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28-459: The name P wave can stand for either pressure wave (as it is formed from alternating compressions and rarefactions ) or primary wave (as it has high velocity and is therefore the first wave to be recorded by a seismograph). The name S wave represents another seismic wave propagation mode, standing for secondary or shear wave, a usually more destructive wave than the primary wave. Primary and secondary waves are body waves that travel within

56-409: A ( M ¯ ) + b ρ {\displaystyle v_{\mathrm {p} }=a({\bar {M}})+b\,\rho } which later became known as Birch's law . (The symbol a () is an empirically tabulated function, and b is a constant.) Compression (physical) In mechanics , compression is the application of balanced inward ("pushing") forces to different points on

84-540: A sound wave . Every ordinary material will contract in volume when put under isotropic compression, contract in cross-section area when put under uniform biaxial compression, and contract in length when put into uniaxial compression. The deformation may not be uniform and may not be aligned with the compression forces. What happens in the directions where there is no compression depends on the material. Most materials will expand in those directions, but some special materials will remain unchanged or even contract. In general,

112-442: A material is under a state of compression, at some specific point and along a specific direction x {\displaystyle x} , if the normal component of the stress vector across a surface with normal direction x {\displaystyle x} is directed opposite to x {\displaystyle x} . If the stress vector itself is opposite to x {\displaystyle x} ,

140-465: A material or structure , that is, forces with no net sum or torque directed so as to reduce its size in one or more directions. It is contrasted with tension or traction, the application of balanced outward ("pulling") forces; and with shearing forces, directed so as to displace layers of the material parallel to each other. The compressive strength of materials and structures is an important engineering consideration. In uniaxial compression ,

168-440: A portion of the exhaust steam in the cylinder , before the stroke of the piston is quite complete. This steam being compressed as the stroke is completed, a cushion is formed against which the piston does work while its velocity is being rapidly reduced, and thus the stresses in the mechanism due to the inertia of the reciprocating parts are lessened. This compression, moreover, obviates the shock which would otherwise be caused by

196-491: A result, there is a P wave " shadow zone " between 103° and 142° from the earthquake's focus, where the initial P waves are not registered on seismometers. In contrast, S waves do not travel through liquids. Advance earthquake warning is possible by detecting the nondestructive primary waves that travel more quickly through the Earth's crust than do the destructive secondary and Rayleigh waves . The amount of warning depends on

224-484: Is pressure dependent and has the form where, μ 0 is the shear modulus at the reference state ( T = 300 K, p = 0, η = 1), p is the pressure, and T is the temperature. The Nadal-Le Poac (NP) shear modulus model is a modified version of the SCG model. The empirical temperature dependence of the shear modulus in the SCG model is replaced with an equation based on Lindemann melting theory . The NP shear modulus model has

252-403: Is the bulk modulus (the modulus of incompressibility), μ is the shear modulus (modulus of rigidity, sometimes denoted as G and also called the second Lamé parameter ), ρ is the density of the material through which the wave propagates, and λ is the first Lamé parameter . In typical situations in the interior of the Earth, the density ρ usually varies much less than K or μ , so

280-406: Is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M L T , replacing force by mass times acceleration . The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law : These moduli are not independent, and for isotropic materials they are connected via

308-424: The Earth. The motion and behavior of both P and S waves in the Earth are monitored to probe the interior structure of the Earth . Discontinuities in velocity as a function of depth are indicative of changes in phase or composition. Differences in arrival times of waves originating in a seismic event like an earthquake as a result of waves taking different paths allow mapping of the Earth's inner structure. Almost all

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336-459: The Varshni equation) has the form: where μ 0 {\displaystyle \mu _{0}} is the shear modulus at T = 0 K {\displaystyle T=0K} , and D {\displaystyle D} and T 0 {\displaystyle T_{0}} are material constants. The Steinberg-Cochran-Guinan (SCG) shear modulus model

364-401: The admission of the fresh steam for the return stroke. Shear modulus In materials science , shear modulus or modulus of rigidity , denoted by G , or sometimes S or μ , is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain : where The derived SI unit of shear modulus is the pascal (Pa), although it

392-444: The compression forces disappear. In the latter case, the deformation gives rise to reaction forces that oppose the compression forces, and may eventually balance them. Liquids and gases cannot bear steady uniaxial or biaxial compression, they will deform promptly and permanently and will not offer any permanent reaction force. However they can bear isotropic compression, and may be compressed in other ways momentarily, for instance in

420-514: The delay between the arrival of the P wave and other destructive waves, generally on the order of seconds up to about 60 to 90 seconds for deep, distant, large quakes such as the 2011 Tohoku earthquake . The effectiveness of a warning depends on accurate detection of the P waves and rejection of ground vibrations caused by local activity (such as trucks or construction). Earthquake early warning systems can be automated to allow for immediate safety actions, such as issuing alerts, stopping elevators at

