Shock Waves

Type of physical science: Classical physics

Field of study: Fluids

A shock wave is a very sharp, thin, compression wave front generated when chemical, nuclear, electrical, or mechanical energy is suddenly released or deposited in a gas, liquid, or solid occupying a limited space. Shock waves travel at supersonic speeds, and as they propagate, they raise the pressure, density, and temperature of the medium in which they travel. These changes to the medium often have annoying or destructive results.

Overview

When a source of sound moves at subsonic speeds, the frequency of the sound is altered by the Doppler effect. If a source of sound moves faster than the speed of sound, a shock wave occurs. When a shock wave is formed, the source producing it is actually "outrunning" the waves it creates. When the source is traveling at the speed of sound, the waves it emits in the forward direction "pile up" directly in front of it. When the source moves at supersonic speed, the waves pile up on one another. The different wave crests overlap one another and form a single large crest, which is the shock wave. A shock wave is essentially the result of constructive interference of a large number of waves. A shock wave in air is analogous to the bow wave of a boat traveling faster than the speed of the water waves it produces.

A shock wave, then, is a disturbance moving through a medium at supersonic speed accompanied by an extremely rapid rise in pressure, density, and temperature. Shock waves arise from a sudden release of chemical, nuclear, electrical, or mechanical energy in a limited space.

Such waves can be generated by the detonation of high explosives (chemical energy), the passage of an aircraft traveling at supersonic speeds (mechanical energy), or the discharge of lightning bolts (electrical energy). Unsustained shock waves lose energy through viscous dissipation and are reduced to sound waves. Examples of such sound waves include thunder generated by lightning and sonic booms generated by jet aircraft.

A shock wave is a specialized type of stress wave. The most familiar type of stress wave is the pressure, or sound wave. It is a progressive wave that travels through homogeneous fluids (liquids or gases) at a constant speed. The amplitude of the wave can be described as a pressure fluctuation or as a variation in particle velocity. In pressure waves, the particle velocity is much slower than the propagation velocity of the wave, and the direction of the particle velocity is longitudinal, that is, parallel to the direction of propagation. A key aspect of pressure waves is that they generate no shear stress (stress that causes deformation without any change in volume) or differential stress (a condition in which the stress components are not the same in every direction).

In homogeneous solids, there are two principal types of stress waves: longitudinal and transverse. While longitudinal waves move in the same direction as the direction of energy transfer, transverse waves travel in a direction perpendicular to the direction of propagation.

Transverse waves arise because solids resist compression, distortion, and change in their shape.

Transverse waves travel more slowly than longitudinal waves. Because the speed of transverse waves is less than that of longitudinal waves, the magnitude of stress (force per unit of area) in a transverse wave is less than in a longitudinal wave. Stresses generated by transverse waves are pure shear; thus, the strength of a transverse wave is limited by the shear strength of the medium through which it is traveling, whereas the strength of longitudinal waves has no limit. As liquids have no shear strength, and transverse waves are pure shear, transverse waves do not propagate through fluids.

Another type of stress wave is the elastic wave. Elastic waves are more complex than pressure waves because, unlike gases or liquids, elastic materials can support differential stresses.

The particle velocity and stress in an elastic wave increase as the strength of an initial disturbance increases. Ultimately, the stress reaches a limiting value beyond which plastic, or irreversible, distortions occur in the medium through which the wave is propagating. This plastic yielding affects both the shape and speed of the stress wave. The onset of this plastic wave behavior occurs at a pressure value for the medium known as the Hugoniot elastic limit. Once the wave passes the Hugoniot elastic limit for the medium, its pressure increases dramatically.

Elastic waves are linear, meaning that they arrange themselves in a linelike manner; the result is that they can be superimposed upon themselves. Yet, plastic waves are nonlinear and as a result cannot be superimposed.

