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Showing 181–210 of 1709 reference entries

InformationFinite graphs and trees

Graphs represent pairwise connections; trees impose acyclicity.

DefinitionInformationData-structure interfaces and operation costs

An interface defines operations; an implementation determines costs.

MethodInformationLoop invariants and total correctness

An invariant establishes correctness only with its proof obligations.

MethodInformationComparison sorting lower bound

Distinct-key comparisons need enough branches to distinguish orders.

Mathematical statementInformationBreadth-first and depth-first traversal

Graph searches visit reachable vertices using different orders.

MethodInformationShortest-path algorithm conditions

Edge weights determine which shortest-path method applies.

MethodInformationTuring machines and effective computation

Finite instructions can act on an unbounded writable tape.

DefinitionInformationRelations and tabular data

A relation is a set of tuples from declared domains.

DefinitionPhysicsCentre-of-mass dynamics

External force controls the mass-weighted centre's acceleration.

ModelPhysicsRigid-body inertia tensor

A tensor relates rotation to angular momentum.

ModelPhysicsEuler equations for a rigid body

Body-axis angular acceleration includes rotation of the axes.

ModelPhysics · Mathematics & logicEuler–Lagrange equations

Stationary action supplies coordinate equations of motion.

Mathematical statementPhysics · Mathematics & logicHamilton's canonical equations

Canonical coordinates and momenta evolve from the Hamiltonian.

Mathematical statementPhysicsFluid mass continuity

Density change balances mass flux through a region.

ModelPhysicsBernoulli's streamline relation

An ideal steady flow balances pressure, motion and height.

ModelPhysicsIncompressible Navier–Stokes equation

Fluid inertia balances pressure, viscosity and gravity.

ModelPhysicsReynolds number

Compare inertial and viscous scales of a flow.

ModelPhysicsDriven damped oscillator

A linear restoring force, damping and periodic drive determine response.

ModelPhysicsIdeal-string wave equation

A local differential equation determines small string disturbances.

ModelPhysics · Mathematics & logicWave superposition and interference

Linear disturbances add; their relative phase determines reinforcement.

ModelPhysicsFixed-end string modes

Boundary conditions select standing-wave frequencies.

ModelPhysicsSnell's refraction relation

Angles at an interface depend on refractive indices.

ModelPhysicsThin-lens image equation

A paraxial lens relates object and image distances.

ModelPhysicsSingle-slit diffraction minima

An aperture's finite width selects dark far-field directions.

ModelPhysicsLinear polarization and Malus's law

An ideal analyzer transmits the field component along its axis.

ModelPhysicsElectromagnetic potentials

Scalar and vector potentials encode electric and magnetic fields.

ModelPhysicsCapacitance

A linear two-conductor arrangement stores separated charge.

DefinitionPhysicsSelf-inductance

Changing current changes linked magnetic flux and induced emf.

ModelPhysicsElectromagnetic energy balance

The rate of field-energy change balances outward energy flow and power transferred to charges.

ModelPhysicsKirchhoff circuit balances

Lumped circuit models balance node currents and loop voltages.

Model
ModelSource checked

Wave superposition and interference

PhysicsMathematics & logic

Linear disturbances add; their relative phase determines reinforcement.

Key knowledge

For a homogeneous linear wave equation, sums of solutions are also solutions. Overlapping disturbances add algebraically, allowing constructive or destructive interference.

Values and equations

y_total(x,t) = Σ_j y_j(x,t)

y_total, y_j
Total and component transverse displacements m
x
Position m
t
Time s

Conditions and scope

  • The medium remains in its linear-response regime; a fixed boundary problem also needs compatible homogeneous linear boundary conditions.
  • Stable interference patterns require suitable frequency and relative-phase stability; displacement addition does not imply intensity addition.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics 1: Interference of WavesSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source

Evidence and review

Section 16.5: added disturbances and phase-dependent reinforcement/cancellation.

2026-10-10 · Linear superposition only; nonlinear interaction and arbitrary incoherent intensity rules excluded.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–5 of 5 relationships

Scientific relationships · 5 / 5

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 1

    Linked statements

    • For a homogeneous linear wave equation, sums of solutions are also solutions. Overlapping disturbances add algebraically, allowing constructive or destructive interference.

    The ideal-string homogeneous linear equation is one model where superposition applies.

  2. Related to
    Relationship sources · 1

    Linked statements

    • For uniform monochromatic illumination of a single slit, Fraunhofer diffraction minima occur at a sin θ = mλ for nonzero integers m within the allowed angular range.

    Uniform-phase aperture contributions cancel at the stated nonzero far-field minima.

  3. Related to
    Relationship sources · 1

    Linked statements

    • For scalar co-polarized fields, averaged intensity includes a cross-correlation term. Define γ₁₂=⟨E₁*E₂⟩/√(⟨|E₁|²⟩⟨|E₂|²⟩); then phase scanning gives visibility V=2√(I₁I₂)|γ₁₂|/(I₁+I₂). Correlation over delay describes temporal coherence and over separated positions describes spatial coherence.

    Intensity is the averaged squared field sum and keeps the coherence cross term.

  4. Related to
    Relationship sources · 1

    Linked statements

    • For a homogeneous plane-parallel transparent plate at normal incidence with two effective indices for the common wave-normal direction, optical path retardation is Γ=d(n_slow−n_fast). Phase retardation at vacuum wavelength λ₀ is Δφ=2πΓ/λ₀. Under crossed polarizers, interference depends on phase difference and the angle of the principal vibration directions to the polarizers; an extinction orientation can hide birefringence.

    An optical path difference corresponds to a phase difference.

  5. Uses definition
    Relationship sources · 1

    Linked statements

    • At a fixed observation point, equal-amplitude coherent sinusoidal components with nearby frequencies f₁ and f₂ have amplitude factor 2Acos[π(f₁−f₂)t] multiplying a carrier at their average frequency. The rate of successive loudness/intensity maxima is |f₁−f₂|; the envelope’s signed cosine has half that cycle frequency.

    This relation concerns the stated beats from nearby frequencies claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

Entry detailsPermanent link to this entry ↗
Record identity
physics-wave-superposition-interference
Revision
university-reference.1
Structured reference record
University reference · University core expansion