# What is the speed of a shock wave?

• I
gary350
TL;DR Summary
What is the speed of a shock wave?
There is lots of good information online about shock waves but I'm not finding what I want.

If dynamite has a detonation rate of 6800 m/s does the shock wave travel at 6800 m/s? Is sound we hear 1 mile away the shock wave or the sound?

What speed is an atom bomb shock wave?

This large horn is interesting watch the video.

The speed a shock wave travels depends on the pressure ratio across the shock. Higher pressure behind the shock makes it travel faster. In the case of a shock wave generated by a bomb, the pressure behind the wave decreases as it expands (since obviously the bomb only generates a certain amount of gas and energy to heat the air around it, so as the volume enclosed by the shock expands, the pressure inside the shock goes down). As a result, the shock from a bomb doesn't have a single "speed", but rather starts very fast (many times the speed of sound) and then slows down as it expands, until eventually, once the pressure is close to the same on the inside of the shock as outside, you end up with it traveling at the speed of sound.

PeroK
Homework Helper
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until eventually, once the pressure is close to the same on the inside of the shock as outside, you end up with it traveling at the speed of sound.
This is the part I have never understood. What does "close to" mean in this context?

If dynamite has a detonation rate of 6800 m/s does the shock wave travel at 6800 m/s? Is sound we hear 1 mile away the shock wave or the sound?
The detonation will propagate at 6800 m/s through the solid explosive charge.
The combustion products will be the same mass, but of compressed gas, and so be at a greater pressure and temperature.
That gas volume will flow outwards at a velocity Vm, determined by the root of the absolute temperature, T, of the compressed gasses.
For air, that would be; Vm = 331 m/s * √( T / 273 )
The shock wave is an upward step of pressure and temperature, traveling at greater than the normal speed of sound in air.
The speed of the shock wave will be reduced as it travels further and the expanding gasses cool.
The distance run before the shock velocity falls to the normal speed of sound in air will depend on how much charge was detonated.
I would hope that it is a sound wave at one mile.

This is the part I have never understood. What does "close to" mean in this context?
Depends how close to the actual speed of sound you want it to be going? It does drop to basically mach 1 pretty fast though - to drive a shock at mach 1.1 for example, the pressure behind the shock needs to be 25% higher (absolute, of course) than in front of it, and even just to get mach 1.02, you'd need a 5% overpressure behind the shock (0.7 PSI for normal atmospheric conditions).

PeroK, DaveE and hutchphd
Gold Member
This is the part I have never understood. What does "close to" mean in this context?
Atmospheric pressure is roughly 105Pa. If you look at the table of sound pressure examples in https://en.wikipedia.org/wiki/Sound_pressure#Examples_of_sound_pressure
it looks like the transition occurs by 103Pa or 1% overpressure.

There is probably a formal definition involving the amount of change of shape of the sound pulse, but I have never seen it.

hutchphd
This is the part I have never understood. What does "close to" mean in this context?
The speed of sound in gases is related to the RMS speed of particles in the gas. Since the particles have a speed distribution, once the speed of the shock wave becomes comparable with the speeds in the distribution, the step edge will begin to decay. The high frequency components of the step will then be rapidly attenuated.

gary350
I read where it says, when explosive detonates it becomes a gas, every time the gas volume doubles detonation rate reduces by 1/2. If 1 cu ft of dynamite is detonates at 6800 m/s and volume increases 100 times detonation rate should be 6800 /100 = 68 m/s. Ok that makes sense now. At some point detonation rate will become slower than speed of sound.

How does anyone know the detonation rate of a atom bomb?

Watch the first 20 seconds of this video you can see the shock wave coming.

I read where it says, when explosive detonates it becomes a gas, every time the gas volume doubles detonation rate reduces by 1/2. If 1 cu ft of dynamite is detonates at 6800 m/s and volume increases 100 times detonation rate should be 6800 /100 = 68 m/s.

If you made a long thin thread of dynamite, then detonated one end, the explosion would travel along the tread at 6800 m/s.

How does anyone know the detonation rate of a atom bomb?
The rate is not important as it is all over in an instant.
The total energy released will heat the air, which creates the shock wave.

As Baluncore said, 6800m/s isn't the speed of the shockwave created in the atmosphere, it's the rate of propagation of the detonation wave within the actual dynamite itself. As for a nuclear weapon, there's not a "detonation speed" per se. Initially, high explosives go off around the nuclear core, and this detonation wave travels at a few km/s, similar to dynamite. This is an inward traveling detonation wave from all sides though, not an outward one, since the point of this is to compress the fissile core. After a few tens of microseconds or so, this detonation wave reaches the core and collapses it together, which takes another few tens of microseconds or so.

At this point, nothing has really happened other than a fairly sizeable conventional explosion, and perhaps a hundred microseconds or so has elapsed (so the shock has barely had a chance to form, really, and not much has left the immediate vicinity of the bomb). At this point, the fission reaction starts to occur, but it takes a few hundred nanoseconds for the exponential growth to become significant. Once it has taken off though, the vast majority of fission energy gets released in another 50 nanoseconds or so. This energy is primarily released as x-rays, not as any physical "explosion". In a pure fission bomb, these X-rays are then absorbed by the surrounding atmosphere (and/or ground, buildings, or anything else in the immediate vicinity of the bomb, and it's the massive heating and vaporization of these surrounding materials that actually causes the huge pressure spike that generates the shock wave.

In a more modern thermonuclear (fusion) bomb, there's one additional stage where this initial radiation energy is then used to compress a second stage, causing fusion, but this energy release all happens across a timescale of tens to hundreds of nanoseconds (and I would think the compression of the secondary is on timescales of tens of microseconds, similar to the primary, but I can't actually find confirmation of this, and I'm not sure if that's even publicly available information), and is followed by basically the same events afterwards (the fusion energy is dumped into the surrounding atmosphere and heats/vaporizes everything around the bomb, creating a shockwave)

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berkeman
gary350
When explosive goes off do we hear the sound or hear the shock wave or does the shock wave make no sound?

When explosive goes off do we hear the sound or hear the shock wave or does the shock wave make no sound?
When you are inside the shock wave zone, you "sense" or "feel" a click, without any audible lower frequencies. Try to avoid being inside a shock wave zone, it is not a good place for your nervous system.

Outside the shock wave zone, you "hear" a sound like a gun, a thump, or the rumble of thunder.