Consider the three waves z_1, z_2 and z_3 as | vedclass

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(A) standing wave (or stationary wave) is formed by the superposition of two waves of the same frequency and amplitude traveling in opposite direction

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$z_1 + z_2$

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(A) standing wave (or stationary wave) is formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions along the same line.Given:$z_1 = A \sin(kx - \omega t)$ (traveling in $+x$ direction)$z_2 = A \sin(kx + \omega t)$ (traveling in $-x$ direction)$z_3 = A \sin(ky - \omega t)$ (traveling in $+y$ direction)Adding $z_1$ and $z_2$:$z_1 + z_2 = A \sin(kx - \omega t) + A \sin(kx + \omega t)$Using the identity $\sin(C) + \sin(D) = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$:$z_1 + z_2 = 2A \sin(kx) \cos(\omega t)$This represents a standing wave because the spatial part $\sin(kx)$ and temporal part $\cos(\omega t)$ are separated.Waves $z_3$ and $z_1$ (or $z_2$) travel in different directions ($y$ and $x$ respectively),so they do not form a standing wave along a single axis.

Consider the three waves $z_1, z_2$ and $z_3$ as $z_1 = A \sin(kx - \omega t)$,$z_2 = A \sin(kx + \omega t)$ and $z_3 = A \sin(ky - \omega t)$. Which of the following represents a standing wave?

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