# Phase Velocity

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## Phase velocity

The velocity of propagation of a pure sine wave of infinite extent. In one dimension, for example, the form of the disturbance for such a wave is given by y(x, t) = A sin [2π(x/λ - t/T)]. Here x is the position at which the disturbance y(x, t) exists at time t, λ is the wavelength, T is the period which is related to the wave frequency by T = 1/f, and A is the disturbance amplitude. The argument of the sine function is called the phase. The phase velocity is the speed with which a point of constant phase can be said to move. Thus x/λ - ft = constant, so the phase velocity vp is given by dx/dt = vp = λf. This is the basic relationship connecting phase velocity, wavelength, and frequency. See Phase (periodic phenomena), Sine wave, Wave motion

The phase velocity for waves in a medium is determined in part by intrinsic properties of the medium. For all mechanical waves in elastic media, the square of the phase velocity is proportional to the ratio of the appropriate elastic property of the medium to the appropriate inertia property. The phase velocity of electromagnetic waves depends upon the medium as well. In vacuum, the phase velocity c is given by c2 = l/&epsi;0μ0 &ap; 9 × 1016 m2/s2, where &epsi;0 and μ0 are respectively the permittivity and permeability of the vacuum. Phase velocity may also depend upon the mode of wave propagation—in general, upon the frequency of the wave. Waves of different frequencies will travel at different speeds, resulting in a phenomenon called dispersion. See Electromagnetic radiation, Light, Wave equation

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Phase Velocity

(phase speed), the velocity of propagation of the phase of a harmonic wave. The phase velocity c can be expressed in terms of the frequency f and the wavelength λ or in terms of the angular frequency ω = 2πf and the wave number k = 2π/λ: c = fλ = ω/k.

The concept of phase velocity is valid if the harmonic wave is propagated with constant wave form; this condition is always satisfied in linear media. Velocity dispersion occurs if the phase velocity is dependent on frequency or, stated differently, on wavelength. In the absence of dispersion any wave will propagate, without changing its wave form, at a velocity equal to the phase velocity. If dispersion occurs, nonharmonic waves change their wave form, and the conventional concept of velocity no longer applies. In such cases the concepts of group velocity and wave-front velocity become important. The phase velocity for a given frequency can be found experimentally by determining the wavelength in interference experiments. The ratio of phase velocities in two different media can be determined from the refraction of a plane wave at the interface surface of the media, because the refractive index is equal to the ratio of the phase velocities.

M. A. ISAKOVICH

## phase velocity

[′fāz və‚läs·əd·ē]
(physics)
The velocity of a point that moves with a wave at constant phase. Also known as celerity; phase speed; wave celerity; wave speed; wave velocity.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Next, using the inhomogeneous wave theory, we recast the dispersion equations in a general complex form which separable real solutions to define the phase velocity and attenuation are admitted.
Solutions to this equation contain the phase velocity and frequency (assuming no absorption by the medium).
The phase velocity and attenuation coefficients of plane waves are studied numerically for a particular model.
Figure 10 displays the variation of the Stoneley wave velocity and attenuation coefficient with respect to phase velocity c that has oscillatory behavior in the whole range of c for L-S theory, which changes from the positive to the negative gradually.
(2) There exists only one critical velocity equal to the lowest phase velocity of waves in the Timoshenko beam if the loading frequency is zero, provided that the lowest phase velocity of waves is less than the shear wave velocity.
In the phase velocity search, the analysis begins with the production of the Gabor spectrum (Figure 6) of the impulse response.
where [omega] is the frequency of wave propagation, q is the wave number, and l = [square root of (D[tau])]; the phase velocity is given by c = [[omega].sub.r]/q and attenuation constant by [GAMMA] = -[[omega].sub.i], where [[omega].sub.r] = Re([omega]) and [[omega].sub.i] = Im([omega]) mean, respectively, the real and imaginary parts of [omega].
The influence of depth of irregularity on phase velocity and some special cases have been studied.
The curves that depict the relationships between frequency and eigenvalue, as well as phase velocity and group velocity, are called dispersion curves.
Firstly, phase velocity was expressed in terms of pseudo energy and power flow.
The whole RF circuit consists of input section [L.sub.0] with pitch [P.sub.0] followed by an increased phase velocity section [L.sub.1] with pitch [P.sub.1] and then a negative tapered section [L.sub.2] with pitch [P.sub.2], as shown in Figure 6.
Both stare and look OKNe cannot be driven solely by retinal slip because slow phase velocity can often match the stimulus velocity (unity gain) and would eliminate the retinal slip.

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