- #1
Terry Bing
- 48
- 6
Consider an elastic rod lying on a table. If one end of the rod is pulled/pushed along the length of the rod with speed [itex]v[/itex], the other end will not immediately start moving, because any disturbance takes time to propagate along the rod. To be precise, the other end will move after a time [itex]t=L/c[/itex] where L is the length of the rod and [itex]c=\sqrt{\frac{Young's modulus}{density}}[/itex] is the speed of longitudinal disturbance in the rod. What will happen if we (a) pull one end with [itex]v>c[/itex] (b) push the end with [itex]v>c[/itex]. (ignoring relativistic effects)
I imagine that in these cases the expression for speed of longitudinal waves I wrote isn't valid. At least in the compression case, intuitively, I think that as the strain increases, maybe the amount of deformation created by a given stress decreases, i.e Modulus of elasticity itself increases with strain after some point and can go arbitrarily high. So the object starts to behave more like a rigid body? I am just thinking out aloud , because I am not an expert on elasticity, deformations etc. I got these questions as I was reading up on waves and sound.
I imagine that in these cases the expression for speed of longitudinal waves I wrote isn't valid. At least in the compression case, intuitively, I think that as the strain increases, maybe the amount of deformation created by a given stress decreases, i.e Modulus of elasticity itself increases with strain after some point and can go arbitrarily high. So the object starts to behave more like a rigid body? I am just thinking out aloud , because I am not an expert on elasticity, deformations etc. I got these questions as I was reading up on waves and sound.
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