S - wave - wikipedia S - wave For the lowest energy electronic wavefunction in atomic physics, see atomic orbital. For the S wave on an electrocardiogram, see QRS complex. This article has multiple issues. Please help improve it or discuss these issues on the talk page. ( Learn how and when to remove these template messages ) This article may be in need of reorganization to comply with Wikipedia 's layout guidelines. Please help by editing the article to make improvements to the overall structure. ( January 2009 ) This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. ( January 2009 ) Part of a series on Earthquakes Types Foreshock Aftershock Blind thrust Doublet Interplate Intraplate Megathrust Remotely triggered Slow Submarine Supershear Tsunami Earthquake swarm Causes Fault movement Volcanism Induced seismicity Characteristics Epicenter Hypocenter Shadow zone Seismic waves P - wave S - wave Measurement Seismometer Seismic magnitude scales Seismic intensity scales Prediction Coordinating Committee for Earthquake Prediction Forecasting Other topics Shear wave splitting Adams -- Williamson equation Flinn -- Engdahl regions Earthquake engineering Seismite Seismology Earth Sciences Portal Category Related topics Plane shear wave Propagation of a spherical S - wave in a 2d grid ( empirical model ) In seismology, S - waves, secondary waves, or shear waves ( sometimes called an elastic S - wave ) are a type of elastic wave, and are one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves. The S - wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation. The wave moves through elastic media, and the main restoring force comes from shear effects. These waves do not diverge, and they obey the continuity equation for incompressible media : ∇ ⋅ u = 0 ( displaystyle \nabla cdot mathbf ( u ) = 0 ) The shadow zone of a P - wave. S - waves do n't penetrate the outer core, so they 're shadowed everywhere more than 104 ° away from the epicenter ( from USGS ) Its name, S for secondary, comes from the fact that it is the second direct arrival on an earthquake seismogram, after the compressional primary wave, or P - wave, because S - waves travel slower in rock. Unlike the P - wave, the S - wave can not travel through the molten outer core of the Earth, and this causes a shadow zone for S - waves opposite to where they originate. They can still appear in the solid inner core : when a P - wave strikes the boundary of molten and solid cores, S - waves will then propagate in the solid medium. And when the S - waves hit the boundary again they will in turn create P - waves. This property allows seismologists to determine the nature of the inner core. Theory The prediction of S - waves came out of theory in the 1800s. Starting with the stress - strain relationship for an isotropic solid in Einstein notation : τ i j = λ δ i j e k k + 2 μ e i j ( displaystyle \tau _ ( ij ) = lambda delta _ ( ij ) e_ ( kk ) + 2 mu e_ ( ij ) ) where τ ( displaystyle \tau ) is the stress, λ ( displaystyle lambda ) and μ ( displaystyle mu ) are the Lamé parameters ( with μ ( displaystyle mu ) as the shear modulus ), δ i j ( displaystyle delta _ ( ij ) ) is the Kronecker delta, and the strain tensor is defined e i j = 1 2 ( ∂ i u j + ∂ j u i ) ( displaystyle e_ ( ij ) = ( \frac ( 1 ) ( 2 ) ) left ( partial _ ( i ) u_ ( j ) + partial _ ( j ) u_ ( i ) \right ) ) for strain displacement u. Plugging the latter into the former yields : τ i j = λ δ i j ∂ k u k + μ ( ∂ i u j + ∂ j u i ) ( displaystyle \tau _ ( ij ) = lambda delta _ ( ij ) partial _ ( k ) u_ ( k ) + mu left ( partial _ ( i ) u_ ( j ) + partial _ ( j ) u_ ( i ) \right ) ) Newton 's 2nd law in this situation gives the homogeneous equation of motion for seismic wave propagation : ρ ∂ 2 u i ∂ t 2 = ∂ j τ i j ( displaystyle \rho ( \frac ( partial ^ ( 2 ) u_ ( i ) ) ( partial t ^ ( 2 ) ) ) = partial _ ( j ) \tau _ ( ij ) ) where ρ ( displaystyle \rho ) is the mass density. Plugging in the above stress tensor gives : ρ ∂ 2 u i ∂ t 2 = ∂ i λ ∂ k u k + ∂ j μ ( ∂ i u j + ∂ j u i ) = λ ∂ i ∂ k u k + μ ∂ i ∂ j u j + μ ∂ j ∂ j u i ( displaystyle ( \begin ( aligned ) \rho ( \frac ( partial ^ ( 2 ) u_ ( i ) ) ( partial t ^ ( 2 ) ) ) & = partial _ ( i ) lambda partial _ ( k ) u_ ( k ) + partial _ ( j ) mu left ( partial _ ( i ) u_ ( j ) + partial _ ( j ) u_ ( i ) \right ) & = lambda partial _ ( i ) partial _ ( k ) u_ ( k ) + mu partial _ ( i ) partial _ ( j ) u_ ( j ) + mu partial _ ( j ) partial _ ( j ) u_ ( i ) end ( aligned ) ) ) Applying vector identities and making certain approximations gives the seismic wave equation in homogeneous media : ρ u  ̈ = ( λ + 2 μ ) ∇ ( ∇ ⋅ u ) − μ ∇ × ( ∇ × u ) ( displaystyle \rho ( ddot ( \boldsymbol ( u ) ) ) = left ( lambda + 2 mu \right ) \nabla ( \nabla cdot ( \boldsymbol ( u ) ) ) - mu \nabla \times ( \nabla \times ( \boldsymbol ( u ) ) ) ) where Newton 's notation has been used for the time derivative. Taking the curl of this equation and applying vector identities eventually gives : ∇ 2 ( ∇ × u ) − 1 β 2 ∂ 2 ∂ t 2 ( ∇ × u ) = 0 ( displaystyle \nabla ^ ( 2 ) ( \nabla \times ( \boldsymbol ( u ) ) ) - ( \frac ( 1 ) ( \beta ^ ( 2 ) ) ) ( \frac ( partial ^ ( 2 ) ) ( partial t ^ ( 2 ) ) ) left ( \nabla \times ( \boldsymbol ( u ) ) \right ) = 0 ) which is simply the wave equation applied to the curl of u with a velocity β ( displaystyle \beta ) satisfying β 2 = μ ρ ( displaystyle \beta ^ ( 2 ) = ( \frac ( mu ) ( \rho ) ) ) This describes S - wave propagation. Taking the divergence of seismic wave equation in homogeneous media, instead of the curl, yields an equation describing P - wave propagation. The steady - state SH waves are defined by the Helmholtz equation ( ∇ 2 + k 2 ) u = 0 ( displaystyle ( \nabla ^ ( 2 ) + k ^ ( 2 ) ) ( \boldsymbol ( u ) ) = 0 ) where k is the wave number. See also Earthquake early warning ( Japan ) Lamb waves Longitudinal wave Love wave P - wave Rayleigh wave Seismic wave Shear wave splitting Surface wave References Jump up ^ University of Illinois at Chicago ( 17 July 1997 ). `` Lecture 16 Seismographs and the earth 's interior ''. Retrieved 8 June 2010. Jump up ^ In 1830, the French mathematician Siméon Denis Poisson ( 1781 -- 1840 ) presented a theory of the propagation of elastic waves in solids : Poisson, S.D. ( 1831 ), `` Mémoire sur la propagation du mouvement dans les milieux élastiques '' ( Memoir on the propagation of motion in elastic media ), Mémoires de l'Académie des Sciences de l'Institut de France, 10 : 549 -- 605. On pp. 595 -- 596 of his memoir, he states that an earthquake would produce two different waves, one having a speed a and the other having a speed a / √ 3. From pp. 595 -- 596 : `` On verra aisément que cet ébranlement donnera naissance à deux ondes sphériques qui se propageront uniformément, l'une avec une vitesse a, l'autre avec une vitesse b ou a / √ 3... '' ( One will easily see that this quake will give birth to two spherical waves that will be propagated uniformly, one with a speed a, the other with a speed b or a / √ 3... ) On pp. 602, Poisson states that of the two kinds of waves that an earthquake generates, one wave consists of expansions and compressions propagating parallel to the wave 's direction of motion, whereas the other wave consists of stretching motions occurring in a plane perpendicular to wave 's direction of motion. From p. 602 : ``... à une grande distance de l'ébranlement primitif, et lorsque les ondes mobiles sont devenues sensiblement planes dans chaque partie très - petite par rapport à leurs surfaces entières, il ne subsiste plus que des vitesses propres des molécules, normales ou parallèles à ces surfaces ; les vitesses normal ayant lieu dans les ondes de la première espèce, où elles sont accompagnées de dilations qui leur sont proportionnelles, et les vitesses parallèles appartenant aux ondes de la seconde espèce, où elles ne sont accompagnées d'aucune dilatation ou condensation de volume, mais seulement de dilatations et de condensations linéaires. '' (... at a great distance from the original quake, and when the moving waves have become roughly planes in every tiny part in relation to their entire surface, there remain ( in the elastic solid of the Earth ) only the molecules ' own speeds, normal or parallel to these surfaces ; the normal speeds occur in waves of the first type, where they are accompanied by expansions that are proportional to them, and the parallel speeds belonging to waves of the second type, where they are not accompanied by any expansion or contraction of volume, but only by linear stretchings and squeezings. ) Jump up ^ Sheikhhassani, Ramtin ( 2013 ). `` Scattering of a plane harmonic SH wave by multiple layered inclusions ''. Wave Motion. 51 ( 3 ) : 517 -- 532. doi : 10.1016 / j. wavemoti. 2013.12. 002. Further reading Shearer, Peter ( 1999 ). Introduction to Seismology ( 1st ed. ). Cambridge University Press. ISBN 0 - 521 - 66023 - 8. Aki, Keiiti ; Richards, Paul G. ( 2002 ). Quantitative Seismology ( 2nd ed. ). University Science Books. ISBN 0 - 935702 - 96 - 2. Fowler, C.M.R. ( 1990 ). The solid earth. Cambridge, UK : Cambridge University Press. ISBN 0 - 521 - 38590 - 3. 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Question: s waves cannot travel through which part of the earth
Answer: the molten outer core of the Earth