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See searches and references containing PHASE VELOCITY!PHASE VELOCITY
Rate at which the phase of the wave propagates in space
The phase velocity of a wave is the speed of any wavefront, a surface of constant phase. This is the velocity at which the phase of any constant-frequency
Phase_velocity
Velocity at which the overall shape of a wave's amplitudes propagates
the leading edge of the group. The idea of a group velocity distinct from a wave's phase velocity was first proposed by W.R. Hamilton in 1839, and the
Group_velocity
Relation of wavelength/wavenumber as a function of a wave's frequency
dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a
Dispersion_relation
Dynamic disturbance in a medium or field
are two velocities that are associated with waves, the phase velocity and the group velocity. Phase velocity is the rate at which the phase of the wave
Wave
Dispersion of waves on a water surface
phase speed. While the phase velocity is a vector and has an associated direction, celerity or phase speed refer only to the magnitude of the phase velocity
Dispersion_(water_waves)
Light wave refraction with opposite properties to those usually observed
opposition of wave vector to group velocity, and energy to velocity. "Phase velocity" is used conventionally, as phase velocity has the same sign as the wave
Negative_refraction
Quantum mechanical waves describing matter
{\displaystyle \mathbf {v} } is the velocity of the center of mass of the particle, identical to the group velocity. The phase velocity in isotropic media is defined
Matter_wave
Wave on the surface of a fluid, dominated by surface tension
capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics and phase velocity are dominated by the effects of surface tension
Capillary_wave
Speed and direction of a motion
motion. Four-velocity (relativistic version of velocity for Minkowski spacetime) Group velocity Hypervelocity Phase velocity Proper velocity (in relativity
Velocity
Effect of a material on light
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to
Dispersion_(optics)
Pattern of movement across water
the group velocity of a deep water wave is half of its phase velocity, which, in turn, goes as the square root of the wavelength. Two velocity parameters
Kelvin_wake_pattern
Elapsed fraction of a cycle of a periodic function
cancellation Phase problem Phase spectrum Phase velocity Phasor Polarization (waves) Coherence (physics), the quality of a wave to display a well defined phase relationship
Phase_(waves)
Property in optics
{1}{v}}.} The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at
Refractive_index
Particle that is not bound by an external force
classical velocity of the particle. The group velocity is the (approximate) speed at which the whole wave packet propagates, while the phase velocity is the
Free_particle
Elastic waves propagating in solid plates or spheres
number k. Numerical methods are used to find the phase velocity cp = fλ = ω/k, and the group velocity cg = dω/dk, as functions of d/λ or fd. cl and ct
Lamb_waves
Speed of electromagnetic waves
velocities can exceed c. The phase velocity of X-rays through most glasses can routinely exceed c, but phase velocity does not determine the velocity
Speed_of_light
Monochrome light beam whose amplitude envelope is a Gaussian function
Gouy phase at z, an extra phase term beyond that attributable to the phase velocity of light. The physical electric field is obtained from the phasor field
Gaussian_beam
Smooth curve outlining the extremes of an oscillating signal
the distance Δx is related to the time interval Δt by the so-called phase velocity vp v p = Δ x Δ t = λ f . {\displaystyle v_{\rm {p}}={\frac {\Delta
Envelope_(waves)
Topics referred to by the same term
Wave velocity may refer to: Phase velocity, the velocity at which a wave phase propagates Pulse wave velocity, the velocity at which a pulse travels through
Wave_velocity
Parameter characterizing an AC conductor
flows through a given conductor such as a wire or cable at a particular phase velocity v p {\displaystyle v_{p}} . It takes time for later portions of the
Electrical_length
Electromagnetic radiation from a charged particle in a medium
dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium
Cherenkov_radiation
Material with a negative refractive index
reverse of the electromagnetic wave, characterized by an antiparallel phase velocity is also an indicator of negative index of refraction. Furthermore, negative-index
Negative-index_metamaterial
Short "burst" or "envelope" of restricted wave action that travels as a unit
carrier waves, phase velocity, and group velocity – date from the mid-1800s. The idea of a group velocity distinct from a wave's phase velocity was first proposed
Wave_packet
Phemomenon of physical optics
in free space. The Gouy phase results in an increase in the apparent wavelength near the waist (z ≈ 0). Thus the phase velocity in that region formally
Gouy_phase_shift
Type of low-frequency compressive wave
pressure oscillations that are either in-phase or anti-phase, respectively. This results in the phase velocity of any given fast mode always being greater
Magnetosonic_wave
Effect in physics
Landau (1908–68). As the oscillation moves through the medium with phase velocity v ph {\displaystyle v_{\text{ph}}} it will accelerate slightly slower
