Question

The Group Velocity and Phase Velocity relation can be mathematically written as
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Answer 1

Answer:

Relation Between Group Velocity And Phase Velocity Equation

For the amplitude of wave packet let- ω is the angular velocity given by ω=2πf. k is the angular wave number given by – k=\frac{2\pi }{\lambda } t is time. x be the position.

Answer 2

Answer:

Group velocity: Vg=δw/δk ( angular frequency of the wave / angular wavenumber)

Phase velocity: Vp=λ/T (wavelength/time taken).

Explanation:

Waves can simply be described as a disturbance along a flat surface. Imagine, for example, a sea where waves move from one place along the surface of the sea to another. The tops of the waves move at regular intervals, so they travel a certain distance over a certain period. In this chapter, you will learn about the wave's properties, phase, and group velocity. When a wave moves at a group velocity, the speed at which the wave moves is called the group velocity.

What is group velocity?

The group velocity of a wave is defined as the velocity at which the entire envelope of the wave passes through the medium. The most common example, in this case, is to throw a stone into the body of water and generate multiple waves on the surface of the water. When you throw a stone, a wave is generated around the point where the stone falls. Ripple is formed by small wavelets that propagate in multiple directions away from the drop point. Here, the wavelet with the shortest wavelength propagates faster than other waves.

What is the phase velocity?

Because waves are composed of two important parts, peaks and valleys, their phase velocity also depends on this. This is the speed at which a particular component of the wave, such as the top of the wave, propagates through space. This function, or speed, is directly dependent on the period and wavelength. In addition to this, it is necessary to pay attention to the relationship between the phase velocity and the group velocity.

mathematically :

group velocity: Vg=δw/δk ( angular frequency of the wave / angular wavenumber)

phase velocity: Vp=λ/T (wavelength/time taken)

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