A perfectly free end of a string is chosen as x = 0. Which stationary-wave expression has a displacement antinode at the free end?
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Question

A perfectly free end of a string is chosen as x = 0. Which stationary-wave expression has a displacement antinode at the free end?

G1 Physics · Accepted Answer

In a stationary wave, y = 2A cos(kx) cos(ωt) has position-dependent amplitude Aₗₒc = 2A|cos(kx)|. At x = 0, Aₗₒc = 2A. This is the maximum possible amplitude, so x = 0 is an antinode. Correct option: B.