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109-833: High-order explosives (HE) are more powerful than low-order explosives (LE). HE detonate to produce a defining supersonic over-pressurization shock wave . Sources of HE include trinitrotoluene ( TNT ), C-4 , Semtex , nitroglycerin , and ammonium nitrate fuel oil ( ANFO ). LE deflagrate to create a subsonic explosion and lack HE's over-pressurization wave. Sources of LE include pipe bombs , gunpowder , and most pure petroleum-based incendiary bombs such as Molotov cocktails or aircraft improvised as guided missiles. HE and LE induce different injury patterns. Only HE produce true blast waves. The classic flow solution—the so-called Taylor–von Neumann–Sedov blast wave solution—was independently devised by John von Neumann and British mathematician Geoffrey Ingram Taylor during World War II . After

218-444: A l = γ ⋅ p ρ = γ ⋅ R ⋅ T M = γ ⋅ k ⋅ T m , {\displaystyle c_{\mathrm {ideal} }={\sqrt {\gamma \cdot {p \over \rho }}}={\sqrt {\gamma \cdot R\cdot T \over M}}={\sqrt {\gamma \cdot k\cdot T \over m}},} where This equation applies only when

327-402: A dispersive medium , the speed of sound is a function of sound frequency, through the dispersion relation . Each frequency component propagates at its own speed, called the phase velocity , while the energy of the disturbance propagates at the group velocity . The same phenomenon occurs with light waves; see optical dispersion for a description. The speed of sound is variable and depends on

436-409: A sound wave as it propagates through an elastic medium. More simply, the speed of sound is how fast vibrations travel. At 20 °C (68 °F), the speed of sound in air is about 343  m/s (1,125  ft/s ; 1,235  km/h ; 767  mph ; 667  kn ), or 1  km in 2.91 s or one mile in 4.69 s . It depends strongly on temperature as well as the medium through which

545-426: A sound wave is propagating. At 0 °C (32 °F), the speed of sound in air is about 331 m/s (1,086 ft/s; 1,192 km/h; 740 mph; 643 kn). The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior. In colloquial speech, speed of sound refers to

654-404: A blast that starts on the opposite side of the building. Scientists use sophisticated mathematical models to predict how objects will respond to a blast in order to design effective barriers and safer buildings. Mach stem formation occurs when a blast wave reflects off the ground and the reflection catches up with the original shock front, therefore creating a high pressure zone that extends from

763-420: A chemically pure compound, such as nitroglycerin , or a mixture of a fuel and an oxidizer , such as black powder or grain dust and air. Some chemical compounds are unstable in that, when shocked, they react, possibly to the point of detonation. Each molecule of the compound dissociates into two or more new molecules (generally gases) with the release of energy. The above compositions may describe most of

872-453: A compression wave in a fluid is determined by the medium's compressibility and density . In solids, the compression waves are analogous to those in fluids, depending on compressibility and density, but with the additional factor of shear modulus which affects compression waves due to off-axis elastic energies which are able to influence effective tension and relaxation in a compression. The speed of shear waves, which can occur only in solids,

981-410: A computation of the speed of sound in air as 979 feet per second (298 m/s). This is too low by about 15%. The discrepancy is due primarily to neglecting the (then unknown) effect of rapidly fluctuating temperature in a sound wave (in modern terms, sound wave compression and expansion of air is an adiabatic process , not an isothermal process ). This error was later rectified by Laplace . During

1090-402: A crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant crest wave amplitude is increased, forming a much more powerful wave than either of the beginning waves. Similarly two troughs make a trough of increased amplitude. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude

1199-410: A decrease (destructive interference). In this way the interaction of blast waves is similar to that of sound waves or water waves. Blast waves cause damage by a combination of the significant compression of the air in front of the wave (forming a shock front ) and the subsequent wind that follows. A blast wave travels faster than the speed of sound , and the passage of the shock wave usually lasts only

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1308-634: A degree of water resistance. Explosives based on ammonium nitrate have little or no water resistance as ammonium nitrate is highly soluble in water and is hygroscopic. Many explosives are toxic to some extent. Manufacturing inputs can also be organic compounds or hazardous materials that require special handling due to risks (such as carcinogens ). The decomposition products, residual solids, or gases of some explosives can be toxic, whereas others are harmless, such as carbon dioxide and water. Examples of harmful by-products are: "Green explosives" seek to reduce environment and health impacts. An example of such

1417-460: A few milliseconds. Like other types of explosions, a blast wave can also cause damage to things and people by the blast wind, debris, and fires. The original explosion will send out fragments that travel very fast. Debris and sometimes even people can get swept up into a blast wave, causing more injuries such as penetrating wounds, impalement and broken bones. The blast wind is the area of low pressure that causes debris and fragments to rush back towards

1526-430: A free field: that is, with no surfaces nearby with which it can interact. Blast waves have properties predicted by the physics of waves . For example, they can diffract through a narrow opening and refract as they pass through materials. Like light or sound waves, when a blast wave reaches a boundary between two materials, part of it is transmitted, part of it is absorbed, and part of it is reflected. The impedances of

