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Consider a standing wave formed on a string. It results due to the superposition of two waves travelling in opposite directions. The waves are travelling along the length of the string in the \( x \)-direction and displacements of elements on the string are along the \( y \)-direction. Individual equations of the two waves can be expressed as
\[
\begin{array}{l}
Y_{1}=6(\mathrm{~cm}) \sin [5(\mathrm{rad} / \mathrm{cm}) x-4(\mathrm{rad} / \mathrm{s}) t] \\
Y_{2}=6(\mathrm{~cm}) \sin [5(\mathrm{rad} / \mathrm{cm}) x+4(\mathrm{rad} / \mathrm{s}) t]
\end{array}
\]
Here \( x \) and \( y \) are is \( \mathrm{cm} \).
Maximum value of the \( y \)-positions coordinate in the simple harmonic motion of an element of the string that is located at an antinode will be
(1) \( \pm 6 \mathrm{~cm} \)
(2) \( \pm 8 \mathrm{~cm} \)
(3) \( \pm 12 \mathrm{~cm} \)
(4) \( \pm 3 \mathrm{~cm} \)
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