Physics - Wave on String Question with Solution | TestHub

The equation of a stationary wave is given by $y=2A\sin (kx)\cos (\omega t)$.

This can be written as $y=A^{\prime }\cos (\omega t)$, where $A^{\prime }=2A\sin (kx)$ is the amplitude of the particle at position $x$.

The amplitude $A^{\prime }$ depends on the position $x$, meaning different particles vibrate with different amplitudes.

The time-dependent part $\cos (\omega t)$ is the same for all particles, indicating that they all vibrate in Simple Harmonic Motion (S.H.M.) with the same angular frequency $\omega$ and the same period $T=\frac{2\pi }{\omega }$.

At the nodes, $\sin (kx)=0$, so the amplitude is zero and the particles do not vibrate.

Therefore, all particles except those at the nodes vibrate in S.H.M. with the same period but different amplitudes.

Answer: except at node vibrate in S.H.M. of same period but of different amplitudes