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ω₁ ≅ ω₂

A case of interest occurs when ω1 is almost equal to ω2. Let us say ω1 - ω2 = Δω      and      ω1 + ω2 = 2ω Furthermore using k = 2π/λ = 2π/vT = ω/v we define Δk = k1 - k2 = (ω1 - ω2)/v = Δω/v      and      2k = k1 + k2 = (ω1 + ω2)/v = ω/v From the results of the previous page, choosing moreover φ1=φ2=0, we obtain then 2a = 2ωt - 2kx      and      2b = Δωt - Δkx Hence, for the total disturbance of the floaters we find u(x,t) = 2A cos((Δωt-Δkx)/2) sin(ωt-kx)

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