I know this question has been asked before, but I still don’t completely understand. I understand that different stations are given different frequencies, but waves are able to interfere with each other if they meet. If they do, they produce a completely new wave. So how are we still able to single out one wave?
I understand that different stations are given different frequencies, but waves are able to interfere with each other if they meet. If they do, they produce a completely new wave.
You are misunderstanding. When waves meet they typically superimpose and then pass through one another without generating a new wave. Generation of a new waveform requires nonlinearity at the point where they meet. This nonlinearity breaks superposition, resulting in the generation of new frequencies. For example, in light, a photographic plate can record a new frequency because it's response is nonlinear. A radio receiver can generate a new frequency because it has a diode or other nonlinear element. Without those nonlinear devices, there is no new wave or frequency.
You mean why don't you hear all radio stations at once in you radio? That's because your radio has a filter which selects a narrow band of frequencies. Your antenna sees a superposition (a fancy word which means that values add linearly and not say multiply by each other) of all signals at all frequencies that it can detect. If the fiter was too broad you could hear all radio stations at once and it would be unintelligible.