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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?

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    \$\begingroup\$ In a word, linearity, which keeps the mathematics clean. Even on the ocean where unlike with EM waves the mechanism is ultimately non-linear, there is more linear behavior of distinct waves passing through each other going on than you probably credit from casual observation. \$\endgroup\$ – Chris Stratton Jul 25 at 0:29
  • \$\begingroup\$ In other domains (acoustics, quantum mechanics, optics ), only waves of the same frequency and mutually coherent produce interesting interference phenomena. Why do you expect rf to be different? \$\endgroup\$ – The Photon Jul 25 at 0:55
  • \$\begingroup\$ We can separate individual waves from the combined wave if the the original waves are different in either: space, time, frequency, polarisation, or encoding. There may be other parameters also which help in separating the waves out. \$\endgroup\$ – AJN Jul 25 at 2:54
  • \$\begingroup\$ If the interfering wave occupy same space, time, have same frequency, polarisation etc, we can never really separate them out perfectly. This is why we cannot perfectly filter out noise once it gets into the system. The part of the noise having same characteristic as the desired signal cannot be separated out. \$\endgroup\$ – AJN Jul 25 at 2:55
  • \$\begingroup\$ How can we hear people speaking to us in a room full of other non-related sounds? \$\endgroup\$ – Andy aka Jul 25 at 8:00
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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.

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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.

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