1635-523: A mixture containing at least two substances. The potential energy stored in an explosive material may, for example, be: Explosive materials may be categorized by the speed at which they expand. Materials that detonate (the front of the chemical reaction moves faster through the material than the speed of sound ) are said to be "high explosives" and materials that deflagrate are said to be "low explosives". Explosives may also be categorized by their sensitivity . Sensitive materials that can be initiated by

1744-433: A number of more exotic explosive materials, and exotic methods of causing explosions. Examples include nuclear explosives , and abruptly heating a substance to a plasma state with a high-intensity laser or electric arc . Laser- and arc-heating are used in laser detonators, exploding-bridgewire detonators , and exploding foil initiators , where a shock wave and then detonation in conventional chemical explosive material

1853-427: A physical shock signal. In other situations, different signals such as electrical or physical shock, or, in the case of laser detonation systems, light, are used to initiate an action, i.e., an explosion. A small quantity, usually milligrams, is sufficient to initiate a larger charge of explosive that is usually safer to handle. Speed of sound The speed of sound is the distance travelled per unit of time by

1962-486: A pipe aligned with the x {\displaystyle x} axis and with a cross-sectional area of A {\displaystyle A} . In time interval d t {\displaystyle dt} it moves length d x = v d t {\displaystyle dx=v\,dt} . In steady state , the mass flow rate m ˙ = ρ v A {\displaystyle {\dot {m}}=\rho vA} must be

2071-685: A practical measure, primary explosives are sufficiently sensitive that they can be reliably initiated with a blow from a hammer; however, PETN can also usually be initiated in this manner, so this is only a very broad guideline. Additionally, several compounds, such as nitrogen triiodide , are so sensitive that they cannot even be handled without detonating. Nitrogen triiodide is so sensitive that it can be reliably detonated by exposure to alpha radiation . Primary explosives are often used in detonators or to trigger larger charges of less sensitive secondary explosives . Primary explosives are commonly used in blasting caps and percussion caps to translate

2180-399: A reaction to be classified as a detonation as opposed to just a deflagration, the propagation of the reaction shockwave through the material being tested must be faster than the speed of sound through that material. The speed of sound through a liquid or solid material is usually orders of magnitude faster than the speed of sound through air or other gases. Traditional explosives mechanics

2289-559: A relatively small amount of heat or pressure are primary explosives and materials that are relatively insensitive are secondary or tertiary explosives . A wide variety of chemicals can explode; a smaller number are manufactured specifically for the purpose of being used as explosives. The remainder are too dangerous, sensitive, toxic, expensive, unstable, or prone to decomposition or degradation over short time spans. In contrast, some materials are merely combustible or flammable if they burn without exploding. The distinction, however,

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2398-459: A single given gas (assuming the molecular weight does not change) and over a small temperature range (for which the heat capacity is relatively constant), the speed of sound becomes dependent on only the temperature of the gas. In non-ideal gas behavior regimen, for which the Van der Waals gas equation would be used, the proportionality is not exact, and there is a slight dependence of sound velocity on

2507-618: A thermodynamically favorable process in addition to one that propagates very rapidly. Thus, explosives are substances that contain a large amount of energy stored in chemical bonds . The energetic stability of the gaseous products and hence their generation comes from the formation of strongly bonded species like carbon monoxide, carbon dioxide, and nitrogen gas, which contain strong double and triple bonds having bond strengths of nearly 1 MJ/mole. Consequently, most commercial explosives are organic compounds containing –NO 2 , –ONO 2 and –NHNO 2 groups that, when detonated, release gases like

2616-709: Is mining . Whether the mine is on the surface or is buried underground, the detonation or deflagration of either a high or low explosive in a confined space can be used to liberate a fairly specific sub-volume of a brittle material (rock) in a much larger volume of the same or similar material. The mining industry tends to use nitrate-based explosives such as emulsions of fuel oil and ammonium nitrate solutions, mixtures of ammonium nitrate prills (fertilizer pellets) and fuel oil ( ANFO ) and gelatinous suspensions or slurries of ammonium nitrate and combustible fuels. In materials science and engineering, explosives are used in cladding ( explosion welding ). A thin plate of some material

2725-446: Is a dimensionless constant that is a function of the ratio of the specific heat of air at constant pressure to the specific heat of air at constant volume. The value of C is also affected by radiative losses, but for air, values of C of 1.00-1.10 generally give reasonable results. In 1950, Taylor published two articles in which he revealed the yield E of the first atomic explosion, which had previously been classified and whose publication

2834-427: Is a pure substance ( molecule ) that in a chemical reaction can contribute some atoms of one or more oxidizing elements, in which the fuel component of the explosive burns. On the simplest level, the oxidizer may itself be an oxidizing element , such as gaseous or liquid oxygen . The availability and cost of explosives are determined by the availability of the raw materials and the cost, complexity, and safety of

