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A transverse wave given by y₁ = A sin(ωt - kx) is sent down a string. Upon reflection, it becomes y₂ = -1/2A sin(ωt + kx). Show that the resultant of these two waves on the string can be written as the combination (sum) of a traveling wave φ₃(x, t) and a standing wave φ₄(x, t). Specify the amplitude of φ₃(x, t) and φ₄(x, t). Reminder: sin(u ± v) = sin(u) cos(v) ± cos(u) sin(v).
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