When you turn on a lightbulb, the light coming from the bulb travels at the speed of light, which is 299,792,458 meters per second. Radio waves also travel at this same speed, since it is also light.
It's worth mentioning that neither light nor radio waves travel at 299,792,458 m/s through atmosphere. That's the speed of light in a vacuum.
An interesting question is whether radio waves, gamma radiation, and visible light all travel an identical speed through atmosphere.
The reason light slows down in atmosphere is because it hits atoms. It travels between each atom at the speed of light, but when it reaches an atom the radiation is absorbed and re-emitted, which introduces a delay. So the question that I'm wondering is: do different frequencies of radiation get absorbed and re-emitted at the same rate as every other frequency? That would give it identical speed. But if the absorption is different then presumably the speed would also be different.
> An interesting question is whether radio waves, gamma radiation, and visible light all travel an identical speed through atmosphere.
They don't. The index of refraction tells you about how the speed of light is changed by a medium, and the fact that it's different for different colors of visible light is why you get effects like rainbows.
GBNST (guilt by non-scientific thinking): Radio waves = sound = speed of sound, therefore wtf sound = light, but now I 'see the light.'
After having a second cup of coffee I did a doh! and realized conflating 'radio' with sound is non-sensical, but I wonder if I'm in the minority thinking this way. Or maybe it's just my non-tech background!