In a standing wave on a string rigidly fixed | vedclass

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(C) In a standing wave, the displacement of a particle at position $x$ is given by $y(x, t) = A \sin(kx) \cos(\omega t + \phi)$.All particles in a giv

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in one time period all the particles are simultaneously at rest twice.

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(C) In a standing wave, the displacement of a particle at position $x$ is given by $y(x, t) = A \sin(kx) \cos(\omega t + \phi)$.All particles in a given loop oscillate in phase with the same angular frequency $\omega = \frac{2\pi}{T}$.When $\cos(\omega t + \phi) = 0$, the displacement $y$ becomes zero for all particles simultaneously.This occurs when $\omega t + \phi = \frac{\pi}{2}$ and $\frac{3\pi}{2}$ within one time period $T$.Therefore, all particles pass through their mean position (i.e., are at rest momentarily) twice in one time period $T$.

In a standing wave on a string rigidly fixed at both ends:

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