# Difference between phase velocity and group velocity

## Key difference - phase velocity vs. group velocity

According to quantum physics, particles sometimes behave like waves. In some cases waves behave like particles. This property of particles and waves is known as wave-particle duality. This dual nature of particles and waves enables us to represent a particle in the form of waves. Based on this concept, waves are used to represent particles as this is an essential step when we study particles in quantum physics. However, we have to add many waves with different angular frequencies and amplitudes in a certain way to get a wave packet that represents a particle. Within this concept there are two types of velocities, namely phase velocity and group velocity. These two quantities have very different and particular definitions and properties. The main difference between phase velocity and group velocity is that the phase velocity is greater than the group velocity in a normal medium. This article tries to differentiate these differences in detail.

## What is group speed?

To understand the nature of group speed, let's consider a race. At any given point in time, a particular runner's speed is relative to others. The speed of each individual runner within the group is simply different. But they run within a group. The speed at which the group of runners is moving can be viewed as the group speed in this simple example. In quantum physics, the idea of ​​group speed goes hand in hand with the idea of ​​wave packets or pulses. A wave packet can be obtained by adding many waves with different wave numbers and amplitudes. In this way, the position of a particle can be localized within a certain area by using such a wave packet that represents a particle. The resulting amplitude of a wave packet differs with x as shown in Fig. 1. Nevertheless, this wave package is a combination of many waves. The resulting wave packet represents the particle and is a group of many waves. In this model, the speed of the particle is therefore equal to the speed of the wave packet. In other words, the speed of the particle is equal to the group of waves that make up the wave packet. The speed of the group or the wave packet is called the group speed. The group speed can be expressed mathematically as v g = Dω / dk.   It is the speed at which the particle is moving.

Monochromatic harmonic waves cannot transport information through space. In order to convey information, a superposition of many waves is required, which result in a wave packet.

## The phase velocity ( wave velocity ) of a wave is the speed at which any phase of the wave propagates. For example, point A of the wave (Fig: 02) moves with the phase velocity. It is given by v p = ωk.

In a wave packet, the carrier wave moves with the phase velocity. But when we are dealing with a packet of particles or waves, the phase velocity is not important.

The relationship between phase velocity and group velocity depends on the material properties of the medium. In nondispersive media we have sv g = v p . In normal dispersion media, sv g < v p applies. But in abnormal media v g > v p.

In non-dispersive media, the phase velocity of waves does not depend on the wavelength . The phase velocity is therefore equal to the group velocity. For example, the phase velocity is equal to the group velocity when sound waves propagate through air, since air is a non-dispersive medium for sound waves.

## Difference between phase velocity and group velocity

### speed

Group velocity : In an anomalous medium, the group velocity is greater than the phase velocity.

Phase Velocity : In a normal medium, the phase velocity is greater than the group velocity.

### meaning

Group speed : The concept of group speed is very important when a particle is represented by waves.

Phase Velocity : The phase velocity is important when dealing with individual waves.

### In a wave packet

Group speed : In a wave packet , the envelope curve moves with the group speed.

Phase velocity : In a wave packet , the carrier wave moves with the phase velocity.

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