Two sinusoidal waves of equal amplitude A and equal frequency travel in opposite directions on a string and superpose near a perfectly fixed end at x = 0. Which expression can represent the resulting stationary wave while ensuring that x = 0 is always a node?
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Question

Two sinusoidal waves of equal amplitude A and equal frequency travel in opposite directions on a string and superpose near a perfectly fixed end at x = 0. Which expression can represent the resulting stationary wave while ensuring that x = 0 is always a node?

Options

G1 Physics · Accepted Answer

At a fixed end, y(0,t) = 0 for every t. For y = 2A sin(kx) cos(ωt), putting x = 0 gives y = 0 for all t. Thus the fixed end is a permanent node. Correct option: A.