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    • https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_I_(Raymond)/05%3A_Applications_of_Special_Relativity/5.02%3A_Math_Tutorial__Four-Vectors
      From Figure \PageIndex1: it is clear that the slope of the line representing the four-vector is ω/ck, which is just the inverse of the slope of the wave fronts. Thus, for ins...From Figure \PageIndex1: it is clear that the slope of the line representing the four-vector is ω/ck, which is just the inverse of the slope of the wave fronts. Thus, for instance, the wavenumber for some wave may be zero in the primed frame, which means that the wavenumber and frequency in the unprimed frame are related to the frequency in the primed frame by

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