The Wikipedia defintion of a shock wave pretty much sums up all I've found online about what a shock wave is:

A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium (solid, liquid, gas or plasma) or in some cases in the absence of a material medium, through a field such as an electromagnetic field. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow.... A shock wave travels through most media at a higher speed than an ordinary wave.

To me, however, this doesn't seem to provide a very rigorous definition that would allow me to look at a bunch of propagating disturbances and be able to clearly classify it as being a shock wave or (as Wikipedia puts it) a "normal" wave. Although this definition provides a qualitative definition of what sets a shock wave apart from a normal wave, I am wondering if there is a definite difference between a shock wave and normal waves that would allow me to definitively classify a wave as one or the other or if there is a continuous spectrum of wave properties between normal waves and shock waves with no clear boundary between the two (like the electromagnetic spectrum, with only arbitrary boundaries being drawn between the various classes of EM waves).

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    $\begingroup$ The quote you cited does say right at the end that a shock wave travels through most media at a higher speed than an ordinary wave. If you know the speed of sound of a medium, then it is relatively cut and dried to say that any wave travelling faster than this is a shock wave $\endgroup$ – Jim Aug 20 '14 at 14:37
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    $\begingroup$ A better definition of the term can be found in britannica.com/EBchecked/topic/541339/shock-wave. In general, to have a shockwave usually requires a phenomenon that exceeds the local sound velocity. $\endgroup$ – CuriousOne Aug 20 '14 at 14:38
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    $\begingroup$ To paraphrase the US Supreme Court: I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description ["shock wave"]; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it... $\endgroup$ – tpg2114 Aug 20 '14 at 14:39
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    $\begingroup$ Joking aside, what part of the definition you've given trips you up? Faster propagation, nearly discontinuous change in properties... What is not precise enough for you to identify a shock? $\endgroup$ – tpg2114 Aug 20 '14 at 14:40
  • $\begingroup$ @tpg2114 As I said in my question, I am wondering if there is a distinct change in the wave properties (such as pressure and temperature) as one goes from subsonic to supersonic speeds or if it is a more gradual transition in the properties as one crosses the $v=c$ boundary. Put another way, are shock waves completely distinct from ordinary waves in properties (as crystalline solids are from liquids) or is there a spectrum of properties in the transition (such as an amorphous solid becoming a liquid). $\endgroup$ – NeutronStar Aug 20 '14 at 15:06

The first thing that distinguishes a shock wave from an "ordinary" wave is that the initial disturbance in the medium that causes a shock wave is always traveling at a velocity greater than the phase velocity of sound (or light) in the medium. Notice that I said light - that is because there is also a kind of electromagnetic analogue to a shock wave known as Cherenkov radiation (Wikipedia article is here )that is created when a charged particle travels through a medium at a velocity faster than that of the phase velocity of light in the medium (which for many media is some fraction of c).

So getting back to acoustic waves in a gas, the main characteristic that divides a shock wave from an ordinary wave is the thermodynamics of the changes in pressure and temperature due to the wave. For ordinary waves (disturbance less than the phase velocity of sound), the compression and rarefaction of the gas does not entail a change in entropy of the gas - thus an ordinary wave is a reversible process thermodynamically speaking.

For shock waves, this is not the case. The process of compression and rarefaction caused by a shock wave is an irreversible process - it leads to a change in entropy of the gas.

Why is this the case ? Without going too deep into the mathematics, it relates to your question as to how distinct shock waves are from ordinary sound waves. The zone of discontinuity is quite sharp between the disturbance and the shock waves, and the changes in pressure, temperature, and density are large enough that dissipative effects like heat transfer and gas friction come into play.

The boundary conditions involved in analyzing shock waves are known as the Rankine-Hugoniot conditions. The Wikipedia article on Rankine-Hugoniot conditions is actually more detailed about explaining shock waves than the Wikipedia article on shock waves itself.

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    $\begingroup$ The main distinction between shock waves and compression waves is not the change in entropy of the gas. Even for compression waves, there is a change in entropy, it is so small that it is often neglected. The transition, if you will is a grayscale and not black-and-white. There's more to shock waves than this. $\endgroup$ – user3814483 Sep 21 '14 at 20:58
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    $\begingroup$ @user3814483 Feel free to write a more detailed answer if you wish- I tried to match mine to the detail level of the question. $\endgroup$ – paisanco Sep 22 '14 at 0:45

Well, shock waves are kind of inappropriately named because they do not oscillate, they are actually a discontinuity. A shock wave is the final stage of a nonlinearly steepening wave that has reached a balance between steepening and energy dissipation (i.e., irreversible energy transformation). An contrasting example would be water waves, where there is insufficient energy dissipation to limit steepening resulting in wave breaking (e.g., white caps or waves that surfers like).

In regular fluids like Earth's atmosphere, energy dissipation arises from binary particle collisions that transform the bulk flow kinetic energy into random kinetic energy (i.e., heat). Sound waves can produce heat as well, but the primary difference is the abrupt and sustained increase in bulk flow speed, density, and thermal pressure across a shock wave (Obviously, if one moves far enough away from a shock, the system will asymptotically return to a quasi-equilibrium with the background... but that's being nit-picky).

In short, shock waves are very different from "normal" waves, using your terminology.

I have a more exhaustive answer here that gives a better explanation of what exactly is a shock wave and how they can form.

  • $\begingroup$ What exactly does "nonlinearly steepening wave" mean? $\endgroup$ – NeutronStar Jul 10 '15 at 16:15
  • $\begingroup$ I guess the simple answer would be a wave that satisfied $\mathbf{V} \cdot \nabla \mathbf{V} \neq 0$. $\endgroup$ – honeste_vivere Jul 11 '15 at 0:00

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