2943-402: Is an important consideration in selecting an explosive for a particular purpose. The explosive in an armor-piercing projectile must be relatively insensitive, or the shock of impact would cause it to detonate before it penetrated to the point desired. The explosive lenses around nuclear charges are also designed to be highly insensitive, to minimize the risk of accidental detonation. The index of

3052-440: Is an important element influencing the yield of the energy transmitted for both atmospheric over-pressure and ground acceleration. By definition, a "low explosive", such as black powder, or smokeless gunpowder has a burn rate of 171–631 m/s. In contrast, a "high explosive", whether a primary, such as detonating cord , or a secondary, such as TNT or C-4, has a significantly higher burn rate about 6900–8092 m/s. Stability

3161-419: Is associated with compression and decompression in the direction of travel, and is the same process in gases and liquids, with an analogous compression-type wave in solids. Only compression waves are supported in gases and liquids. An additional type of wave, the transverse wave , also called a shear wave , occurs only in solids because only solids support elastic deformations. It is due to elastic deformation of

3270-520: Is based on the shock-sensitive rapid oxidation of carbon and hydrogen to carbon dioxide, carbon monoxide and water in the form of steam. Nitrates typically provide the required oxygen to burn the carbon and hydrogen fuel. High explosives tend to have the oxygen, carbon and hydrogen contained in one organic molecule, and less sensitive explosives like ANFO are combinations of fuel (carbon and hydrogen fuel oil) and ammonium nitrate . A sensitizer such as powdered aluminum may be added to an explosive to increase

3379-417: Is called the object's Mach number . Objects moving at speeds greater than the speed of sound ( Mach 1 ) are said to be traveling at supersonic speeds . In Earth's atmosphere, the speed of sound varies greatly from about 295 m/s (1,060 km/h; 660 mph) at high altitudes to about 355 m/s (1,280 km/h; 790 mph) at high temperatures. Sir Isaac Newton 's 1687 Principia includes

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3488-443: Is created by laser- or electric-arc heating. Laser and electric energy are not currently used in practice to generate most of the required energy, but only to initiate reactions. To determine the suitability of an explosive substance for a particular use, its physical properties must first be known. The usefulness of an explosive can only be appreciated when the properties and the factors affecting them are fully understood. Some of

3597-401: Is decreased, thus making a wave that is much smaller than either of the parent waves. The formation of a mach stem is one example of constructive interference. Whenever a blast wave reflects off of a surface, such as a building wall or the inside of a vehicle, different reflected waves can interact with each other to cause an increase in pressure at a certain point (constructive interference) or

3706-412: Is determined by the medium's compressibility , shear modulus , and density. The speed of shear waves is determined only by the solid material's shear modulus and density. In fluid dynamics , the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The ratio of the speed of an object to the speed of sound (in the same medium)

3815-811: Is determined simply by the solid material's shear modulus and density. The speed of sound in mathematical notation is conventionally represented by c , from the Latin celeritas meaning "swiftness". For fluids in general, the speed of sound c is given by the Newton–Laplace equation: c = K s ρ , {\displaystyle c={\sqrt {\frac {K_{s}}{\rho }}},} where K s = ρ ( ∂ P ∂ ρ ) s {\displaystyle K_{s}=\rho \left({\frac {\partial P}{\partial \rho }}\right)_{s}} , where P {\displaystyle P}

3924-452: Is evaluated by a tailored series of tests to assess the material for its intended use. Of the tests listed below, cylinder expansion and air-blast tests are common to most testing programs, and the others support specific applications. In addition to strength, explosives display a second characteristic, which is their shattering effect or brisance (from the French meaning to "break"). Brisance

4033-577: Is fully excited (i.e., molecular rotation is fully used as a heat energy "partition" or reservoir); but at the same time the temperature must be low enough that molecular vibrational modes contribute no heat capacity (i.e., insignificant heat goes into vibration, as all vibrational quantum modes above the minimum-energy-mode have energies that are too high to be populated by a significant number of molecules at this temperature). For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature (see tables below). See

4142-472: Is important in determining the effectiveness of an explosion in fragmenting shells, bomb casings, and grenades . The rapidity with which an explosive reaches its peak pressure ( power ) is a measure of its brisance. Brisance values are primarily employed in France and Russia. The sand crush test is commonly employed to determine the relative brisance in comparison to TNT. No test is capable of directly comparing

4251-420: Is not very clear. Certain materials—dusts, powders, gases, or volatile organic liquids—may be simply combustible or flammable under ordinary conditions, but become explosive in specific situations or forms, such as dispersed airborne clouds , or confinement or sudden release . Early thermal weapons , such as Greek fire , have existed since ancient times. At its roots, the history of chemical explosives lies in

4360-400: Is placed atop a thick layer of a different material, both layers typically of metal. Atop the thin layer is placed an explosive. At one end of the layer of explosive, the explosion is initiated. The two metallic layers are forced together at high speed and with great force. The explosion spreads from the initiation site throughout the explosive. Ideally, this produces a metallurgical bond between

