Explicit physics instruction
Superposition can produce constructive/destructive interference. Two nearby frequencies can create beats with a beat rate equal to the frequency difference.
Standing waves arise when reflections and superposition create persistent nodes and antinodes.
Boundary conditions determine the allowed standing-wave modes.
Core relation: v=fλ; resonance near natural frequency.
Worked example
Tones at 440 Hz and 444 Hz produce a 4 Hz beat pattern in the simple model.
Guided question
Two tones are 500 and 506 Hz. What beat frequency is predicted?
Independent work
- Solve three sound/resonance questions.
- Interpret one standing-wave or resonance graph.
- State one damping/boundary assumption.
Misconception check
Resonance does not mean energy is created; it means energy transfer from the driver is especially effective.
Formative check
What happens to response near a natural frequency?
Reveal response
Amplitude can increase because energy transfer from the driver becomes especially effective.
Mentor evidence conference
Ask Archaemenes to audit frequency/wavelength units, resonance evidence, and damping assumptions.
Teacher guidance
Foundation: Calculate with v=fλ and identify resonance.
Core: Interpret beats, standing waves, and resonance curves.
Extended: Analyze damping and engineering tradeoffs.