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(D) In a stationary wave, the displacement of a particle is given by $y = A \sin(kx) \cos(\omega t)$.The velocity of the particle is $v = \frac{\parti

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straight line

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(D) In a stationary wave, the displacement of a particle is given by $y = A \sin(kx) \cos(\omega t)$.The velocity of the particle is $v = \frac{\partial y}{\partial t} = -A\omega \sin(kx) \sin(\omega t)$.The kinetic energy of the string is maximum when the velocity of all particles is maximum.This occurs when $\sin(\omega t) = \pm 1$, which implies $\cos(\omega t) = 0$.Substituting $\cos(\omega t) = 0$ into the displacement equation, we get $y = 0$ for all $x$.Therefore, at the instant of maximum kinetic energy, the string appears as a straight line along the equilibrium position.

At a certain instant, a stationary transverse wave is found to have maximum kinetic energy. The appearance of the string at that instant is:

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