>p_1$. If you pop both diaphragms at the same time and the pressure ratios across each are sufficiently high, you can start two shocks in the same tube. Assuming the two shocks are of equal strength (pressure ratio), they will have the same Mach number but the trailing shock will be traveling through a medium with higher sound speed and therefore will eventually catch the leading shock given enough time. So the answer is yes, it is possible to do and it depends on the shock strength of the two shocks. If you made the trailing shock sufficiently weak, it would never catch up or even fall behind.

The problem with just talking about interference is that superposition only works for linear phenomena. Shock waves are, by their very definition, nonlinear, so simple superposition does not hold like that. Instead what would happen (if I recall correctly) is that the second shock would catch the first and the two would essentially merge into a new, stronger shock. After all, the first shock had a pressure ratio of $p_2/p_1$ and the second shock would have a pressure ratio of $p_3/p_2$ when it gets close to the first shock, so right when they touch, the ratio across the combined shock would then be $p_3/p_1$. This simply represents a stronger shock.

 

[pyroknife]

Thanks! What if the lagging shock was travleing at say 2m/s and the leading @ 1m/s. When the lagging shock catches up and collides with the leading shock, does stronger shock travel at a combined speed of 2+1m/s?