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What would happen if you were to accelerate one end of a material, say a steel rod for instance, at faster per second than the speed of sound in that material?

For example, if the speed of sound in steel is 6100m/s, what would happen if you pushed the end of that piece of steel at more than 6100m/s/s?

This only occurred to me because I heard that the speed of sound is the speed an impulse travels through a material, and I was wondering if there could be some sort of limit to acceleration which would arise from this.

I appologize in advance if I'm comparing apples with irrelevant oranges. Thanks!

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"One second" is not a time scale relevant to a piece of steel, so there is nothing special about an acceleration of the speed of sound divided by one second.

If you smack the steel hard enough that some pieces of it are going faster than the speed of sound, you can set up a shock wave which travels faster than sound. So waves in general do not have to travel at the speed of sound; that is just the speed that small mechanical disturbances travel.

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If your acceleration exceeds the speed of sound divided by one second, it simply means that starting from the rest, you exceed the speed of sound in one second.

Similarly, if your acceleration is greater than the speed of sound divided by one minute, then your speed will exceed the speed of sound in one minute.

There is nothing special about one second. Yes, if you're comparing accelerations with speeds, you are comparing apples with oranges – we say that you are comparing quantities with different dimensions – and it doesn't help that you divide it by 1 second. If you divide it by 0.034 seconds, one minute, or one week, it would still be comparing apples with oranges.

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As Mark says there is nothing magical about 1 second, but I'm trying to guess why you are asking and get at the physics that apply under those circumstances.

If we assume a steady state (i.e. you have increased the acceleration slowly and and therefore maintained the material in equilibrium) then the only thing to ask is if the stuff you've chosen will stand up to the internal stresses.

This is the case in a high speed centrifuge, and obviously the structure of the machine is able to withstand some extremely high accelerations (and indeed support the sample too).

If you are thinking of suddenly applying these kinds of accelerations at the boundary of the material the problem becomes equivalent to to a high speed impact. The rule there is that at kilometers per second relative speeds everything is a liquid: thin pieces of plastic film impacting on steel cause the metal to flow and splash. That is because the speed of sound represents the speed at which a solid can adjust to accommodate new stresses. Deformations in the shock wave are unlikely to be elastic and they are dissipative so they can not travel over arbitrarily long distances even with a favorable geometry.

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