Landau_damping
Pulse that is substantially slowed to less than the speed of light
time-varying amplitude does not propagate at the phase velocity but rather at the group velocity. The group velocity depends not only on the refractive index
Slow_light
Propagation of information or matter faster than the speed of light
deal with a phase velocity or group velocity faster than the vacuum velocity of light. However, as stated above, a superluminal phase velocity cannot be
Faster-than-light
Physical phenomenon relating to the direction of waves
refraction θ 2 {\displaystyle {\theta _{2}}} is equal to the ratio of phase velocities v 1 v 2 {\textstyle {\frac {v_{1}}{v_{2}}}} in the two media, or equivalently
Refraction
Model of electrically conducting fluids
magnetosonic waves Fast magnetosonic waves Phase velocity plotted with respect to θ These modes have phase velocities that are independent of the magnitude
Magnetohydrodynamics
Relation in chromatography
variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a
Van_Deemter_equation
Branch of physics that studies light
Dispersion occurs when different frequencies of light have different phase velocities, due either to material properties (material dispersion) or to the
Optics
Wave where gravity is the main restoring force
traveling ionospheric disturbances and could be observed by radars. The phase velocity c {\displaystyle c} of a linear gravity wave with wavenumber k {\displaystyle
Gravity_wave
Light rays follow quickest paths
velocity. However, the "ray velocity" is defined not as the group velocity, but as the phase velocity measured in that direction, so that "the phase velocity
Fermat's_principle
Tendency of AC current flow in a conductor's outer layer
only about 0.5 mm with a phase velocity of only about 500 m/s. As a consequence of Snell's law and this very tiny phase velocity in a conductor, any wave
Skin_effect
Measure of change in amplitude and phase of a wave
amplitude decreases as the wave propagates in the x direction. Wavelength, phase velocity, and skin depth have simple relationships to the components of the propagation
Propagation_constant
Speed of sound wave through elastic medium
propagates at its own speed, called the phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with
Speed_of_sound
Layer of the Earth's ionosphere
were two velocities of light, the phase velocity and the group velocity. The phase velocity can in fact be greater than c, but the group velocity, being
Kennelly–Heaviside_layer
1 ) {\displaystyle \alpha (w)=a_{1}|w|^{1-\gamma }\quad (1.1)} The phase velocity is written: 1 c ( w ) = 1 c ∞ + a 1 | w | − γ + cot ( π γ 2 ) ( 1
Azimi_Q_models
Transport of energy by wind waves, and the capture of that energy to do useful work
Deep-water group velocity is half the phase velocity. Shallow water waves are dispersionless: group velocity is equal to phase velocity, and wavetrains
Wave_power
Equations describing classical electromagnetism
There are cases (anomalous dispersion) where the phase velocity can exceed c, but the "signal velocity" will still be ≤ c In some books—e.g., in U. Krey
Maxwell's_equations
Fluid dynamics theory on gravity waves
surfactants. The group velocity ∂Ω/∂k of capillary waves – dominated by surface tension effects – is greater than the phase velocity Ω/k. This is opposite
Airy_wave_theory
Concept in condensed matter physics
In wave mechanics, anomalous velocity refers to the group velocity of a wave packet that is transverse to an applied electric field, arising even in the
Anomalous_velocity
Hypothetical flow velocity
fluid velocity (excluding the other phase, solids, etc.), m/s. The local physical velocity can still be different than the average fluid velocity because
Superficial_velocity
Single-mode optical fiber for linearly polarized light
fiber, different polarization modes have the same nominal phase velocity due to the fiber's circular symmetry. Stress induced birefringence in
Polarization-maintaining optical fiber
Polarization-maintaining_optical_fiber
Atmospheric wave disturbance
Now, in water waves, the group velocity (which is also the energy-transport velocity) is less than the phase velocity. Therefore, on average, wave energy
Undular_bore
Rapid oscillations of electron density
independent of wavelength, Langmuir waves have infinite phase velocity and zero group velocity. For m ∗ = m e {\displaystyle m^{*}=m_{\mathrm {e} }} ,
Plasma_oscillation
Formula for refraction angles
{n_{2}}{n_{1}}}\right)} of the two media, or equivalently, to the ratio of the phase velocities ( v 1 v 2 ) {\displaystyle \left({\tfrac {v_{1}}{v_{2}}}\right)} in
Snell's_law
Rotation of the plane of linearly polarized light as it travels through a chiral material
difference in the phase velocity of light of two different linear polarizations, circular birefringence implies a small difference in the velocities between right
Optical_rotation
Seismological method
inversion, phase velocities are used more often than group velocities because it is easier to create a dispersion curve of phase velocities. A dispersion
Surface-wave_inversion
Separation of a sound wave into component frequencies while passing through a material
into its component frequencies as it passes through a material. The phase velocity of the sound wave is viewed as a function of frequency. Hence, separation
