In a stationary wave,all particles are

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(A) In a stationary wave,the displacement of any particle is given by $y = A \sin(kx) \cos(\omega t)$.For the particles to be at rest,the velocity $v

Vedclass · Accepted Answer

At rest at the same time twice in every period of oscillation

Vedclass · Answer

(A) In a stationary wave,the displacement of any particle is given by $y = A \sin(kx) \cos(\omega t)$.For the particles to be at rest,the velocity $v = \frac{dy}{dt} = -A \omega \sin(kx) \sin(\omega t)$ must be zero.This condition is satisfied when $\sin(\omega t) = 0$,which occurs at $\omega t = 0, \pi, 2\pi, \dots$Since $\omega = \frac{2\pi}{T}$,the condition $\sin(\omega t) = 0$ implies $t = 0, \frac{T}{2}, T, \dots$Thus,all particles in the medium come to rest simultaneously twice in every period of oscillation $T$.Therefore,option $A$ is correct.

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