The electric field of a plane wave in vacuum, in V/m, is Ey = 42 sin(1.05x + 3.15 × 10⁸t) with x in…

Step 1. The speed. $c = \dfrac{\omega}{k} = \dfrac{3.15 \times 10^{8}\ \text{rad/s}}{1.05\ \text{rad/m}} = 3.00 \times 10^{8}\ \text{m/s}$, so the wave is in vacuum.

Step 2. The frequency. $f = \dfrac{\omega}{2\pi} = 50.1$ MHz.

Step 3. The wavelength. $\lambda = \dfrac{2\pi}{k} = \dfrac{2\pi}{1.05\ \text{rad/m}} = 5.98$ m.

Step 4. The magnetic field. $B_0 = \dfrac{E_0}{c} = \dfrac{42\ \text{V/m}}{3.00 \times 10^{8}\ \text{m/s}} = 140$ nT.

Step 5. The directions. The phase is $kx + \omega t$, so the wave travels along $-x$. With $\vec{E}$ along $+y$ and travel along $-x$, we need $\hat{y}\times\hat{b} = -\hat{x}$. Since $\hat{y}\times\hat{z} = \hat{x}$, the magnetic field is along $-z$ when $E_y$ is positive.