Acoustic_dispersion
Vector describing a wave; often its propagation direction
in the direction of phase velocity. In other words, the wave vector points in the normal direction to the surfaces of constant phase, also called wavefronts
Wave_vector
Information sent faster than light
known phenomenon of phase velocity to carry information, a property which in fact is impossible. The limitations of phase velocity beyond the speed of
Faster-than-light communication
Faster-than-light_communication
Spatial frequency of a wave
amplitude decreases as the wave propagates in the x-direction. Wavelength, phase velocity, and skin depth have simple relationships to the components of the wavenumber:
Wavenumber
Inertial wave in rotating fluids
fundamental principles of the wave, e.g., its restoring force and westward phase velocity. The rotation causes fluids to turn to the right as they move in the
Rossby_wave
identical), the group and phase velocities are separate. Relation between space, time, angle analogues used to describe the phase: Δ r λ = Δ t T = ϕ 2 π
List of equations in wave theory
List_of_equations_in_wave_theory
Low-frequency plasma wave
{B}{\sqrt {\mu _{0}\,\rho }}}} is the Alfvén wave group velocity. (The formula for the phase velocity assumes that the plasma particles are moving at non-relativistic
Alfvén_wave
Front velocity Phase velocity Propagation delay Time of flight Velocity factor Dielectric constant Brillouin, Léon. Wave propagation and group velocity. Academic
Signal_velocity
System for describing optical polarization
crystal depending on the crystal at hand. Light travels with a higher phase velocity along an axis that has the smallest refractive index and this axis is
Jones_calculus
Microelectromechanical sensor
wave. We can express the synchronous frequency f0 of the device with phase velocity vp and pitch p as: f 0 = v p p {\displaystyle f_{0}={\frac {v_{p}}{p}}}
Surface_acoustic_wave_sensor
Topics referred to by the same term
absolute value of: phase velocity, the velocity at which a wave phase propagates at a certain frequency group velocity, the propagation velocity for the envelope
Wave_speed
Distance over which a wave's shape repeats
the phase speed (magnitude of the phase velocity) of the wave and f {\displaystyle f} is the wave's frequency. In a dispersive medium, the phase speed
Wavelength
Materials engineered to have properties that have not yet been found in nature
allows an electromagnetic wave to convey energy (have a group velocity) against its phase velocity. Pendry hypothesized that metallic wires aligned along the
Metamaterial
Delays experienced through a linear time-invariant system
Group velocity – "The group velocity of light in a medium is the inverse of the group delay per unit length." Phase velocity Wave packet This article incorporates
Group_delay_and_phase_delay
Precursor of the free-electron laser
electrons. Essentially, this is a form of Cherenkov radiation where the phase velocity of the light has been altered by the periodic grating. However, unlike
Smith–Purcell_effect
How one process influences another
group velocity cannot be faster than the speed of light. The phase of a wave packet travels at the phase velocity; since phase is not causal, the phase velocity
Causality
Type of bilateral nystagmus
an exponentially decreasing slow-phase velocity. In contrast, the fine nystagmus with constant slow-phase velocity is attributed to peripheral vestibular
Bruns_nystagmus
Refractive property of materials
In the second case the extraordinary ray propagates at a different phase velocity (corresponding to ne) but still has the power flow in the direction
Birefringence
Partial differential equation used in physics
}={\frac {1}{\sqrt {\mu \varepsilon }}}} is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇2 is the
Electromagnetic_wave_equation
Wave in the ocean or large lakes
where the phase velocity of shallow water gravity wave (c) can be noted as c = ( g H ) 1 / 2 {\displaystyle c=(gH)^{1/2}} and the group velocity (cg) of
Sverdrup_wave
Equations of light transmission and reflection
be constant, ℓ must increase at the velocity ω / k , {\displaystyle \omega /k\,,\,} known as the phase velocity (vp). This in turn is equal to c / n
Fresnel_equations
Microwave antenna
the same as an optical lens: the microwaves have a different speed (phase velocity) within the lens material than in air, so that the varying lens thickness
Lens_antenna
Technique in analytical chemistry
adsorbent, the stationary phase. The velocity of each component depends on its chemical nature, on the nature of the stationary phase (inside the column) and
High-performance liquid chromatography
High-performance_liquid_chromatography
which have the same velocity as the wave. The existence of a greater number of particles that move slower than the wave phase velocity v p h {\displaystyle
Two-stream_instability
Time of electromagnetic wave coherence
designated τ, is calculated by dividing the coherence length by the phase velocity of light in a medium; approximately given by τ = 1 Δ ν ≈ λ 2 c Δ λ {\displaystyle
Coherence_time
Equations that describe the behavior of a physical system
alternating current circuit, and v is the phase velocity. Nonlinear equations model the dependence of phase velocity on amplitude, replacing v by v(X). There
