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(A) stationary wave is formed when two progressive waves of the same frequency and amplitude travel in opposite directions along the same line.$1$. $Z

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$Z_1$ and $Z_2$

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(A) stationary wave is formed when two progressive waves of the same frequency and amplitude 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 $\omega$.$2$. $Z_2 = A \cos(\omega t + kx)$ represents a wave traveling in the $-x$ direction with the same frequency $\omega$ and amplitude $A$.$3$. Since $Z_1$ and $Z_2$ have the same frequency and travel in opposite directions along the same axis ($x$-axis),their superposition results in a stationary wave.Therefore,the correct option is $A$.

The following equations represent progressive transverse waves:
$Z_1 = A \cos(\omega t - kx)$,
$Z_2 = A \cos(\omega t + kx)$,
$Z_3 = A \cos(\omega t + ky)$,
$Z_4 = A \cos(2\omega t - 2ky)$.
$A$ stationary wave will be formed by superposing:

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In stationary waves,

In the case of a stationary wave pattern, which of the following statements is $CORRECT$?

$Assertion :$ For the formation of stationary waves,the medium must be bounded having definite boundaries.
$Reason :$ In the stationary wave,some particles of the medium remain permanently at rest.

$A$ pulse of a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with

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The following equations represent progressive transverse waves:$Z_1 = A \cos(\omega t - kx)$,$Z_2 = A \cos(\omega t + kx)$,$Z_3 = A \cos(\omega t + ky)$,$Z_4 = A \cos(2\omega t - 2ky)$.$A$ stationary wave will be formed by superposing: