# Wave Equation Lesson

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# 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.