The standard equation for the magnetic field of an electromagnetic wave travelling in the x-direction is given by: $B_y = B_0 \sin(kx + \omega t)$ where $k$ is the propagation constant (or wave number) and $\omega$ is the angular frequency.

1. Identify $k$ from the given equation: Comparing the given equation $B_y = 2 \times 10^{-7} \sin(\pi \times 10^3x + 3\pi \times 10^{11}t)$ with the standard form, the coefficient of $x$ is $k$: $k = \pi \times 10^3 \text{ rad/m}$

2. Calculate Wavelength ($\lambda$): The relationship between wavelength and propagation constant is: $k = \frac{2\pi}{\lambda}$ $\lambda = \frac{2\pi}{k}$

Substituting the value of $k$: $\lambda = \frac{2\pi}{\pi \times 10^3}$ $\lambda = 2 \times 10^{-3} \text{ m}$