The Poynting vector $\vec S$ is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically,it is given by $\vec S = \frac{1}{{\mu _0}}(\vec E \times \vec B)$. Show the nature of the $\vec S$ vs $t$ graph.

(N/A) In an electromagnetic wave,let $\vec E$ be in the $y$-direction,$\vec B$ be in the $z$-direction,and the electromagnetic wave propagate in the $x$-direction. The energy propagation will be in the direction of $\vec E \times \vec B$ (in the $x$-direction).
$\vec E = E_0 \sin(\omega t - kx) \hat j$
$\vec B = B_0 \sin(\omega t - kx) \hat k$
$\therefore \vec S = \frac{1}{\mu_0}(\vec E \times \vec B) = \frac{1}{\mu_0} E_0 B_0 \sin^2(\omega t - kx) (\hat j \times \hat k)$
$\therefore \vec S = \frac{E_0 B_0}{\mu_0} \sin^2(\omega t - kx) \hat i$ [since $\hat j \times \hat k = \hat i$]
The variation in the magnitude of $|\vec S|$ with time is shown in the graph below. The magnitude $|\vec S|$ varies as $\sin^2(\omega t - kx)$,meaning it is always non-negative and oscillates with a frequency double that of the electric or magnetic field,with a period of $T = \frac{\pi}{\omega}$.