Equations_of_motion
Electrical cable with concentric conductors
Cafe. Archived from the original on 2012-01-03. Retrieved 2012-01-25. "Phase Velocity". Microwaves 101. 2010-03-30. Archived from the original on 2012-01-14
Coaxial_cable
Speed at which the first rise of a pulse above zero moves forward
are several different velocities. For definiteness, consider an amplitude modulated electromagnetic carrier wave. The phase velocity is the speed of the
Front_velocity
in vacuum. As the electron density increases, the phase velocity increases and the group velocity decreases until the cut-off frequency where the light
Electromagnetic_electron_wave
Topics referred to by the same term
methylphosphonate, a nerve agent Phase velocity ( v p {\displaystyle v_{\mathrm {p} }} ), the velocity at which the phase of a wave propagates, given a certain
VP_(disambiguation)
Shielding an object from view using materials made to redirect light
the group velocity will be identical with phase velocity. In the context of this experiment, group velocity can never exceed the velocity of light, hence
Metamaterial_cloaking
dispersion means that waves of different wavelength propagate at different phase velocities. Euler–Bernoulli beam equation with time-dependent loading Airy equation
Dispersive partial differential equation
Dispersive_partial_differential_equation
Number of occurrences or cycles per unit time
dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: f = v λ . {\displaystyle
Frequency
Electronic circuit in which a signal entering any port exits at the next port
elliptically polarized waves. These circular modes have different phase velocities which can cause them to combine constructively or destructively at
Circulator
Optimal condition for a hypothetical transmission line
the velocity, v, and phase constant, β being given by, v = ω β {\displaystyle v={\frac {\omega }{\beta }}} and the requirement that phase velocity, v,
Heaviside_condition
Concept in astrophysics
anticyclonic vortex. The Rossby waves have the notable property of having the phase velocity opposite to the direction of motion of the atmosphere or disc in the
Rossby_wave_instability
Mathematical models
and phase velocity (1.6) in the frequency band 0–300 Hz. Fig.1. presents the graph for the Kolsky model – attenuation (left) and phase velocity (right)
Q_models_(seismology)
Ionizing radiation
is due to high-speed beta particles traveling faster than the speed of light (phase velocity) in water (which is 75% of the speed of light in vacuum).
Beta_particle
Complete reflection of a wave
velocity ω / k , {\displaystyle \omega /k,} known as the phase velocity. This in turn is equal to c / n , {\displaystyle c/n,} where c is the phase velocity
Total_internal_reflection
Alteration of the original shape of a signal
the output. Can be found only in dispersive media. In a waveguide, phase velocity varies with frequency. In a filter, group delay tends to peak near the
Distortion
Room designed to be completely echo free
{\displaystyle \lambda =v/f} where lambda represents wavelength, v is phase velocity of wave, and f {\displaystyle f} is frequency. To shield for a specific
Anechoic_chamber
Concept in celestial mechanics
In celestial mechanics, escape velocity or escape speed is the minimum speed needed for an object to escape from contact with or orbit of a primary body
Escape_velocity
Nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth
theory, the free surface elevation η, the velocity potential Φ, the phase speed (or celerity) c and the wave phase θ are, for a progressive surface gravity
Stokes_wave
Concept in physics and electrical engineering
dispersion relation (NDR) is a dispersion relation that assigns the correct phase velocity v 0 {\displaystyle v_{0}} to a nonlinear wave structure.[clarification
Nonlinear dispersion relation in Vlasov–Poisson plasmas
Nonlinear_dispersion_relation_in_Vlasov–Poisson_plasmas
Optical polarization rotator based on the Faraday effect
traverses the device, which is explained by a slight difference in the phase velocity between the left and right circular polarizations. Thus it is an example
Faraday_rotator
Velocity of a particle in a medium as it transmits a wave
Particle velocity (denoted v or SVL) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is
Particle_velocity
Structures of the Earth's mantle
Large low-shear-velocity provinces (LLSVPs), also called large low-velocity provinces (LLVPs) or superplumes, are characteristic structures within the
Large low-shear-velocity provinces
Large_low-shear-velocity_provinces
through a homogeneous dielectric medium at a speed greater than the phase velocity of electromagnetic waves in that medium. Transition radiation was demonstrated
Transition_radiation
Space of all possible states that a system can take
dimension, and where the two variables are position and velocity. In this case, a sketch of the phase portrait may give qualitative information about the
Phase_space
Simultaneous flow of materials with two or more thermodynamic phases
velocity and gas-liquid ratio is increased, "bubble flow" transitions into "mist flow". At high liquid-gas ratios, liquid forms the continuous phase and
Multiphase_flow
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