• Representations of plane waves

Estimated Time:

• Students use a Mathematica or Maple worksheet to visualize scalar plane waves by selecting a wave vector, $\vec{k}$.

• Computers with Maple

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.