group velocity

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Group velocity

The velocity of propagation of a group of waves forming a wave packet; also, the velocity of energy flow in a traveling wave or wave packet. The pure sine waves used to define phase velocity vp do not ever really exist, for they would require infinite extent. What do exist are groups of waves, wave packets, which are combined disturbances of a group of sine waves having a range of frequencies and wavelengths. Good approximations to pure sine waves exist, provided the extent of the media is very large in comparison with the wavelength of the sine wave. In nondispersive media, pure sine waves of different frequencies all travel at the same speed vp, and any wave packet retains its shape as it propagates. In this case, the group velocity vg is the same as vp. But if there is dispersion, the wave packet changes shape as it moves, because each different frequency which makes up the packet moves with a different phase velocity. If vp is frequency-dependent, then vg is not equal to vp. See Phase velocity, Sine wave, Wave motion

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

group velocity

[¦grüp və′läs·əd·ē]
The velocity of the envelope of a group of interfering waves having slightly different frequencies and phase velocities.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
From the figure 6 (b) it is evident that there is some energy concentration in the S0 mode at a frequency of 410 kHz the group velocity was cantered at 2.775 m/ms, while the highest energy concentration is in the A0 mode at a frequency of 150 kHz, but the group velocity was found to be 1.871 m/ms which is far less when compared to 2.775 m/ms, therefore this should be an A0 mode.
Knowing the group velocity of the modes [A.sub.0] and [S.sub.0]: Vg ([A.sub.0],300kHz)=1268 m/s, Vg ([S.sub.0],300kHz)=5649 m/s, we can calculate the delamination position from the sensor A noted [P.sub.D] by [DELTA][t.sub.1] (Delta 1) and delamination length noted [L.sub.D] by [DELTA][t.sub.2] (Delta 2) as presented in Table 2.
where [L.sub.max] and [L.sub.min] are the maximum and minimum grid size, respectively; [[lambda].sub.min] is the minimum wavelength; [n.sub.min] is the minimum number of elements within one wavelength (usually [n.sub.min] is in the range of 8~10); [c.sub.s] denotes the velocity of shear waves; and [c.sub.min] is the minimum group velocity of elastic waves.
The results of the joint inversion of the Z and R group velocity spectra and the RPM frequency curve are presented in Figures 10 and 11.
The group velocity vg of the wave packet associated with the electron of rest mass [m.sub.0], coincides with its velocity v.
[] is the phase velocity, and vg is the group velocity. [r.sub.c] is the optimum radius of the integral surface in the process of U scattering [58].
In the case of first derivatives we consider the dispersion error, the error in phase velocity, and the error in group velocity as objective functions.
The cause of this result is that the frequency of DW is determined by the phase-matched condition associated with the nature group velocity, but SS increases the group velocity at resonant frequency eventually because it affects the group velocity in an intensity dependent fashion [30].
The saddle point method is used to determine the solution with zero group velocity. In general, there are two distinct spatial branches of solutions of (4) on the complex k* plane.
In this paper, tapered core is used instead of cylindrical core so as to make the light travel with the lesser group velocity and also to stop the light at the fixed position efficiently.
The Rayleigh-wave group velocity for the trace of each event registered has been measured by means of the combination of digital filtering techniques: Multiple Filter Technique (Dziewonski et al., 1969) and Time Variable Filtering (Cara, 1973), as shown in the flow chart displayed in Figure 2.
The results focused on waveforms, fast Fourier transforms (FFT), and frequency/time analysis (with superimposed group velocity curves) of the signals.