The speed at which a wave is propagating drops precipitously once it exceeds the Hugoniot elastic limit. In an elastic wave, the shear modulus (a value relating rigidity) and bulk modulus (a value relating compressibility--pressure changes on a body) contribute to the longitudinal wave velocity. When the speed of the wave passes the Hugoniot elastic limit, only the bulk modulus contributes significantly, dropping the overall wave speed to nearly that of the bulk wave speed. Because of the high pressure in waves that exceed the Hugoniot elastic limit, and because the bulk modulus increases with pressure, the bulk wave speed in a high-pressure wave is greater than that in a low-pressure wave. In very strong stress waves (shock waves), this effect is so large that the bulk wave speed rises above the longitudinal wave velocity.

Since the propagation speed of a plastic wave is less than that of an elastic wave, any disturbance powerful enough to produce a wave exceeding the Hugoniot elastic limit actually produces two waves: an elastic precursor that travels at the longitudinal wave velocity and in which the longitudinal stress equals the Hugoniot elastic limit, and a slower-moving "plastic" stress wave that travels slightly faster than the bulk wave speed. When a disturbance produces one of these strong "double pulse" compression wavefronts, the stress in the wave first jumps to the Hugoniot elastic limit in the faster elastic precursor, then rises to its final value in the slower plastic wave. In extremely strong compression waves, the plastic wave actually travels faster than the elastic precursor; at this point, the plastic wave is supersonic. The result of the plastic wave's velocity exceeding the elastic precursor's velocity is a single sharp rise in pressure: a shock front.

The fundamental equations describing abrupt shock fronts were derived in 1887 by French physicist Pierre Henri Hugoniot.

Shock waves, like plastic waves, are nonlinear. Since a shock wave travels faster than sound, a propagating shock wave can overrun elastic waves and add the elastic wave's energy to its own. The double-pulse structure of plastic waves is eliminated by the development of a single-pulse supersonic shock front. Shock fronts are usually abrupt and represent a discontinuous jump of pressure, density, particle velocity, and internal energy.

Behind the shock front, where pressure tails off rapidly from its peak value to its pre-shock ambient value, is the wave's rarefaction phase. Rarefaction relieves the high pressure generated in a shock wave by propagating release waves from free surfaces into the medium undergoing shock. This release wave is a pressure wave, not a shock wave, and travels at the speed of sound in the medium. At any instant, immediately ahead of the shock front, the medium through which the shock is propagating remains undisturbed. Yet, an infinitesimal distance behind the shock front, the medium is in a shocked state: It is compressed to a higher density, and its particles are accelerated. This additional particle velocity behind the shock, added to the wave's propagation speed, permits the rarefaction portion of the shock wave to travel faster than the shock front itself. Material engulfed by the shock wave is rapidly accelerated by the sharp pressure gradient at the shock front. At the same time, material affected by rarefaction is accelerated down a more gradual pressure gradient, allowing the compressed material to expand to a low pressure. Gradually, the rarefaction part of the wave overtakes the shock front, and the entire shock wave simultaneously lengthens and decreases in amplitude as it travels. The strength of the shock declines rapidly when the rarefaction catches up with it. In a sense, the shock front, by accelerating particles as it passes, sets in motion its own destruction.

The ultimate cause of this difference in particle velocities produced by a passing shock wave and its accompanying release wave is thermodynamic (the relation of heat to energy). A shock wave conserves mass, energy, and momentum as it compresses the material through which it is traveling. The rarefaction, release wave, conserves all of these as well as entropy (heat absorbed divided by the thermodynamic temperature). Shock compression is thermodynamically irreversible, while rarefaction is reversible and adiabatic (occurs without gain or loss of heat).

Release from high pressure, besides accelerating material down the pressure gradient established by rarefaction, may also result in a change of state for the medium shocked. The state of the shocked medium after release depends on the peak shock pressure it experienced. Shock compression deposits a large amount of internal energy into the medium, and since a shock is not thermodynamically reversible, much of this energy remains as heat even after decompression. If a solid undergoes modest shock pressures, it becomes a hot solid. Materials released from progressively higher shock pressures and higher heat produce first liquid, then vapor.

Applications

Shock waves encountered on Earth are generated both naturally and artificially.

Naturally occurring shock waves result from lightning, volcanic eruptions, earthquakes, and meteorite impacts. Shock waves are generated artificially by supersonic jet aircraft, bull whips, spacecraft re-entering the atmosphere, chemical explosives, and nuclear weapons. In many of these examples, the resulting shock wave phenomena cause severe damage to natural and man-made objects.

