In the "NOTE" at the top of page 938 of your textbook, the book warns you that "diffraction gratings" should probably be called "interference gratings." Why? What makes diffraction (Section 32.3) different from both interference and diffraction gratings?

diffraction is the envelope of the other two phenomena

Explanation:

The fundamental phenomenon is diffraction since the interference can be found as the sum of the diffraction of two grids, separated a small distance.

The diffraction phenomenon is characterized by a very wide and high central band, described by the expression

              I = I₀ ()²

There are other small bands on the sides, but they are getting smaller

The mathematical analysis of the interference is simpler than the analysis of the diffraction, so sometimes when you have many grids they can be analyzed in pairs, using interference analysis.

The result of this analysis are equally spaced lines of equal height.

When the pattern of a spectrum of many slits is observed, the intensity of all the lines is constant which is characteristic of the interference phenomenon, a band with the main width is observed where all the lines are and we see is the entire spectrum of interference in this width, which by the number of lines is extended a lot.

In a detailed analysis diffraction is the envelope of the other two phenomena

true tan speed = ang vel x radius