Understanding Wave Dispersion & Group Velocity: Help Needed!

In summary, for a group of waves, the energy is transmitted with the group velocity. This means that the energy is transferred by the entire wave group rather than just individual waves. Dispersion in a medium refers to the way the phase velocity of a wave depends on its frequency, and vice versa. This is because a dispersive medium can sense the discreteness of a complex wave, whereas a non-dispersive medium is not affected by frequency. The effective energy transfer for any wave can be assumed to occur through the effective wavefront, which propagates at the group velocity.
  • #1
samreen
25
0
*for a group of waves, the energy is transmitted with the group velocity.
what does that mean?

*what is meant, as in actually meant, by dispersion of a wave in a medium? whatever i looked up says phase velocity depends on frequency for a dispersive medium and vice versa. Why?

* wave group=wave train of finite length=wave packet=pulse ? correct the wrong bits in this statement please

i need lots of help because I am in a soup here :(
 
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  • #2
i think I've got it somewhat. a dispersive medium is one that can sense the discreteness of a complex wave. because frequency is an issue for it. whereas a non dispersive medium is too stupid to. for it, there effectively is just that fancy wave propagating thru it. and it isn't much bothered by the frequency. not an issue. unlike a dispersive medium, which reacts somehow to frquency, because the phase velocity is diff for diff frequencies.

and for any wave, the effective energy transfer may be assumed to be happening via the effective wavefront, which propagates with the effective velocity or group velocity. right so far??
 

1. What is wave dispersion?

Wave dispersion is the phenomenon where waves travel at different speeds depending on their wavelength and frequency. This results in the separation of different frequencies of a wave as it travels through a medium.

2. How does wave dispersion affect group velocity?

Wave dispersion affects group velocity by causing the different frequencies of a wave to travel at different speeds. This results in the overall velocity of the wave being determined by the slowest frequency, known as the group velocity. Group velocity is important because it determines the speed at which energy is transferred by a wave.

3. What factors affect wave dispersion?

The main factors that affect wave dispersion are the properties of the medium through which the wave is traveling, such as its density and elasticity, and the wavelength and frequency of the wave itself. These factors determine how much the different frequencies of the wave will be separated and how much the group velocity will be affected.

4. How is wave dispersion measured?

Wave dispersion can be measured by analyzing the relationship between the wavelength and frequency of a wave as it travels through a medium. This can be done through experiments or mathematical calculations using the properties of the medium and the wave.

5. What are some real-world applications of understanding wave dispersion?

Understanding wave dispersion is important in many fields, such as telecommunications, seismology, and oceanography. It is used to design and optimize communication systems, study and predict earthquakes, and track ocean currents. It also plays a role in various medical imaging techniques, such as ultrasound and MRI.

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