Is Dispersion Present in Expanding Cylindrical Waves of an Infinite Radiator?

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SUMMARY

The discussion centers on the properties of expanding cylindrical waves generated by an infinite line radiator. It is established that expanding spherical waves of order 0 are non-dispersive, while the assumption that expanding cylindrical waves of order 0 exhibit dispersion is debated. Thadman raises the question of dispersion in cylindrical waves, and Bob S clarifies that in a vacuum, all radiated waves are non-dispersive as all wavelengths travel at the same velocity, emphasizing the relationship between dispersion and attenuation.

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  • Familiarity with dispersion relations in physics
  • Knowledge of cylindrical wave characteristics
  • Basic concepts of attenuation in wave mechanics
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thadman
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Let us assume we possesses a line radiator. It's extent is infinite and it radiates 360*.

As far as I understand, an expanding spherical wave of order 0 is not dispersive. I assume an expanding cylindrical wave of order 0 would possesses dispersion, however I am not certain.

Could any members offer insight on this?

Best Regards,
Thadman:biggrin:
 
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i don't think any radiated wave can be dispersive in a vacuum, because all wavelengths travel at the same velocity. To be non-dispersive, there can not be any (wavelength dependent) attenuation either, because dispersion and attenuation are coupled through the dispersion relations. See
http://en.wikipedia.org/wiki/Dispersion_relation
Bob S
 

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