Brian Howie wrote:

" It was known that different frequencies travel with different speeds
on a
long cable".

Is the same in air and space?

Yes in air , and no in space.

B

Depends what you mean by "space".. perfect vacuum, sure..

But what's between the planets in the Solar System isn't a perfect
vacuum, and so, it shows dispersion due to the presence of small amounts
of ionization.

Granted, it's generally a better vacuum than you are likely to achieve
on Earth by mechanical means.