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I know a fact that says a wave can go through barriers thinner than its length. This is why for example FM radio can be picked anywhere while antenna TV needs direct sight to the transmitter.

Is this correct? If so, what is the explanation?

Related, if my wifi is 2.4GHz, then the wave length is 12.5 cm (right?), so I will not go thorough walls thicker than that?

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No, this isn't correct. What matters is how strongly the barrier absorbs EM waves. For example metal is a very strong absorber and even a thin mesh of metal wire will absorb virtually all the EM radiation incident upon it. This is the principle behind the Faraday cage.

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  • $\begingroup$ Ok, but some waves travel through walls while others don't. And the thickness of the wall matters, right? Is it just that the thicker it is the more it is capable to absorb energy? And how does it relate to frequency? Are lower frequencies more packed with energy per quanta and so can make it through to the other side of the barrier? $\endgroup$
    – user46265
    Commented May 11, 2014 at 14:01
  • $\begingroup$ Actually it's viceversa... High frequencies have more energy. $\endgroup$
    – Noldor130884
    Commented Jul 16, 2015 at 12:41
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The problem is how waves interact with matter. Thickness of walls is not to be taken into account, since basically a wall is (partially) not metallic, therefore attenuates e.m. waves but doesn't reflect them. You cannot generalize on the material too, because air is in fact not very different from concrete. What changes? Epsilon and Mu of the medium in which the wave propagates. Both are not conductive though.

So what are you (maybe) meaning is that a wave cannot travel though a thick conductive wall. That is also false if you consider reflections, multipath and so on.

Now let me say this: my mobile phones gets my wifi (I'm using the 6GHz band so the walls should be even thinner, right?) about up to 15 meters away from a reinforced concrete wall behind which the wifi router was placed.

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