Encouraging students to understand the 1D wave equation

Despite its crucial importance in physics, there are not many studies focusing on student difficulties and teaching strategies related to the (1D) wave equation in the PER literature. In order to contribute to fill this gap, we conducted a study with university students which focused on specific aspects that are crucial for understanding this equation. Our results include not only key learning difficulties and potential teaching strategies to circumvent them, but they also suggest that students can search for a deeper understanding of physics equations when prompted to do so.

Figure 1

Horizontal graph transformations of $f(x)$.

Figure 2

The proportional relation between force and concavity.

Figure 3

The design of tutorial IV using the conceptual blending framework.

Figure 4

How students understand the 1D WE.

Figure 5

Wave profile posed in the first phase of tutorial IV.

Figure 6

Wave profile posed in the second phase of tutorial IV.

Figure 7

Slopes on the points in the wave profile.

Figure 8

A pair plotted $y=x^2$ in GeoGebra and changed the argument from $x$ to $x-2$ and $x-4$.

Figure 9

Three wave functions plotted in GeoGebra.

Figure 10

The graph of $y=e^{-(x-vt{)}^2}$.

Figure 11

Students’ drawing based on the assumption of wave motion.

Figure 12

A student drew the forces that can be decomposed into $x$ and $y$ components.

Figure 13

Students drew the forces acting on the points based on the analysis of concavity on the graph.

Figure 14

A student failed to draw the slope on the points correctly.

Figure 15

The drawing of Mika (a) and David (b) describes the proportionality relation between concavity and acceleration.

Figure 16

The pulse profile.

Figure 17

The pulse profile has seven points placed on it.

Figure 18

The pulse profile has nine points placed on it.