# Shock-wave physics

I was hoping to gain a general understanding of how shock-waves propagate a medium such as the air. Let me explain what I am curious about by stating an example I thought about.

Let's say we have two different explosives. Each explosive weighs the same, and contains the same total energy.

One of the explosives creates a very fast expansion and very high pressure. The second explosive is a bit slower; its shock-wave lasts longer but at a lower pressure than the first.

Up close, one of the explosives clearly leaves different effects on objects. Because of ones higher pressure, objects like metals may be deformed, while the lower pressure one could not do this the same. However, what about if at some distance away from both explosives, the shock-wave was observed that travels through a mild medium such as the air. Could the difference of these two waves still be seen, and all the way out until the complete wave was gone? At some distance do the waves both evolve and become the same, with equal length and pressure?

I believe that waves must all slow to reach the speed of sound in the given material after some distance. Since the speed of all waves becomes the same in a given medium, duration and height are only left to change with total distance propagated. My hypothesis is that only the height of the wave would decrease, because the wave duration changing would mean that a sound would change frequency at distance, but sounds do not change frequency unless effected by doppler effect. I would surely like to learn more on this topic. Thanks

## Answers and Replies

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SpectraCat
Science Advisor
A shock wave from a detonation is by definition supersonic. It is clear that a slower detonation produces a smaller shock wave, and in the lower limit, you get a sub-sonic shock wave, such as from a deflagration.

If I recall correctly, the direct damage from a shock wave is caused by the jerk (or time-derivative of acceleration) associated with the highly-compressed gas traveling ahead of the supersonic wave. Thus I think it's all about speed of detonation on this one, and the two shock waves will remain different throughout their relative propagations.

Andy Resnick
Science Advisor
Education Advisor
I was hoping to gain a general understanding of how shock-waves propagate a medium such as the air. Let me explain what I am curious about by stating an example I thought about.

Let's say we have two different explosives. Each explosive weighs the same, and contains the same total energy.

One of the explosives creates a very fast expansion and very high pressure. The second explosive is a bit slower; its shock-wave lasts longer but at a lower pressure than the first.

Up close, one of the explosives clearly leaves different effects on objects. Because of ones higher pressure, objects like metals may be deformed, while the lower pressure one could not do this the same. However, what about if at some distance away from both explosives, the shock-wave was observed that travels through a mild medium such as the air. Could the difference of these two waves still be seen, and all the way out until the complete wave was gone? At some distance do the waves both evolve and become the same, with equal length and pressure?

I believe that waves must all slow to reach the speed of sound in the given material after some distance. Since the speed of all waves becomes the same in a given medium, duration and height are only left to change with total distance propagated. My hypothesis is that only the height of the wave would decrease, because the wave duration changing would mean that a sound would change frequency at distance, but sounds do not change frequency unless effected by doppler effect. I would surely like to learn more on this topic. Thanks

Shock fronts can attenuate as they propagate:

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4152320

And this has been modeled for propagation in viscous fluids:

http://adsabs.harvard.edu/full/1993EM&P...62..273O

For explosions:

http://www.google.com/url?sa=t&sour...sg=AFQjCNElefmK-IVU2nwgby81h_LV4SjdQQ&cad=rja

And viscoelastic materials:

http://www.google.com/url?sa=t&sour...sg=AFQjCNFjeKdNh8Y_hCYGODe5fe8wMns6QQ&cad=rja

cjl
Science Advisor
Interestingly enough, the shock wave behavior far from the source is only dependent on the pressure jump across the wave (which I would imagine is proportional to the total energy released, and inversely proportional to the square of the distance, assuming a spherical wavefront). Even a very slow energy release, if of sufficient total energy, will create a shock, since the lagging waves will catch up to the leading waves until there is a single shock (and the gradient of pressure and other properties across the shock will not depend on how it was created).