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(A) For two waves to produce a stationary wave,they must have the same frequency,same amplitude,and travel in opposite directions along the same line.

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$A$ and $B$

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(A) For two waves to produce a stationary wave,they must have the same frequency,same amplitude,and travel in opposite directions along the same line.Wave $A$ $(z_1 = a\cos(kx - \omega t))$ travels in the positive $x$-direction.Wave $B$ $(z_2 = a\cos(kx + \omega t))$ travels in the negative $x$-direction.Both waves $A$ and $B$ have the same amplitude $a$,the same angular frequency $\omega$,and the same wave number $k$,and they propagate along the same axis ($x$-axis).Wave $C$ $(z_3 = a\cos(ky - \omega t))$ propagates along the $y$-axis,so it cannot form a stationary wave with $A$ or $B$.Therefore,the superposition of $A$ and $B$ results in a stationary wave: $z = z_1 + z_2 = a[\cos(kx - \omega t) + \cos(kx + \omega t)] = 2a\cos(kx)\cos(\omega t)$.

Which two of the given transverse waves will produce stationary waves when superimposed?
${z_1} = a\cos(kx - \omega t)$.....$(A)$
${z_2} = a\cos(kx + \omega t)$.....$(B)$
${z_3} = a\cos(ky - \omega t)$.....$(C)$

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Which two of the given transverse waves will produce stationary waves when superimposed?${z_1} = a\cos(kx - \omega t)$.....$(A)$${z_2} = a\cos(kx + \omega t)$.....$(B)$${z_3} = a\cos(ky - \omega t)$.....$(C)$