what is the relationship between group velocity and phase velocity?
233830
The phase velocity is: vp = ω/k. The function ω(k), which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity.
1365105
Average speed is not necessarily the same as the magnitude of the average velocity, which is found by dividing the magnitude of the total displacement by the elapsed time. For example, if a trip starts and ends at the same location, the total displacement is zero, and therefore the average velocity is zero.
573560
The group velocity is the velocity of the wave with lower frequency, but the phase velocity is the velocity of the wave with higher frequency. The resulting wave may be a perturbation that acts over a short distance, i.e. a wave packet.
609758
The term '(wt+d)' is called phase and 'd' the phase constant. So, as A(amplitude) is the patthar ki lakeer(I mean constant :P), it is the phase which determines the position(x) of particle or wave. So you can consider phase as the "status" of particle, and this status tells you the position!
171045
The instantaneous velocity is the specific rate of change of position (or displacement) with respect to time at a single point (x,t) , while average velocity is the average rate of change of position (or displacement) with respect to time over an interval.
372362
The definition for phase difference is "the amount one wave lags behind another" (if it's the phase difference between two waves, that is). Displacement isn't mentioned - it's simply how much of the cycle one wave (or point on the wave) is behind the other.
537818
The phase difference is the difference in the phase angle of the two waves. Path difference is the difference in the path traversed by the wave. The relation between phase difference and path difference are direct. They are directly proportional to each other.
603130
Frequency And Velocity Relation For a constant wavelength, Increase in frequency will increase in velocity of the wave. Example: For a constant wavelength, If frequency is doubled. The velocity of the wave will also double.
1416822
Wavelength and frequency are related by the wave's velocity. Imagine a wave with a frequency of 10 Hz, or 10 cycles per second. ... So the velocity doesn't vary the frequency, but the wavelength depends on the frequency and the velocity.
437839
d²Y/dt² is acceleration of SHM , d²Y/dt² = w²Asin(wt ± ∅ + π) hence , phase difference between acceleration and velocity is π/2 and acceleration and displacement is π
928058
The wave velocity and the wavelength are related to the wave's frequency and period by vw=λT or vw=fλ. The time for one complete wave cycle is the period T. The number of waves per unit time is the frequency ƒ.
28909
A wave has a wavelength λ, which is the distance between adjacent identical parts of the wave. The wave velocity and the wavelength are related to the wave's frequency and period by vw=λT or vw=fλ. The time for one complete wave cycle is the period T.
544852
The wave velocity and the wavelength are related to the wave's frequency and period by vw=λT or vw=fλ. The time for one complete wave cycle is the period T.
908481
Wave velocity in common usage refers to speed, although, properly, velocity implies both speed and direction. The velocity of a wave is equal to the product of its wavelength and frequency (number of vibrations per second) and is independent of its intensity.
464121
Displacement in SHM is given by x = A sin( wt) where A is amplitude, w is angular velocity, t is instantaneous time. Phase difference between sin and cos function is 90 degrees or pi/2 radians . Hence phase difference between displacement and velocity is 90 degrees or pi/2 radians.
138844
A wave has a wavelength λ, which is the distance between adjacent identical parts of the wave. The wave velocity and the wavelength are related to the wave's frequency and period by vw=λT or vw=fλ. The time for one complete wave cycle is the period T. The number of waves per unit time is the frequency ƒ.
96573
The relationship between the propagation speed, frequency, and wavelength is vw=fλ. The relationship between the propagation speed, frequency, and wavelength is vw=λf. The relationship between the propagation speed, frequency, and wavelength is vw=√fλ.