448-527: The equations The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object shaped like a rectangular prism, it will deform into a parallelepiped . Anisotropic materials such as wood , paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions. In this case, one may need to use

476-453: The explosive mixture gets compressed before it is ignited; the compression improves the efficiency of the engine. In the Otto cycle , for instance, the second stroke of the piston effects the compression of the charge which has been drawn into the cylinder by the first forward stroke. The term is applied to the arrangement by which the exhaust valve of a steam engine is made to close, shutting

504-432: The forces are directed along one direction only, so that they act towards decreasing the object's length along that direction. The compressive forces may also be applied in multiple directions; for example inwards along the edges of a plate or all over the side surface of a cylinder , so as to reduce its area ( biaxial compression ), or inwards over the entire surface of a body, so as to reduce its volume . Technically,

532-402: The full tensor-expression of the elastic constants, rather than a single scalar value. One possible definition of a fluid would be a material with zero shear modulus. In homogeneous and isotropic solids, there are two kinds of waves, pressure waves and shear waves . The velocity of a shear wave, ( v s ) {\displaystyle (v_{s})} is controlled by

560-469: The information available on the structure of the Earth's deep interior is derived from observations of the travel times, reflections , refractions and phase transitions of seismic body waves, or normal modes . P waves travel through the fluid layers of the Earth's interior , and yet they are refracted slightly when they pass through the transition between the semisolid mantle and the liquid outer core . As

588-407: The material is said to be under normal compression or pure compressive stress along x {\displaystyle x} . In a solid , the amount of compression generally depends on the direction x {\displaystyle x} , and the material may be under compression along some directions but under traction along others. If the stress vector is purely compressive and has

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616-683: The nearest floors, and switching off utilities. In isotropic and homogeneous solids, a P wave travels in a straight line longitudinally ; thus, the particles in the solid vibrate along the axis of propagation (the direction of motion) of the wave energy. The velocity of P waves in that kind of medium is given by v p = K + 4 3 μ ρ = λ + 2 μ ρ {\displaystyle v_{\mathrm {p} }\;=\;{\sqrt {\frac {\,K+{\tfrac {4}{3}}\mu \;}{\rho }}}\;=\;{\sqrt {\frac {\,\lambda +2\mu \;}{\rho }}}} where K

644-466: The object enlarges or increases in volume. In a mechanical wave , which is longitudinal , the medium is displaced in the wave's direction, resulting in areas of compression and rarefaction . When put under compression (or any other type of stress), every material will suffer some deformation , even if imperceptible, that causes the average relative positions of its atoms and molecules to change. The deformation may be permanent, or may be reversed when

672-414: The range 5 to 8 km/s. The precise speed varies according to the region of the Earth's interior, from less than 6 km/s in the Earth's crust to 13.5 km/s in the lower mantle, and 11 km/s through the inner core. Geologist Francis Birch discovered a relationship between the velocity of P waves and the density of the material the waves are traveling in: v p =

700-844: The relation between the stress applied to a material and the resulting deformation is a central topic of continuum mechanics . Compression of solids has many implications in materials science , physics and structural engineering , for compression yields noticeable amounts of stress and tension . By inducing compression, mechanical properties such as compressive strength or modulus of elasticity , can be measured. Compression machines range from very small table top systems to ones with over 53 MN capacity. Gases are often stored and shipped in highly compressed form, to save space. Slightly compressed air or other gases are also used to fill balloons , rubber boats , and other inflatable structures . Compressed liquids are used in hydraulic equipment and in fracking . In internal combustion engines

728-437: The same magnitude for all directions, the material is said to be under isotropic compression , hydrostatic compression , or bulk compression . This is the only type of static compression that liquids and gases can bear. It affects the volume of the material, as quantified by the bulk modulus and the volumetric strain . The inverse process of compression is called decompression , dilation , or expansion , in which

756-579: The shear modulus, where The shear modulus of metals is usually observed to decrease with increasing temperature. At high pressures, the shear modulus also appears to increase with the applied pressure. Correlations between the melting temperature, vacancy formation energy, and the shear modulus have been observed in many metals. Several models exist that attempt to predict the shear modulus of metals (and possibly that of alloys). Shear modulus models that have been used in plastic flow computations include: The Varshni-Chen-Gray model (sometimes referred to as

784-517: The velocity is mostly "controlled" by these two parameters. The elastic moduli P-wave modulus , M {\displaystyle M} , is defined so that M = K + 4 3 μ {\textstyle \,M=K+{\tfrac {4}{3}}\mu \,} and thereby v p = M ρ {\displaystyle v_{\mathrm {p} }={\sqrt {\frac {\,M\;}{\rho }}}} Typical values for P wave velocity in earthquakes are in

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