Relationship between Wave Packet Wavelength & Group Velocity

[yellowgold]

What is the relationship wavelength and group velocity in wave packet ? If a wave packet has big wavelength its group velocity bigger or not ?

 

[malawi_glenn]

What is the relationship wavelength and group velocity in wave packet ? If a wave packet has big wavelength its group velocity bigger or not ?

If you know the definition of group velocity you can do this by yourself as an exercise. Recall the relation between (de Broigle) wavelenght v.s momentum and then you have it.

 

[Entropia]

The relationship between wave packet wavelength and group velocity is an important concept in the study of waves. The wavelength of a wave packet refers to the distance between two consecutive peaks or troughs in the wave. Group velocity, on the other hand, refers to the speed at which the overall shape or envelope of the wave packet propagates.

The relationship between wavelength and group velocity can be described by the dispersion relation, which relates the wave's frequency, wavelength, and group velocity. In general, a shorter wavelength will result in a higher group velocity, meaning that the overall shape of the wave packet will travel faster.

However, it is important to note that this relationship is not always straightforward, as factors such as the medium through which the wave is traveling and the type of wave can also affect the group velocity. For example, in some cases, a longer wavelength may result in a higher group velocity due to the wave's interaction with the medium.

Therefore, it is not accurate to say that a wave packet with a bigger wavelength will always have a bigger group velocity. The relationship between the two is more complex and depends on various factors. As scientists, it is important to carefully analyze and understand these relationships in order to accurately predict the behavior of waves and their propagation.