Question

reason for different wave patterns for various values of Δω and Δk

Answer 1

The wave patterns of various Δω and Δk values are not same , even though the group velocity Vg is 1 for each wave pattern( due to Δω and Δk being equal to each other).

Explanation:

• When these two monochrome waves are propagating in vacuum, they have the same phase velocity c (the speed of light in vacuum), and the superposed wave's phase velocity equals its group velocity.

• Waves can be in the group and such groups are called wave packets, so the velocity with a wave packet travels is called group velocity.

• The velocity with which the phase of a wave travels is called phase velocity.

• The relation between group velocity and phase velocity are proportionate.

• The phase velocity υp, is a function of wavelength, in the case of a signal containing many frequency components, which is any signal other than a single frequency sinusoid, the various frequency components will travel down the line at different speeds.