The most general form of a harmonic wave is given by ψ = A cos[k(x - vt)] , where v is the phase velocity and k is the wave number. Expanding this we have ψ = A cos(kx - kvt) . We know that the argument of the cosine must be dimensionless, so the expression kvt must be dimensionless, thus kv must be an inverse time, or the angular frequency of the wave (we know it is an angular frequency and not a regular frequency since we want the argument of the cosine to be in radians, which are dimensionless). Thus σ = kv . But the wavenumber is just k = 2Π/λ

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