4469-473: Is the ability of an explosive to be stored without deterioration . The following factors affect the stability of an explosive: The term power or performance as applied to an explosive refers to its ability to do work. In practice it is defined as the explosive's ability to accomplish what is intended in the way of energy delivery (i.e., fragment projection, air blast, high-velocity jet, underwater shock and bubble energy, etc.). Explosive power or performance

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4578-534: Is the density of the air and E {\displaystyle E} is the energy released by the explosion. This result allowed Taylor to estimate the nuclear yield of the Trinity test in New Mexico in 1945 using only photographs of the blast, which had been published in newspapers and magazines. The yield of the explosion was determined by using the equation: where C {\displaystyle C}

4687-411: Is the lead-free primary explosive copper(I) 5-nitrotetrazolate, an alternative to lead azide . Explosive material may be incorporated in the explosive train of a device or system. An example is a pyrotechnic lead igniting a booster, which causes the main charge to detonate. The most widely used explosives are condensed liquids or solids converted to gaseous products by explosive chemical reactions and

4796-472: Is the pressure and the derivative is taken isentropically, that is, at constant entropy s . This is because a sound wave travels so fast that its propagation can be approximated as an adiabatic process , meaning that there isn't enough time, during a pressure cycle of the sound, for significant heat conduction and radiation to occur. Thus, the speed of sound increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of

4905-407: Is used to describe an explosive phenomenon whereby the decomposition is propagated by a shock wave traversing the explosive material at speeds greater than the speed of sound within the substance. The shock front is capable of passing through the high explosive material at supersonic speeds   —   typically thousands of metres per second. In addition to chemical explosives, there are

5014-446: The ozone layer . This produces a positive speed of sound gradient in this region. Still another region of positive gradient occurs at very high altitudes, in the thermosphere above 90 km . For an ideal gas, K (the bulk modulus in equations above, equivalent to C , the coefficient of stiffness in solids) is given by K = γ ⋅ p . {\displaystyle K=\gamma \cdot p.} Thus, from

5123-548: The springs , and the mass of the spheres. As long as the spacing of the spheres remains constant, stiffer springs/bonds transmit energy more quickly, while more massive spheres transmit energy more slowly. In a real material, the stiffness of the springs is known as the " elastic modulus ", and the mass corresponds to the material density . Sound will travel more slowly in spongy materials and faster in stiffer ones. Effects like dispersion and reflection can also be understood using this model. Some textbooks mistakenly state that

5232-614: The "One o'Clock Gun" is fired at the eastern end of Edinburgh Castle. Standing at the base of the western end of the Castle Rock, the sound of the Gun can be heard through the rock, slightly before it arrives by the air route, partly delayed by the slightly longer route. It is particularly effective if a multi-gun salute such as for "The Queen's Birthday" is being fired. In a gas or liquid, sound consists of compression waves. In solids, waves propagate as two different types. A longitudinal wave

5341-590: The 17th century there were several attempts to measure the speed of sound accurately, including attempts by Marin Mersenne in 1630 (1,380 Parisian feet per second), Pierre Gassendi in 1635 (1,473 Parisian feet per second) and Robert Boyle (1,125 Parisian feet per second). In 1709, the Reverend William Derham , Rector of Upminster, published a more accurate measure of the speed of sound, at 1,072 Parisian feet per second. (The Parisian foot

5450-405: The Newton–Laplace equation above, the speed of sound in an ideal gas is given by c = γ ⋅ p ρ , {\displaystyle c={\sqrt {\gamma \cdot {p \over \rho }}},} where Using the ideal gas law to replace p with nRT / V , and replacing ρ with nM / V , the equation for an ideal gas becomes c i d e

5559-419: The adoption of TNT in artillery shells. World War II saw extensive use of new explosives (see: List of explosives used during World War II ) . In turn, these have largely been replaced by more powerful explosives such as C-4 and PETN . However, C-4 and PETN react with metal and catch fire easily, yet unlike TNT, C-4 and PETN are waterproof and malleable. The largest commercial application of explosives

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5668-413: The aforementioned (e.g., nitroglycerin , TNT , HMX , PETN , nitrocellulose ). An explosive is classified as a low or high explosive according to its rate of combustion : low explosives burn rapidly (or deflagrate ), while high explosives detonate . While these definitions are distinct, the problem of precisely measuring rapid decomposition makes practical classification of explosives difficult. For

5777-615: The bamboo firecrackers; when fired toward the enemy, the flaming rats created great psychological ramifications—scaring enemy soldiers away and causing cavalry units to go wild. The first useful explosive stronger than black powder was nitroglycerin , developed in 1847. Since nitroglycerin is a liquid and highly unstable, it was replaced by nitrocellulose , trinitrotoluene ( TNT ) in 1863, smokeless powder , dynamite in 1867 and gelignite (the latter two being sophisticated stabilized preparations of nitroglycerin rather than chemical alternatives, both invented by Alfred Nobel ). World War I saw

5886-434: The building. The so-called Sedov-Taylor solution (see § Bombs ) has become useful in astrophysics . For example, it can be applied to quantify an estimate for the outcome from supernova -explosions. The Sedov-Taylor expansion is also known as the "blast wave" phase, which is an adiabatic expansion phase in the life cycle of supernova. The temperature of the material in a supernova shell decreases with time, but

