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Question 2 (F): We showed above that a function f(k.1-wt) satisfies the 3D wave equation where v = w/k and k is the magnitude of k. If this function is a sinusoid f(K:1 - wt) = Asin(k - - wt) then moving a distance in the direction of propagation at a fixed time must correspond to an increase of the phase of 21. If k = 2ñ/1 where an is the direction of propagation, then moving a distance in the direction of propagation from a point r is accomplished by adding \ñ to . Show that (*--* - to) - (2.7-) k (F+ \ñ) - wto wt = is 27 if k = 27 /lambda. This concept of adding lân to ř is illustrated in Figure 5. This means that the correct interpretation of the wave vector is that it is k = 2tn/1 and the wave number is k = 27/1, as before, and the phase velocity is w W= k 2πνλ =νλ 271