Conceptual challenges with the graphical representation of the propagation of a pulse in a string

Student difficulties with making sense of graphs in physics have been thoroughly reported. In the study of one-dimensional waves, the issue is even trickier since the amplitude is a function of two variables (position and time). In this work, we investigate students’ reasoning and difficulties with interpreting the graphical representation of the propagation of a pulse in a string. A profile $y(x)$ of the pulse was provided and students were asked to estimate the velocities of several points at the profile. This forced them to consider the time dimension, by focusing their attention on the motion of these points. This turned out to be extremely challenging to the students, who manifested several conceptual challenges which were categorized and analyzed in the first phase of the study. Based on these findings, three levels of scaffolding support were provided, where each level gradually guided the students to draw the wave profile after some time has elapsed. The scaffolding turned out to be effective, since many students managed to identify the new positions of the points successfully. The study reveals how static representations of intrinsically dynamic phenomena can be challenging for students to grasp.

Figure 1

Problem graph.

Figure 2

A graph of two wave profiles at two instants.

Figure 3

Solving question (a) by drawing slope.

Figure 4

Johan’s derivation of a periodical wave to estimate the magnitude of the speed.

Figure 5

Student’s drawing with the next profile become smaller.

Figure 6

Hendri’s drawing in scaffolding level 1.

Figure 7

Ivan drew the next wave profile after a complete wavelength.

Figure 8

Yuda’s difficulty drawing two wave profiles in one graph.

Figure 9

Student’s difficulty to place the displacement of points on the new wave profile.

Figure 10

Indra’s drawing as if the wave moves to the left.

Figure 11

Student’s drawing after scaffolding level 2.

Figure 12

A correct drawing from a student, but it did not help him to change his prior reasoning.

Figure 13

A student still could not imagine how to draw two identical wave profiles in scaffolding level 3.

Figure 14

Students’ drawings after scaffolding level 3.