5995-479: The capacity of an explosive to be initiated into detonation in a sustained manner. It is defined by the power of the detonator which is certain to prime the explosive to a sustained and continuous detonation. Reference is made to the Sellier-Bellot scale that consists of a series of 10 detonators, from n. 1 to n. 10 , each of which corresponds to an increasing charge weight. In practice, most of

6104-425: The choice being determined by the characteristics of the explosive. Dependent upon the method employed, an average density of the loaded charge can be obtained that is within 80–99% of the theoretical maximum density of the explosive. High load density can reduce sensitivity by making the mass more resistant to internal friction . However, if density is increased to the extent that individual crystals are crushed,

6213-456: The denser materials. An illustrative example of the two effects is that sound travels only 4.3 times faster in water than air, despite enormous differences in compressibility of the two media. The reason is that the greater density of water, which works to slow sound in water relative to the air, nearly makes up for the compressibility differences in the two media. For instance, sound will travel 1.59 times faster in nickel than in bronze, due to

6322-421: The development of pressure within rounds of ammunition and separation of mixtures into their constituents. Volatility affects the chemical composition of the explosive such that a marked reduction in stability may occur, which results in an increase in the danger of handling. The introduction of water into an explosive is highly undesirable since it reduces the sensitivity, strength, and velocity of detonation of

6431-498: The energy of the detonation. Once detonated, the nitrogen portion of the explosive formulation emerges as nitrogen gas and toxic nitric oxides . The chemical decomposition of an explosive may take years, days, hours, or a fraction of a second. The slower processes of decomposition take place in storage and are of interest only from a stability standpoint. Of more interest are the other two rapid forms besides decomposition: deflagration and detonation. In deflagration, decomposition of

6540-604: The energy released by those reactions. The gaseous products of complete reaction are typically carbon dioxide , steam , and nitrogen . Gaseous volumes computed by the ideal gas law tend to be too large at high pressures characteristic of explosions. Ultimate volume expansion may be estimated at three orders of magnitude, or one liter per gram of explosive. Explosives with an oxygen deficit will generate soot or gases like carbon monoxide and hydrogen , which may react with surrounding materials such as atmospheric oxygen . Attempts to obtain more precise volume estimates must consider

6649-445: The explosive material is propagated by a flame front which moves relatively slowly through the explosive material, i.e. at speeds less than the speed of sound within the substance (which is usually still higher than 340 m/s or 1,220 km/h in most liquid or solid materials) in contrast to detonation, which occurs at speeds greater than the speed of sound. Deflagration is a characteristic of low explosive material. This term

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6758-651: The explosive material, but a practical explosive will often include small percentages of other substances. For example, dynamite is a mixture of highly sensitive nitroglycerin with sawdust , powdered silica , or most commonly diatomaceous earth , which act as stabilizers. Plastics and polymers may be added to bind powders of explosive compounds; waxes may be incorporated to make them safer to handle; aluminium powder may be introduced to increase total energy and blast effects. Explosive compounds are also often "alloyed": HMX or RDX powders may be mixed (typically by melt-casting) with TNT to form Octol or Cyclotol . An oxidizer

6867-442: The explosive may become more sensitive. Increased load density also permits the use of more explosive, thereby increasing the power of the warhead . It is possible to compress an explosive beyond a point of sensitivity, known also as dead-pressing , in which the material is no longer capable of being reliably initiated, if at all. Volatility is the readiness with which a substance vaporizes . Excessive volatility often results in

6976-414: The explosive properties of two or more compounds; it is important to examine the data from several such tests (sand crush, trauzl , and so forth) in order to gauge relative brisance. True values for comparison require field experiments. Density of loading refers to the mass of an explosive per unit volume. Several methods of loading are available, including pellet loading, cast loading, and press loading,

7085-409: The explosive. Hygroscopicity is a measure of a material's moisture-absorbing tendencies. Moisture affects explosives adversely by acting as an inert material that absorbs heat when vaporized, and by acting as a solvent medium that can cause undesired chemical reactions. Sensitivity, strength, and velocity of detonation are reduced by inert materials that reduce the continuity of the explosive mass. When

7194-429: The explosives on the market today are sensitive to an n. 8 detonator, where the charge corresponds to 2 grams of mercury fulminate . The velocity with which the reaction process propagates in the mass of the explosive. Most commercial mining explosives have detonation velocities ranging from 1,800 m/s to 8,000 m/s. Today, velocity of detonation can be measured with accuracy. Together with density it

7303-445: The fastest it can travel under normal conditions. In theory, the speed of sound is actually the speed of vibrations. Sound waves in solids are composed of compression waves (just as in gases and liquids) and a different type of sound wave called a shear wave , which occurs only in solids. Shear waves in solids usually travel at different speeds than compression waves, as exhibited in seismology . The speed of compression waves in solids

