Well, if you are really interested in equations you can see some that were made up by Maxwell, Gauss, Faraday, or Ampere.
https://en.wikipedia.org/wiki/Electromagnetic_wave_equation. These guys did all their work well over 100 years ago and the results of those equations are verified everyday. They are an adequate description to just how electromagnetic waves behave. How good is your calculus? If you've had 4 or 5 semesters in college you are all set. If you want something short and easy just see
http://www.tpub.com/neets/book10/40j.htm. All I know is what I learned working on radios for more than 50 years, and my many semesters in college studying mathematics. I was just trying to distill all that down in a short explanation of how radio waves can be influenced by weather and stay away from all the equations that 99% of the people won't understand. Mostly radio waves always travel at the speed of light. Air has little to do with the actual propagation of electromagnetic waves as radios work just fine in outer space where there's no air. Light (just another electromagnetic wave) propagates just fine in space. I don't think that there's too much left that's unclear or unsubstantiated. If you need more then consider that radio waves can have effects on things in their path. Just try putting a cat inside a microwave oven. The cat will be exposed to microwaves and the results will be interesting. I always had to watch my exposure to microwave radiation when working around radars. The biggest risk was getting cataracts in my eyes. People get sun burned. That's just another form of electromagnetic radiation. The risk is less on a cloudy day, but doesn't go away completely. Of course radio waves will be effected by the rain and moisture in the air. Any radio system no matter what frequency can be influenced by the earth's atmosphere and can easily be noticed at times. The sun can also have an effect as it excites the ionosphere. The sun spots run in roughly 11 year cycles. I was just talking with another amateur radio operator the other day and he was complaining about the sun spot cycle being at the low this year. That fact has an effect on the propagation of HF radio signals. All of this only indirectly relates to the subject matter of this thread.