# Δκ of a superposition of waves

I am trying read through a chapter on properties of matter waves in Eisberg & Resnick's Quantum Physics. In section 3-4, a superposition Ψ of 7 sinusoidal waves, each with a different reciprical wavelength and amplitude, is shown along with all the component waves(fig. 3-9). He defines the extent of the group Δx as the maximum amplitude to half-maximum amplitude width of Ψ and estimates that it is about 1/12, which I understand from looking at the figure. However, we then defines Δκ as "the range of reciprical wavelengths of the components of Ψ from maximum amplitude to half-maximum amplitude" and estimates that it is about 1. I don't quite understand this definition, or how he estimated Δκ from the figure. Can someone carefully explain what he's doing?

$$\Delta x \Delta k \geq \frac{1}{2}$$