7412-477: The gas pressure. Humidity has a small but measurable effect on the speed of sound (causing it to increase by about 0.1%–0.6%), because oxygen and nitrogen molecules of the air are replaced by lighter molecules of water . This is a simple mixing effect. In the Earth's atmosphere , the chief factor affecting the speed of sound is the temperature . For a given ideal gas with constant heat capacity and composition,

7521-615: The greater stiffness of nickel at about the same density. Similarly, sound travels about 1.41 times faster in light hydrogen ( protium ) gas than in heavy hydrogen ( deuterium ) gas, since deuterium has similar properties but twice the density. At the same time, "compression-type" sound will travel faster in solids than in liquids, and faster in liquids than in gases, because the solids are more difficult to compress than liquids, while liquids, in turn, are more difficult to compress than gases. A practical example can be observed in Edinburgh when

7630-417: The ground up to a certain point called the triple point at the edge of the blast wave. Anything in this area experiences peak pressures that can be several times higher than the peak pressure of the original shock front. In physics, interference is the meeting of two correlated waves and either increasing or lowering the net amplitude , depending on whether it is constructive or destructive interference. If

7739-401: The ground, creating an acoustic shadow at some distance from the source. The decrease of the speed of sound with height is referred to as a negative sound speed gradient . However, there are variations in this trend above 11 km . In particular, in the stratosphere above about 20 km , the speed of sound increases with height, due to an increase in temperature from heating within

7848-413: The gunshot with a half-second pendulum. Measurements were made of gunshots from a number of local landmarks, including North Ockendon church. The distance was known by triangulation , and thus the speed that the sound had travelled was calculated. The transmission of sound can be illustrated by using a model consisting of an array of spherical objects interconnected by springs. In real material terms,

7957-667: The history of gunpowder . During the Tang dynasty in the 9th century, Taoist Chinese alchemists were eagerly trying to find the elixir of immortality. In the process, they stumbled upon the explosive invention of black powder made from coal, saltpeter, and sulfur in 1044. Gunpowder was the first form of chemical explosives and by 1161, the Chinese were using explosives for the first time in warfare. The Chinese would incorporate explosives fired from bamboo or bronze tubes known as bamboo firecrackers. The Chinese also inserted live rats inside

8066-466: The important factors, since fluids do not transmit shear stresses. In heterogeneous fluids, such as a liquid filled with gas bubbles, the density of the liquid and the compressibility of the gas affect the speed of sound in an additive manner, as demonstrated in the hot chocolate effect . In gases, adiabatic compressibility is directly related to pressure through the heat capacity ratio (adiabatic index), while pressure and density are inversely related to

8175-412: The incidence of blast lung. However, as soldiers are better protected from penetrating injury and surviving previously lethal exposures, limb, eye, ear, and brain injuries have become more prevalent. Structural behaviour during an explosion depends on the materials used in the construction of the building. Upon hitting the face of a building, the shock front from an explosion is reflected. This impact with

8284-412: The interaction of blast waves with inanimate and biological structures. Validated models are useful for "what if" experiments—predictions of outcomes for different scenarios. Depending on the system being modeled, it can be difficult to have accurate input parameters (for example, the material properties of a rate-sensitive material at blast rates of loading). Lack of experimental validation severely limits

8393-689: The internal energy of the material is always 72% of E 0 , the initial energy released. This is helpful for astrophysicists interested in predicting the behavior of supernova remnants. Blast waves are generated in research environments using explosive or compressed-gas driven shock tubes in an effort to replicate the environment of a military conflict to better understand the physics of blasts and injuries that may result, and to develop better protection against blast exposure. Blast waves are directed against structures (such as vehicles), materials, and biological specimens or surrogates. High-speed pressure sensors and/or high speed cameras are often used to quantify

8502-450: The manufacturing operations. A primary explosive is an explosive that is extremely sensitive to stimuli such as impact , friction , heat , static electricity , or electromagnetic radiation . Some primary explosives are also known as contact explosives . A relatively small amount of energy is required for initiation . As a very general rule, primary explosives are considered to be those compounds that are more sensitive than PETN . As

8611-473: The material and decreases with an increase in density. For ideal gases, the bulk modulus K is simply the gas pressure multiplied by the dimensionless adiabatic index , which is about 1.4 for air under normal conditions of pressure and temperature. For general equations of state , if classical mechanics is used, the speed of sound c can be derived as follows: Consider the sound wave propagating at speed v {\displaystyle v} through

8720-563: The medium perpendicular to the direction of wave travel; the direction of shear-deformation is called the " polarization " of this type of wave. In general, transverse waves occur as a pair of orthogonal polarizations. These different waves (compression waves and the different polarizations of shear waves) may have different speeds at the same frequency. Therefore, they arrive at an observer at different times, an extreme example being an earthquake , where sharp compression waves arrive first and rocking transverse waves seconds later. The speed of

8829-436: The moisture content evaporates during detonation, cooling occurs, which reduces the temperature of reaction. Stability is also affected by the presence of moisture since moisture promotes decomposition of the explosive and, in addition, causes corrosion of the explosive's metal container. Explosives considerably differ from one another as to their behavior in the presence of water. Gelatin dynamites containing nitroglycerine have

