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(A) For the formation of a standing wave,two progressive waves must have the same frequency,same amplitude,and must travel in opposite directions alon

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$z_1$ and $z_2$

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(A) For the formation of a standing wave,two progressive waves must have the same frequency,same amplitude,and must travel in opposite directions along the same line.$1$. $z_1 = A \cos(\omega t - kx)$ represents a wave traveling in the $+x$ direction with frequency $\omega$ and wave number $k$.$2$. $z_2 = A \cos(\omega t + kx)$ represents a wave traveling in the $-x$ direction with the same frequency $\omega$ and wave number $k$.Since $z_1$ and $z_2$ satisfy the conditions of having the same frequency,same amplitude,and opposite directions along the same axis ($x$-axis),their superposition results in a standing wave.Therefore,the correct option is $A$.

From the given progressive wave equations,which waves are used to produce a standing wave?
$z_1 = A \cos(\omega t - kx)$
$z_2 = A \cos(\omega t + kx)$
$z_3 = A \cos(\omega t + ky)$
$z_4 = A \cos(2\omega t - 2ky)$

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From the given progressive wave equations,which waves are used to produce a standing wave?$z_1 = A \cos(\omega t - kx)$$z_2 = A \cos(\omega t + kx)$$z_3 = A \cos(\omega t + ky)$$z_4 = A \cos(2\omega t - 2ky)$