This activity is part of a sequence of activities addressing Plane Waves and their representations in physics. Other activities included in this sequence are as follow:
Preceding activities:
Recall the Dot Product: This small whiteboard question prompts students to recall something they recall regarding the dot product which reminds students of the different ways in which the dot product can be represented.
Visualizing Plane Waves: In this small group activity, students calculate $\vec{k}\cdot\vec{r}$ for a given $\vec{k}$ for each point on a grid and then connect points with constant value of $\vec{k}\cdot\vec{r}$ and then has students connecting the algebraic expression of a plane wave with its geometric content, allowing students to visualize what is planar about plane waves.
Follow-up activities:
Visualizing Electromagnetic Plane Waves: This Mathematica (or Maple) activity is designed to allow students to visualize electromagnetic plane waves by choosing a $\vec{k}$ and exploring the electric and magnetic field vectors of a given plane wave.
Comparing Representations of Plane Waves: This activity can be used as a homework problem or as a small group activity where students analyze multiple representations of plane waves, noting which features are present and which are ignored in each representation.