# Instructor guide: Standing-wave mode record

Course: Waves, resonance, and spectra

Suggested time: 35–45 minutes

## Learning target

Learners connect boundary conditions with discrete modes and keep resonant response separate from energy creation.

## Prepare

- Provide string, slinky, or paper-node demonstration if available.
- Review v=fλ.
- Choose a baseline run for the whole class.

## Facilitation moves

- Ask learners to count spatial segments before calculating.
- Use ratio language before formula substitution.
- Trace energy back to the driver whenever resonance is described.

## Misconception checks

- **Resonance creates energy.** It increases response when a driver transfers energy efficiently into an allowed mode.
- **Any wavelength fits any boundary.** Only patterns satisfying the boundary conditions persist as standing modes.

## Accessibility and participation

- Use large node markers and high-contrast strings.
- Let learners clap or tap the spatial pattern.
- Provide the equation in words as well as symbols.

## Evidence of learning

- Accurate mode sketch
- A ratio-based prediction
- Explicit driver-energy accounting

## Extension

Compare an open-open air column with a fixed-fixed string and explain the shared mathematics.

## Evidence boundary

Assess the learner's reasoning only within the declared model and recorded observations. Do not upgrade a simulation result into a claim about an unmodeled physical system.