# Why does a blast wave travel faster than sound?

https://en.wikipedia.org/wiki/Blast_wave#Characteristics_and_properties says: "A blast wave travels faster than the speed of sound and the passage of the shock wave usually lasts only a few milliseconds."

I thought a blast wave was a sound wave, so I don't understand this.

• There is absolutely no reason why an explosion couldn't push air molecules faster than 330 m/s. – user253751 May 8 at 12:15

I think what it is referring to is the difference between an oscillating pressure wave propagating through air molecules (like sound) and the air molecules themselves moving in one direction, without oscillation, and experiencing significant displacement (like wind).

The expanding gasses in a gun barrel, for example. The bullet is supersonic so the expanding gasses pushing it must be supersonic too, but that's not the same as the sonic boom you hear which only travels at the speed of sound.

EDIT: There is some vagueness of where the line is crossed between oscillation and displacement in my above description since it is pretty qualitative, but I found this answer: How do we get supersonic bullets?

which states the speed of sound increases with pressure, so if you have a high pressure front it will be able to move faster than sound at ambient.

I thought a blast wave was a sound wave

In the technical literature, a distinction is made between detonation, and deflagration. In both of these there is a rapid chemical reaction. The chemical reaction in one area stimulates the same reaction in a neighboring area. This creates a reaction "front", that moves rapidly from through the reactive material. The speed at which this front moves depends upon the type of "explosive". If the speed is supersonic, the "explosion" is called detonation. If the speed of the reaction front is below the speed of sound, the explosion is called deflagration. Both detonation and deflagration may cause loud "bangs" and destroy objects. So, to a casual observer, deflagration may appear similar to detonation. However the physics of detonations are different from those of deflagrations.

High explosives detonate, while black gun powder deflagrates. [Smokeless powder can detonate].

The Wikipedia article that describes as blast wave as supersonic is referring to the wave produced by detonation.

• Maybe this is a stupid question, but: what does it mean for a chemical reaction to occur at a velocity? I guess I've never really carefully thought about what units are on "fast" in phrases like "that reaction happens fast", but is it really meters/second? – Daniel Wagner May 8 at 17:11
• @DanielWagner, I thought about this for a moment, and decided that "fast" is subjective when talking about, say, a quick colour change or phase change, but regarding explosion, one could precisely talk about the power of an exothermic reaction (energy released per time), and I suppose that this is what most people mean in that context. Perhaps "vigorous" is a better term for that, though... However, googling "definition of fast chemical reaction" turned up the notion of reaction half-life, which makes perfect sense. That is, how quickly do half of the reactants become the products? – Jivan Pal May 8 at 17:18
• @DanielWagner — There is a formal definition. Regarding exothermic power, the notion of power half-life also applies, and I would guess is equal to the reaction half-life (since heat released is directly proportional to the amount of reactants consumed). The consensus seems to be that a reaction with a half-life on the order of milliseconds or less is deemed "fast". – Jivan Pal May 8 at 17:18
• @JivanPal All of that makes perfect sense to me... but doesn't fit in at all with the usage from this answer, namely, "a chemical reaction that occurs at sub-sonic speeds". The term "sub-sonic" doesn't seem obviously malleable from m/s to half-life. – Daniel Wagner May 8 at 17:22
• @DanielWagner. If you sprinkle black gunpowder on the ground in a long path, and light one end of the path, it will take some time for the reaction to reach the other end of the path. The distance between the ends of the path divided by the time between first ignition and the reaction reaching the far end is the speed of the reaction. If the black powder is packed very close together, instead of sprinkled, the speed will increase. But, as far as I know, the speed will never exceed the speed of sound for black gunpowder. On the other hand, for nitroglycerin, the speed will be supersonic. – Math Keeps Me Busy May 9 at 5:50

Note that the piston or driver of a shock wave is not limited by the speed of sound. Some common examples of pistons in Earth's atmosphere would be bullets, fighter jets, and space debris/rocks/meteors. Another example are caused by explosions, as your question eludes to.

A blast wave follows certainly relationships dependent upon initial energy, as I show in https://physics.stackexchange.com/a/242450/59023, https://physics.stackexchange.com/a/271329/59023, and https://physics.stackexchange.com/a/340487/59023.

I thought a blast wave was a sound wave, so I don't understand this.

You are correct, a shock wave is a nonlinearly steepened sound wave that has reached a balance between steepening and energy dissipation to form a stable discontinuity. Because it is being "pushed" by a piston/driver, the shock itself is not limited to the speed of sound, so long as the piston/driver has sufficient energy. As I show in the above linked answers, the Mach number, $$M$$, for a blast wave satisfies the following $$M \propto t^{-3/5} \propto R^{-3/2}$$. That is, with increasing time, $$t$$, or increasing radial distance from the explosion source, $$R$$, the Mach number will decrease. Eventually there will be no more shock wave.

Both existing answer touch the periphery of the question.

The underlying reason why the usual sound wave and the blast wave travel at different speeds is that the air (or any real-life acoustic media for that matter) is non-linear.

The acoustic waves travel by adiabatic compression and expansion if the medium. This is profoundly non-linear process.

The speed of sound squared is proportional to the elastic modulus of the media. https://en.wikipedia.org/wiki/Speed_of_sound

Elasticity of the air is the slope of the adiabatic curve.

It can be considered linear-ish for small pressure disturbances (like, less than 1% of the air pressure) and that's what the usual sound is.

A chemical explosion creates a change of pressure that is many times the atmospheric. A nuclear explosion changes the pressure by many orders of magnitude. In either case, the high pressure and temperature makes the elastic modulus of the media pretty much higher.

Roughly said, the blast wave carries its own high-pressure zone where it can travel faster.