Exploring Dispersion in an Infinite Radiator

[thadman]

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

 

[Bob S]

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

 

[sir-pinski]

Dispersion in an infinite radiator is an interesting topic to explore. As you correctly stated, an expanding spherical wave of order 0 is not dispersive, meaning that it does not change its shape or frequency as it travels through space. This is because the wavefronts of an expanding spherical wave are always circular, regardless of the distance from the source.

On the other hand, an expanding cylindrical wave of order 0 would possess dispersion. This is because the wavefronts of a cylindrical wave are not always circular, but can be elliptical or even linear depending on the distance from the source. As the wave travels further away from the source, the shape of the wavefront changes, leading to dispersion.

Dispersion in an infinite radiator can also be seen in the frequency domain. An infinite radiator emits all frequencies equally, but as the wave travels through space, high frequencies will travel faster than low frequencies, leading to a dispersion of the wave. This can be observed in the frequency spectrum of an infinite radiator, where the amplitude of high frequencies will decrease compared to low frequencies.

I hope this helps to provide some insight into the concept of dispersion in an infinite radiator. It is a complex topic and further exploration and research can provide a deeper understanding. Thank you for bringing up this interesting topic for discussion. Best regards.