Seismic P and S Waves

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seismology body-waves wave-modes elastic-waves

Core Idea

P (primary/compressional) waves are longitudinal elastic waves where particles oscillate parallel to the propagation direction; they travel fastest and arrive first at seismometers. S (secondary/shear) waves are transverse waves where particles oscillate perpendicular to propagation, travel slower, and cannot propagate through fluids. The ratio of P to S velocities constrains composition, temperature, and pressure state of crustal and mantle materials.

How It's Best Learned

Study wave equations for both modes, plot particle motion in P and S waves, and examine seismograms from real earthquakes to identify and time P and S arrivals.

Common Misconceptions

P waves are not faster than S waves in the same medium due to wavelength; the speed difference arises from the physical mechanisms (compression vs. shear). S waves do not become P waves; they are distinct wave types. The speeds are not constants—they depend strongly on rock type and physical conditions.

Explainer

When you studied elastic wave propagation in solids, you learned that disturbances travel through materials by transferring energy between neighboring particles via elastic restoring forces. Seismic body waves are exactly this: elastic disturbances radiating outward from an earthquake source through the solid (and partly liquid) Earth. There are two distinct modes, and understanding how each moves its particles is the key to everything else.

P waves — primary or compressional waves — are longitudinal: particles oscillate back and forth in the same direction the wave travels. As a P wave passes, the rock alternately compresses (particles push together) and rarefies (particles pull apart), like sound waves in air. Because the restoring force involves both the bulk modulus (resistance to volume change) and the shear modulus, P waves are fast — roughly 6–8 km/s in the crust. They arrive first at seismometers, which is why they are called "primary." Crucially, P waves can travel through solids, liquids, and gases, since all materials resist compression.

S waves — secondary or shear waves — are transverse: particles oscillate perpendicular to the propagation direction, like a wave on a rope. The restoring force is purely the shear modulus — resistance to shape change without volume change. Since fluids (liquids and gases) have zero shear modulus, S waves cannot propagate through them. This is not a matter of speed; it is a fundamental physical impossibility. S waves travel roughly 60% as fast as P waves in the same rock. When seismologists noticed a global "S-wave shadow zone" in the 1900s, they inferred that Earth must contain a liquid outer core — one of the most important deductions in geophysical history.

The difference in arrival times between P and S waves at a seismometer — the S-P interval — grows with distance from the earthquake. Since both wave types leave the source simultaneously but travel at different speeds, a longer travel path means a larger gap between arrivals. This interval is a distance measurement: it places the seismometer somewhere on a sphere of a certain radius centered on the earthquake. With S-P intervals from three or more stations, seismologists can triangulate the epicenter precisely.

Beyond location, the velocities of P and S waves — and how they change with depth — encode the composition and physical state of every layer they traverse. Higher velocities indicate denser, stiffer material; a drop in Vs to zero marks a liquid zone. Modern seismic tomography uses millions of wave-arrival times to build three-dimensional images of mantle structure, much like a medical CT scan — but using earthquake waves instead of X-rays.

Practice Questions 3 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthHeisenberg Uncertainty PrincipleWavefunction and the Born RuleThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsScattering TheoryIntroduction to Scattering TheoryPartial Wave Analysis in ScatteringSpin Angular MomentumElectron Spin and Intrinsic Magnetic MomentStern-Gerlach Experiment: Spin Quantization and MeasurementElectron Diffraction and Matter Wave PropertiesDavisson-Germer Experiment: Crystal Diffraction of ElectronsElectron Diffraction and Matter Wave InterferenceWavefunctions and Probability Density InterpretationQuantum Superposition and Linear Combinations of StatesQuantum Operators and ObservablesCanonical Commutation Relations and UncertaintyHeisenberg Uncertainty Principle and Measurement LimitsTime-Independent Schrödinger Equation and EigenvaluesHydrogen Atom in Quantum MechanicsSpectral Lines and Energy TransitionsSelection Rules for Atomic TransitionsLS and jj Coupling Schemes in Multi-Electron AtomsPauli Exclusion Principle and Antisymmetric WavefunctionsElectron Configuration and the Aufbau PrincipleThe Periodic Table and Atomic Electronic StructureThe Periodic TableElectron ConfigurationPeriodic TrendsIonization EnergyIonic BondingLewis StructuresResonance Structures and Delocalized ElectronsResonance and Formal ChargeMolecular Polarity and Dipole MomentsIntermolecular ForcesStates of Matter and Phase Changes: Melting, Boiling, and SublimationGas Laws and the Ideal Gas EquationGas Stoichiometry and Volume-Volume CalculationsThermochemistry and EnthalpyHeat Capacity and CalorimetryEntropy and Molecular DisorderSpontaneity and ΔGEntropy and Gibbs Free EnergyChemical EquilibriumStatistical Mechanics: Ensembles and the Boltzmann DistributionMolecular Partition FunctionsStatistical Thermodynamics: Properties from Partition FunctionsSolution Thermodynamics: Partial Molar Quantities and ActivitySolution Thermodynamics and Activity Coefficient ModelsPhase Diagrams of Binary MixturesIgneous RocksMetamorphic RocksThe Rock CyclePlate TectonicsEarthquakes and SeismologySeismic WavesElastic Wave Propagation in SolidsSeismic P and S Waves

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