Materials that have experienced the passing of a shock wave often undergo a change of state. Passing shock waves can permanently alter the electrical and electronic properties of matter. Gases compressed to high temperatures by shock waves may become luminescent. Shock pressures can bond dissimilar metals and also increase the hardness of many metals. A common application of shock waves is the simple volume compression of materials.

One of the most interesting by-products of shock waves is the effect they have on rocks and minerals. When a rock or mineral is exposed to a transient, high-pressure shock wave, its state is often altered by a process known as shock metamorphism. Natural shock metamorphism is produced by the nearly instantaneous transfer of kinetic energy by means of intense shock waves directly into the rocks. The results of this quick energy transfer have distinct and dramatic effects on the density, crystal structure, and composition of the rock. The only known natural method of producing such effects is the hypervelocity impact of a large meteorite.

The two most common by-products of shock waves encountered on Earth are thunder and sonic booms. A sonic boom is the result of an observer sensing the passage of the pressure or shock wave that an aircraft causes when it travels through the atmosphere at supersonic speeds.

The sonic boom is simply the noise generated by air displaced by the aircraft as it travels faster than the speed of sound. Physically, the sonic boom is analogous to the bow wave created by a moving boat. A boat moving over still water compresses surface waves before it, forming a wake. A sonic boom is generated when an aircraft, traveling through the still atmosphere, compacts the pressure waves it is forming in front of itself. All aircraft produce pressure waves, but when they are flying at subsonic speeds (Mach numbers less than one) the pressure waves move away in all directions at the speed of sound and are too weak to be heard. These pressure waves propagate like concentric wavelets generated when an object is dropped into still water.

When the aircraft's speed is supersonic (Mach numbers greater than one), or hypersonic (Mach numbers greater than five), the pressure waves cannot get away ahead of the vehicle, as their natural speed is slower than that of the aircraft. Slower means slightly more than 1,200 kilometers per hour at sea-level conditions (15 degrees Celsius). Because they cannot get away, a shock front develops across which significant and discontinuous changes in air density and temperature occur. Above Mach 1, the aircraft outruns the speed at which pressure waves can travel, and the pressure disturbances coalesce and lag behind the aircraft, which is in effect traveling at the apex of a conical shock wave. The entire atmosphere in front of the main shock remains undisturbed. Ultimately, the pressure waves form two conical shock waves, the main shock wave (compression shock) being generated by the nose of the aircraft, and the tail shock (collapse shock) at the aircraft's rear. The conical main shock wave trails the aircraft like the bow waves of a boat. Any observer contacted by these shock waves would hear the sonic boom. Actually, the sonic boom is a double boom, since a shock wave forms at both the front and the rear of the aircraft.

Even the most modest sonic boom can startle humans and animal life. A common impression is that sonic booms occur only when an aircraft "breaks the sound barrier" as it travels from subsonic to supersonic speeds. In reality, the main shock wave is created continually and propagates as long as the aircraft remains at supersonic speeds. Several observers on the ground will each hear a loud "boom" as the shock wave passes.

Thunder is probably the most common example of a shock wave that people encounter.

During electrical storms, lightning releases heat energy into the atmosphere, displacing air in a manner similar to a supersonic aircraft. The shock waves generated by a lightning bolt, traveling at speeds far greater than that of sound, produce thunder.

The sharp crack of a bull whip is also attributed to a small sonic boom. As the whip is thrown forward and then snapped quickly backward, the tip exceeds the speed of sound, displaces the surrounding air, and produces a weak shock wave.

Context

Naturally generated shock waves have always played a role in the history of humankind. The clap of thunder, the concussion from an exploding volcano, and the rumble of an earthquake are all the result of shock waves and are a constant reminder that humans inhabit a dynamic planet. With the invention of gunpowder, and eventually chemical explosives, humankind has been able to generate shock waves of ever-increasing magnitude. When such powerful shock waves travel through an undisturbed medium (gas, liquid, or solid), the pressure, temperature, and density of the disturbed state are increased many times over. As a result, when living things or structures are hit by such a strong shock wave, they are destroyed by the violent pressure change they experience. Historically speaking, it is this knowledge and the eventual use of shock waves as a destructive weapon that changed the way in which warfare is conducted.

