Initial Conditions

Highlights of the activity

1. This small group activity is designed to help upper-division undergraduate students construct solutions to the non-dispersive wave equation that match given initial conditions.
2. Students used several standard algebraic forms to write down the solution to the 1-D wave equation for specific boundary conditions.
3. The compare and contrast wrap-up discussion focused on the arbitrary constants for two different forms which determine whether the function describes a traveling or a standing wave.

Reasons to spend class time on the activity

Students need to become familiar with analytic solutions to the non-dispersive wave equation, as these solutions are generalizable to many situations (e.g. electromagnetic waves, quantum mechanical probability densities). In this activity, the students build understanding of and intuition about the coefficients of different terms in a solution to the wave equation, and how they can be determined by knowing information about the wave at a given time (specifically, at t=0). This exercise is for a single-frequency solution; in later exercises, superpositions of different frequencies are built.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Student Handouts

wvwaveinitialcondhand.doc

wvwaveinitialcondhand.pdf

wvwaveinitialcondhand.tex

Maple Worksheet

wvwaveinitialcond.mw (Maple 13)

wvwaveinitialcond.mws (Maple 11 Classic)

Mathematica Notebook

wvwaveinitialcond.nb