Undergrad Wave number, frequency, and velocity in dispersive waves

[Ahmed1029]

1) If I generate a dispersive wave, will it have well-defined constant wave number and frequency? Ones that don't change in time?

2) does the velocity of any point on the wave stay constant in time?

3) How does force interact with waves? Does a free wave act in analogy with free particles? with every point having the same velocity over time unless disturbed?

 

[hutchphd]

1) If I generate a dispersive wave, will it have well-defined constant wave number and frequency? Ones that don't change in time?

2) does the velocity of any point on the wave stay constant in time?

3) How does force interact with waves? Does a free wave act in analogy with free particles? with every point having the same velocity over time unless disturbed?

Answers
1)One can produce such an harmonic wave but it will of necessity not be localized
2)Because it is not localized, the velocity is the phase velocity. It is, by its definition, a constant in time
3)You need to be much more specific here. Typically forces will not be constant in time and/or will reshape the wave.

There are many kinds of waves and the specifics depend upon the wave. For example, there are nonlinear systems which admit solitary wave solutions whose shape is fixed but whose amplitude determines the velocity. This world is complicated.

You should first study dispersive harmonic waves (after understanding the nondispersive ones!)

 

[vanhees71]

For electromagnetic waves, have a look at Landau and Lifshitz vol. 8. There you get a comprehensive description from first principles for both the usual "temporal dispersion" (valid, e.g., for usual dielectrics and visible light) as well as including "spatial dispersion" (needed, e.g., for em. waves in a plasma).