With the invention of nuclear weapons, humankind has increased its ability to generate shock waves artificially to a horrific level.

Despite the self-destructive use to which humankind has put its knowledge of shock waves, there are also a number of peaceful applications. Explosives are necessary for building roads, tunnels, and mines; forming metals; and, under controlled circumstances, propelling spacecraft.

A number of universities and government-sponsored laboratories exist that have mechanical, electric, and chemical-driven shock tubes; supersonic wind tunnels; hyperballistic firing ranges; and chemical explosives all used to study both the peaceful applications and destructive effects of shock waves.

The study of shock waves is important because a clear understanding of shock wave-associated phenomena aids in the construction of earthquake-resistant buildings, the efficient and safe design of jet aircraft and space vehicles, the detection of underground nuclear explosions, a number of specific applications in medicine, and the development of protective coverings and armors. Shock waves provide a clearer understanding of the physical forces that shape the planet, solar system, and universe.

Principal terms

DOPPLER EFFECT: a change in the observed frequency of electromagnetic or sound waves, caused by relative motion between the source and the observer

HUGONIOT ELASTIC LIMIT: the greatest stress that can be developed in a material without permanent deformation remaining when the stress is released

MACH NUMBER: the ratio of the velocity of an object to the speed of sound in the surrounding medium

PARTICLE VELOCITY: the velocity of a small area of the medium (smaller than a wavelength but larger than an atom) that is alternately accelerated and decelerated as a wave passes

RAREFACTION: the process by which high pressure in a shock wave is relieved by the propagation of release waves from free surfaces into the shocked material

SHOCK FRONT: a supersonic shock pulse abrupt to the point where it is often represented as a discontinuous jump of pressure, density, internal energy, and particle velocity

SHOCK METAMORPHISM: a term used to describe changes in rocks and minerals resulting from the passage of transient, high-pressure shock waves

SONIC BOOM: a loud transient explosive sound caused by a shock wave preceding an object traveling at supersonic speeds

SOUND BARRIER: the point of sharp increase in aerodynamic drag experienced by an object approaching the speed of sound

SUPERSONIC: having a velocity greater than the speed of sound in a given medium

Bibliography

Courant, Richard, and K. O. Friedrichs. SUPERSONIC FLOW AND SHOCK WAVES. New York: Interscience, 1948. Although somewhat dated, a thorough treatment of the principles and physics of shock waves. Emphasis on mathematics.

French, Bevan M., and Nicholas M. Short, eds. SHOCK METAMORPHISM OF NATURAL MATERIALS. Baltimore, Md.: Mono, 1968. This volume contains the Proceedings of the First Conference on Shock Metamorphism of Natural Materials, held in Greenbelt, Maryland, in 1966.

Glass, I. I. SHOCK WAVES AND MAN. Toronto: University of Toronto Institute for Aerospace Studies, 1974. A broad, easy-to-read discussion of natural and man-made shock waves. Richly illustrated and contains an extensive bibliography. Provides understandable answers to questions such as: What is a shock wave? Where do they occur? How do they affect human life? An excellent reference source.

Wiggins, J. H. EFFECTS OF SONIC BOOM. Palos Verdes Estates, Calif.: Author, 1969. Discusses the damaging effects of shock waves, especially when they result from a sonic boom. Richly illustrated with easy-to-understand graphs, charts, and drawings.

Zel'dovich, Y. B., and Y. P. Raizer. PHYSICS OF SHOCK WAVES AND HIGH-TEMPERATURE HYDRODYNAMIC PHENOMENA. New York: Academic Press, 1967. A two-volume book, superbly written, though highly technical, on shock physics. Chapter 1 gives a clear and complete discussion of the formation and propagation of stress waves (pressure, elastic, plastic, and shock). While intended for the scientist, if carefully read, the book can be of great informational value to the nontechnical reader.

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