# Shock vs compression wave

1. Apr 5, 2006

### Cliff_J

Ok, I watched a TV show where they showed a test of a building designed to handle an attack like the OKC incident.

There was a visible overpressure wave on the high-speed film that hit the building and cracked the glass and knocked a couple pieces of sheetrock loose (the building otherwise held up very well). They listed the speed of the shock wave as something like 4000 m/s.

Since that's nearly Mach 4 and I thought speed of sound was the rate at which a pressure change equalized in the air, I found this strange. But from what I've looked up online, it seems its only true for a compression wave, not a shock wave which is denoted by its sharp change in pressure and can travel supersonic because of the sheer amount of air displaced.

First, is this correct? Its been a while since a prof talked about this in dynamics (he worked for a defense contractor) and his explanation of the rarefraction from a detonation causing more damage than the compression wave because of the flying debris didn't sit well with my idealistic thinking at the time....

Second, at what rate of change does this transition occur from compression wave to shock wave?

2. Apr 5, 2006

### sid_galt

From what I have read, a shock wave forms due to the high pressure compression waves. What happens is that in high pressure compression waves, the temperature of the air where compression is taking place increases significantly increasing the speed of sound. Thus the compression portion is travelling faster than the rarefaction portion and eventually the graph of the sound wave becomes very steep as the crescendo of the wave catches up with the trough.

But since, in reality the compression portion cannot overtake the rarefaction portion, the physics of the waves turns highly non-linear which is what we call a shock wave. Basically it is a thin region with a vast change in pressure.
From what I get, the individual particles in a shock wave travel at the local speed of sound but with respect to the ambient medium, they travel supersonically.

I don't know about the rate of change but the distance at which the shock wave is formed from a compression wave is

distance = density of air * (speed of sound)^3/((angular frequency of wave) * coefficient of non-linearity * max amplitude of wave)) [Hamilton and Blackstock, 1998]

This is known as the shock formation distance.

BTW, 4000m/s is not Mach 4, atleast not with normal air temperature. It would be more than Mach 10 (speed of sound in air = 343 m/s)

Last edited: Apr 5, 2006
3. Apr 5, 2006

### Astronuc

Staff Emeritus
4. Apr 5, 2006

### Cliff_J

Sorry, I'm confused the units, trying to post in SI when good old english units are more intuitive. Arrrgh. I converted whatever number they said to around 4000ft/s and when divided by around 1100 then that's "close" to Mach 4.

Considering the explosion took place at the setback distance (where the design would have the concrete posts to stop a charging vehicle) I was very surprised by the number being so large. I guess that's how its destructive though.

So is a shock wave a non-adiabatic process? Where there is so much excess energy the air remains slightly heated after having work done to it (locally) that caused the rise in temperature and in turn had a secondary effect of allowing the wave to propagate faster via the raised speed of sound?

So the shock wave is really just a specialized compression wave, like a sub-category that simply ends up on the non-linear part of the acoustic equations thats typically left out? I had found another website which said that even at 110db there are very weak shock waves.

http://www.americanscientist.org/template/AssetDetail/assetid/48547/page/3

5. Apr 5, 2006

### sid_galt

For a strong enough shock, the process can be considered adiabatic. However in reality ofcourse the process is not completely adiabatic, otherwise shockwaves would persist forever.

I don't quite get you. In an explosion, a massive release of energy generates excess pressures and temperatures. Relative to the hot gas, the wave travels at sonic speed. However relative to the the ambient air, the shock wave travels supersonically. As the blast volume expands, the net shock area increases, the temperatures decrease as work is done and heat transfer occurs gradually dissipating the shock wave.

From the book Fundamentals of Aerodynamics by Anderson

Keep in mind though that this refers to shock waves formed in supersonic flow like in airplanes. However the essentials are the same.

Technically the shock wave might be a subcategory of sound waves, I really don't know the official stance of the scientific community on this. But its big enough to be a subject of its own.

Given enough distance, all sound waves will form shock waves. However in weak waves, the viscous effects are much more noticeable, therefore, the wave dissipates before forming a shock wave. In strong sound waves, the viscous effects can't dissipate the wave before it forms a shock.

Last edited: Apr 5, 2006
6. Apr 5, 2006

### sid_galt

This might help

It deals with shock waves.

Check out the other chapters too by replacing Chapter3 with Chapter1, etc.

Last edited by a moderator: Apr 22, 2017
7. Apr 5, 2006

### Cliff_J

Sid, thank you very much. I was missing was frame-of-reference for the wave propagation (with respect to explosion gases and not surrounding air) and that was the missing piece that was the key to make it all more clear.

My thoughts about it not being adiabatic was again from the frame of reference issue, as in maybe it would have a bearing on it. But instead, the shock wave exists only in the localized area around the event and would then transition back into a 'regular' sonic wave after leaving that area. Now it makes more sense for an airplane or a projectile as well that would be traveling supersonic.
Thanks again.

8. Apr 5, 2006

### sid_galt

You're welcome. Just keep in mind that the frame of reference is only in regard to the temperature and not in regard to the motion.