Calculate the speed of an Alfven wave for the following cases:

(a) In the Earth's ionosphere, considering that n_e = 10⁵ cm^–3 , B = 0.5 gauss, and that the positive charge carriers are atomic oxygen ions.

(b) In the solar corona, assuming n_e = 10⁶ cm^–3 , B = 10 gauss, and that the positive charge carriers are protons.

(c) In the interstellar space, considering n_e = 10⁷ m^–3 and B = 10^–7 tesla, the positive charge carriers being protons.