Lesson Plan - Wave Equations

Audience

The wave equation activity is designed for use in an undergraduate level course in physics.

Dependence on model parameters

When students set up their vibrating strings, they should see the following properties from the model:

• Increasing the tension of the string increases the frequency of the oscillations.
• Increasing the length of the string decreases the frequency of the oscillations.
• Increasing the mass of the string decreases the frequency of the oscillations.
• Increasing the damping (resistance) of the string does not change the frequency of the oscillations unless it quenches them completely.

Reflections

• Reflections from a fixed boundary do not change sign.
• Reflections from an unfixed boundary do not change sign.

Standing Waves

• For a wave fixed at both ends, the simplest standing wave is one in which the middle section of the string is shaped in a gradual curve with a peak in the middle.
• Higher order standing waves can be created by creating patterns of peaks and troughs, so long as their are zero points at each end.
• These zero points, or nodes, should not move as the wave moves.
• For a wave fixed at only one end, the unfixed end should be a peak or a trough, not a node.