Sound Waves and Shock Waves

JustWonderingx

I'm just trying to get a better grasp on sound waves and shock waves.

Let's say I have a cylindrical rod of length L with no forces acting on it, and I push on the back of it with some constant velocity less than the speed of sound, c, of the material the rod is made of. Will the front of the rod not move until time=L/c?

Now let's say I push on the same rod with a velocity, V, greater than c, and the material cannot fracture but can deform transversely. Would the length of the rod approach 0 at time=L/V as the back of the rod approaches the front? In this situation is the shockwave moving at velocity V?

Thanks

phinds

c has nothing to do with propagation in a rod. It happens at the speed of sound in the material.

You cannot push on the rod faster than c. This is physically impossible, so that part of your question is meaningless.

JustWonderingx

I specified in my post that I am defining c as the speed of sound in the material.

phinds

Ah ... I missed that. BAD choice of symbols.

JustWonderingx

I disagree, c is frequently used as a symbol for sound speed. But we digress.

phinds

Fair enough. I didn't know that and I now notice that this is posted in general physics, not cosmology, which is where my mind was. Sorry to have temporarily derailed your thread.

AlephZero

It's not obvious you can push the rod at a constant speed greater than the speed of sound, without using an "infinite" amount of force. The elastic modulos of mateirals in compression tends to increase, at least until the matieral fails in crushing. A compressive strain of more than 100% is impossible, if you think about what it would mean physically.

The question makes better sense "in real life" if you think about pulling the end of the rod rather than pushing it. In that case, you are right that the far end will not move untill the stress wave has travelled the lengtth of the rod, indepedent of how fast or hard you pull.

FWIW I've seen this happen, in a "fail safe" device that pulled a rod violently to stop part of a machine working. In a test (using high speed video etc to see what happened) the rod broke near the end that was pulled, but the tensile stress wave continued along the rod and moved the other end after the rod had broken, even though there was no pulling force acting on the rod after it broke.

BTW "c" is a standard symbol for the speed of sound, if that is a more interesting quantity for modelling the situation than the speed of light.

JustWonderingx

I don't understand why you would need an "infinite" amount of force to push something faster than its speed of sound. If I have a rod with a low sound speed material, and I impact the back of it with a much harder, much more massive object moving at a speed, V, much greater than the rod's sound speed, c, wouldn't part of the rod be moving at a speed greater than it's sound speed as this object pushes it, while the other end remains undisturbed?

I feel like upon initial impact the atoms in the back plane of the rod begin moving with speed ~V. Since c<V, the next plane of atoms, and all subsequent planes, don't know the impact has occurred and cannot have increased their rigidity, and thus cannot have increased their sound speed.