Two waves of identical amplitude travel in the same direction along a string

PHYSICS · Single correct · A Level · Physics · Waves · Waves

Problem

Two waves of identical amplitude AA travel in the same direction along a string. Their equations are y1=A[tan⁡(kx−ωt)],y2=A[tan⁡(kx−ωt+π2)].y_1 = A\bigl[\tan(kx-\omega t)\bigr],\qquad y_2 = A\bigl[\tan(kx-\omega t+\tfrac{\pi}{2})\bigr]. At position x=0x=0 and time t=0t=0, which of the following best characterizes the type of interference between the two waves? (a) Fully constructive interference resulting in a net displacement of +2A+2A. (b) Partially constructive interference resulting in a net displacement of +A2+A\sqrt{2}. (c) Partially constructive interference resulting in a net displacement of +A+A. (d) Fully destructive interference resulting in zero net displacement.

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