(D) The period of the function $f(x) = \sin(kx)$ is given by $\frac{2\pi}{|k|}$.Here,$k = \frac{1}{n}$.Therefore,the period of $f(x) = \sin \left( \fr

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(D) The period of the function $f(x) = \sin(kx)$ is given by $\frac{2\pi}{|k|}$.Here,$k = \frac{1}{n}$.Therefore,the period of $f(x) = \sin \left( \frac{x}{n} \right)$ is $\frac{2\pi}{|1/n|} = 2n\pi$ (assuming $n > 0$).Given that the period is $4\pi$,we have $2n\pi = 4\pi$.Solving for $n$,we get $n = 2$.