8938-443: The molecule is said to have a zero oxygen balance. The molecule is said to have a positive oxygen balance if it contains more oxygen than is needed and a negative oxygen balance if it contains less oxygen than is needed. The sensitivity, strength , and brisance of an explosive are all somewhat dependent upon oxygen balance and tend to approach their maxima as oxygen balance approaches zero. A chemical explosive may consist of either

9047-457: The more important characteristics are listed below: Sensitivity refers to the ease with which an explosive can be ignited or detonated, i.e., the amount and intensity of shock , friction , or heat that is required. When the term sensitivity is used, care must be taken to clarify what kind of sensitivity is under discussion. The relative sensitivity of a given explosive to impact may vary greatly from its sensitivity to friction or heat. Some of

9156-520: The original explosions. The blast wave can also cause fires or secondary explosions by a combination of the high temperatures that result from detonation and the physical destruction of fuel-containing objects. In response to an inquiry from the British MAUD Committee , G. I. Taylor estimated the amount of energy that would be released by the explosion of an atomic bomb in air. He postulated that for an idealized point source of energy,

9265-410: The possibility of such side reactions, condensation of steam, and aqueous solubility of gases like carbon dioxide. Oxygen balance is an expression that is used to indicate the degree to which an explosive can be oxidized. If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess,

9374-432: The properties of the substance through which the wave is travelling. In solids, the speed of transverse (or shear) waves depends on the shear deformation under shear stress (called the shear modulus ), and the density of the medium. Longitudinal (or compression) waves in solids depend on the same two factors with the addition of a dependence on compressibility . In fluids, only the medium's compressibility and density are

9483-416: The response to blast exposure. Anthropomorphic test devices (ATDs or test dummies ) initially developed for the automotive industry are being used, sometimes with added instrumentation, to estimate the human response to blast events. For examples, personnel in vehicles and personnel on demining teams have been simulated using these ATDs. Combined with experiments, complex mathematical models have been made of

9592-1421: The same at the two ends of the tube, therefore the mass flux j = ρ v {\displaystyle j=\rho v} is constant and v d ρ = − ρ d v {\displaystyle v\,d\rho =-\rho \,dv} . Per Newton's second law , the pressure-gradient force provides the acceleration: d v d t = − 1 ρ d P d x → d P = ( − ρ d v ) d x d t = ( v d ρ ) v → v 2 ≡ c 2 = d P d ρ {\displaystyle {\begin{aligned}{\frac {dv}{dt}}&=-{\frac {1}{\rho }}{\frac {dP}{dx}}\\[1ex]\rightarrow dP&=(-\rho \,dv){\frac {dx}{dt}}=(v\,d\rho )v\\[1ex]\rightarrow v^{2}&\equiv c^{2}={\frac {dP}{d\rho }}\end{aligned}}} And therefore: c = ( ∂ P ∂ ρ ) s = K s ρ , {\displaystyle c={\sqrt {\left({\frac {\partial P}{\partial \rho }}\right)_{s}}}={\sqrt {\frac {K_{s}}{\rho }}},} If relativistic effects are important,

9701-466: The section on gases in specific heat capacity for a more complete discussion of this phenomenon. For air, we introduce the shorthand R ∗ = R / M a i r . {\displaystyle R_{*}=R/M_{\mathrm {air} }.} In addition, we switch to the Celsius temperature θ = T − 273.15 K , which is useful to calculate air speed in

9810-426: The sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for c air have been found to vary slightly from experimentally determined values. Newton famously considered the speed of sound before most of the development of thermodynamics and so incorrectly used isothermal calculations instead of adiabatic . His result

9919-475: The spatial distributions of the flow variables would have the same form during a given time interval, the variables differing only in scale (thus the name of the "similarity solution.") This hypothesis allows the partial differential equations in terms of r (the radius of the blast wave) and t (time) to be transformed into an ordinary differential equation in terms of the similarity variable: where ρ o {\displaystyle \rho _{o}}

10028-404: The speed of sound increases with density. This notion is illustrated by presenting data for three materials, such as air, water, and steel and noting that the speed of sound is higher in the denser materials. But the example fails to take into account that the materials have vastly different compressibility, which more than makes up for the differences in density, which would slow wave speeds in

10137-423: The speed of sound is about 75% of the mean speed that the atoms move in that gas. For a given ideal gas the molecular composition is fixed, and thus the speed of sound depends only on its temperature . At a constant temperature, the gas pressure has no effect on the speed of sound, since the density will increase, and since pressure and density (also proportional to pressure) have equal but opposite effects on

10246-506: The speed of sound is calculated from the relativistic Euler equations . In a non-dispersive medium , the speed of sound is independent of sound frequency , so the speeds of energy transport and sound propagation are the same for all frequencies. Air, a mixture of oxygen and nitrogen, constitutes a non-dispersive medium. However, air does contain a small amount of CO 2 which is a dispersive medium, and causes dispersion to air at ultrasonic frequencies (greater than 28  kHz ). In

10355-404: The speed of sound is dependent solely upon temperature; see § Details below. In such an ideal case, the effects of decreased density and decreased pressure of altitude cancel each other out, save for the residual effect of temperature. Since temperature (and thus the speed of sound) decreases with increasing altitude up to 11 km , sound is refracted upward, away from listeners on

10464-539: The speed of sound waves in air . However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases , faster in liquids , and fastest in solids . For example, while sound travels at 343 m/s in air, it travels at 1481 m/s in water (almost 4.3 times as fast) and at 5120 m/s in iron (almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels at 12,000 m/s (39,370 ft/s),  – about 35 times its speed in air and about

10573-490: The speed of sound, and the two contributions cancel out exactly. In a similar way, compression waves in solids depend both on compressibility and density—just as in liquids—but in gases the density contributes to the compressibility in such a way that some part of each attribute factors out, leaving only a dependence on temperature, molecular weight, and heat capacity ratio which can be independently derived from temperature and molecular composition (see derivations below). Thus, for

10682-402: The spheres represent the material's molecules and the springs represent the bonds between them. Sound passes through the system by compressing and expanding the springs, transmitting the acoustic energy to neighboring spheres. This helps transmit the energy in-turn to the neighboring sphere's springs (bonds), and so on. The speed of sound through the model depends on the stiffness /rigidity of

10791-464: The structure imparts momentum to exterior components of the building. The associated kinetic energy of the moving components must be absorbed or dissipated in order for them to survive. Generally, this is achieved by converting the kinetic energy of the moving component to strain energy in resisting elements. Typically the resisting elements—such as windows, building facades and support columns—fail, causing partial damage through to progressive collapse of

10900-492: The sum of the masses of the two initial layers. There are applications where a shock wave, and electrostatics, can result in high velocity projectiles such as in an electrostatic particle accelerator . An explosion is a type of spontaneous chemical reaction that, once initiated, is driven by both a large exothermic change (great release of heat) and a large positive entropy change (great quantities of gases are released) in going from reactants to products, thereby constituting

11009-429: The temperature and molecular weight, thus making only the completely independent properties of temperature and molecular structure important (heat capacity ratio may be determined by temperature and molecular structure, but simple molecular weight is not sufficient to determine it). Sound propagates faster in low molecular weight gases such as helium than it does in heavier gases such as xenon . For monatomic gases,

11118-499: The test methods used to determine sensitivity relate to: Specific explosives (usually but not always highly sensitive on one or more of the three above axes) may be idiosyncratically sensitive to such factors as pressure drop, acceleration, the presence of sharp edges or rough surfaces, incompatible materials, or even —  in rare cases —  nuclear or electromagnetic radiation. These factors present special hazards that may rule out any practical utility. Sensitivity

11227-425: The two layers. As the length of time the shock wave spends at any point is small, we can see mixing of the two metals and their surface chemistries, through some fraction of the depth, and they tend to be mixed in some way. It is possible that some fraction of the surface material from either layer eventually gets ejected when the end of material is reached. Hence, the mass of the now "welded" bilayer, may be less than

11336-441: The two materials determine how much of each occurs. The equation for a Friedlander waveform describes the pressure of the blast wave as a function of time: where P s is the peak pressure and t* is the time at which the pressure first crosses the horizontal axis (before the negative phase). Blast waves will wrap around objects and buildings. Therefore, persons or objects behind a large building are not necessarily protected from

11445-444: The usefulness of any numerical model. Explosive An explosive (or explosive material ) is a reactive substance that contains a great amount of potential energy that can produce an explosion if released suddenly, usually accompanied by the production of light , heat , sound , and pressure . An explosive charge is a measured quantity of explosive material, which may either be composed solely of one ingredient or be

11554-462: The war, the similarity solution was published by three other authors— L. I. Sedov , R. Latter, and J. Lockwood-Taylor—who had discovered it independently. Since the early theoretical work, both theoretical and experimental studies of blast waves have been ongoing. The simplest form of a blast wave has been described and termed the Friedlander waveform. It occurs when a high explosive detonates in

11663-422: Was 325 mm . This is longer than the standard "international foot" in common use today, which was officially defined in 1959 as 304.8 mm , making the speed of sound at 20 °C (68 °F) 1,055 Parisian feet per second). Derham used a telescope from the tower of the church of St. Laurence, Upminster to observe the flash of a distant shotgun being fired, and then measured the time until he heard

11772-435: Was missing the factor of γ but was otherwise correct. Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes standard Earth sea-level conditions). Also, for diatomic gases the use of γ = 1.4000 requires that the gas exists in a temperature range high enough that rotational heat capacity

11881-570: Was therefore a source of controversy. While nuclear explosions are among the clearest examples of the destructive power of blast waves, blast waves generated by exploding conventional bombs and other weapons made from high explosives have been used as weapons of war because of their effectiveness at creating polytraumatic injury. During World War II and the Vietnam War , blast lung was a common and often deadly injury. Improvements in vehicular and personal protective equipment have helped to reduce

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