Physics

The wave number $k$ is really a measure of how many radians of oscillation fit into one unit of distance—it's the spatial equivalent of angular frequency $\omega$. To find the relationship, think about what happens when the wave completes exactly one full cycle: the argument of the sine function changes by $2\pi$ radians as you move one wavelength $\lambda$ in space. Setting $k\lambda = 2\pi$ directly gives you the connection between these two parameters.

The wave number $k$ is really a measure of how many radians of oscillation fit into one unit of distance—it's the spatial equivalent of angular frequency $\omega$. To find the relationship, think about what happens when the wave completes exactly one full cycle: the argument of the sine function changes by $2\pi$ radians as you move one wavelength $\lambda$ in space. Setting $k\lambda = 2\pi$ directly gives you the connection between these two parameters.