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Showing 31–60 of 1709 reference entries

Physics · MeasurementCaesium-133 defining frequency

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

DefinitionMathematics & logic · InformationClassical propositions and connectives

Classical logic combines truth-valued propositions using defined connectives.

DefinitionMathematics & logicAxioms, deduction and mathematical proof

A mathematical proof derives a conclusion within stated assumptions and rules.

MethodMathematics & logic · InformationSets, membership and basic operations

A set specifies membership without counting duplicate listings.

DefinitionMathematics & logic · InformationFunctions, domain and codomain

A function assigns exactly one output to each input in its domain.

DefinitionMathematics & logic · InformationMathematical induction

A base case and general successor step establish a predicate on all nonnegative integers.

MethodMathematics & logic · MeasurementEuclidean right triangles and the Pythagorean theorem

In a Euclidean right triangle, squared leg lengths sum to the squared hypotenuse length.

Mathematical statementMathematics & logic · PhysicsSine, cosine and the unit circle

Sine and cosine are unit-circle coordinates whose squared values sum to one.

Mathematical statementMathematics & logic · InformationComplex numbers

A complex number has real coordinates a and b and an imaginary unit satisfying i²=−1.

DefinitionMathematics & logic · Information · PhysicsLinear maps and matrix representation

A linear map preserves linear combinations and has a matrix once bases are chosen.

DefinitionMathematics & logicLimit of a real function

A finite limit controls output error through sufficiently small input distance.

DefinitionMathematics & logic · PhysicsDerivative at a point

A derivative is a finite limit of local difference quotients.

DefinitionMathematics & logic · PhysicsDefinite integral and signed accumulation

A definite integral is the limiting signed accumulation of small contributions.

DefinitionMathematics & logic · PhysicsFundamental theorem of calculus

Continuity connects differentiation with integration.

Mathematical statementMathematics & logic · InformationProbability space and axioms

A probability assigns nonnegative, normalised, countably additive weights to events.

DefinitionMathematics & logic · InformationConditional probability and independence

Conditioning restricts attention to an event of positive probability.

DefinitionMathematics & logic · InformationExpected value of a discrete random variable

Expected value weights possible values by their probabilities.

DefinitionMathematics & logic · MeasurementConfidence interval for a population mean

A confidence level describes repeated-sampling coverage of an interval procedure.

MethodInformation · Mathematics & logicBits and unsigned binary encoding

A bit has two possible states; a fixed-width unsigned binary word encodes an integer.

DefinitionInformation · Mathematics & logicShannon entropy of a discrete distribution

Shannon entropy measures uncertainty in a specified probability distribution.

DefinitionInformationAlgorithm and decision procedure

An algorithm specifies effective steps; a decision procedure must terminate on every permitted input.

MethodInformation · Mathematics & logicUndecidability of the halting problem

No total algorithm decides halting for every program and input in a general computation model.

Mathematical statementInformation · Mathematics & logicAsymptotic upper bounds and big O

Big O bounds eventual growth up to a fixed constant factor.

DefinitionMeasurementSI base units

Seven named base units organize the SI quantity system.

DefinitionMeasurementSI decimal prefixes

Prefix symbols specify decimal scale factors.

DefinitionMeasurementMetrological traceability

Connect a result to a reference through documented calibrations.

DefinitionMeasurement · Mathematics & logicFirst-order uncertainty propagation

Combine input uncertainty through a measurement model.

MethodMeasurement · Physics · Mathematics & logicDimensional consistency

Use dimensions to detect impossible quantity equations.

MethodPhysics · Earth & cosmosNewtonian gravitation

An inverse-square force models attraction between point masses.

ModelPhysicsFrequency, wavelength and phase speed

Relate a periodic wave's spatial and temporal repetition.

Definition
DefinitionSource checked

Frequency, wavelength and phase speed

Physics

Relate a periodic wave's spatial and temporal repetition.

Key knowledge

For a traveling periodic wave component, phase speed equals frequency times wavelength: v_phase = fλ. This is the speed of a phase pattern, which need not equal particle speed or signal speed.

Values and equations

v_phase = fλ = ω/k

v_phase
Phase speed m s⁻¹
f
Positive frequency Hz
λ
Positive wavelength m
ω
Positive angular frequency rad s⁻¹
k
Positive angular wavenumber rad m⁻¹

Conditions and scope

  • f and λ refer to the same wave component in the same medium and reference frame; f, λ, ω and k are positive magnitudes in this speed formula.
  • In a dispersive medium, phase speed can depend on frequency.
Sources · 3

References

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

  1. University Physics, volume 1: Mathematics of WavesSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
  2. 8.03SC Vibrations and Waves (2016), Lecture 13: dispersionMassachusetts Institute of Technology — MIT OpenCourseWareCourse notes · PDFocw.mit.eduRead source
  3. Waves · Physics (2026–27 reprint)National Council of Educational Research and Training (NCERT)Textbook chapter · PDFncert.nic.inRead source

Evidence and review

OpenStax 16.2: v = ω/k = λ/T; MIT Lecture 13 pages 1–3: pulse information, frequency-dependent phase speeds and group/phase distinction.

2026-10-10 · Periodic phase relation and its dispersion caveat only; no group-velocity or information-velocity equality is asserted.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Scope or convention differs

Travelling-wave phase speed satisfies v=ω/k=fλ.

The chapter’s mechanical examples support phase propagation; particle, group and signal speeds require separate analysis.

Related reference entries

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

Showing 1–4 of 4 relationships

Scientific relationships · 4 / 4

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

  1. Uses definition
    Relationship sources · 1

    Linked statements

    • An ideal uniform string fixed at both ends has wavelengths λ_n = 2L/n and frequencies f_n = nv/(2L), for positive integer n.

    Each sinusoidal mode uses f = v/λ with positive wave speed and wavelength.

  2. Related to
    Relationship sources · 1

    Linked statements

    • At a stationary interface between isotropic transparent media, geometric-optics refraction obeys n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the surface normal.

    Refractive index changes phase speed at a fixed optical frequency in the stated isotropic media.

  3. Related to
    Relationship sources · 1

    Linked statements

    • For a narrow-band wave packet on a smooth real dispersion branch, its leading envelope velocity is v_g=dω/dk at the carrier, while phase velocity is ω/k. Higher dispersion derivatives broaden or distort the packet; group velocity need not equal signal-front velocity in strongly dispersive or absorbing media.

    Envelope derivative speed and carrier phase speed refer to different features of a narrow-band dispersive packet.

  4. Uses definition
    Relationship sources · 2

    Linked statements

    • A sinusoidal displacement wave can be written y=Acos(kx−ωt+φ), with k=2π/λ and ω=2πf. Its phase advances toward increasing x and its phase speed is ω/k. Transverse displacement is perpendicular to propagation; longitudinal displacement is parallel. Mechanical waves require a medium, while electromagnetic waves can propagate in vacuum.

    This relation concerns the stated amplitude, phase, wavelength and polarization direction 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-speed
Revision
core.1
Structured reference record
Essential core · first collection · University core expansion