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HomeConcept libraryWaves

Starter track

Follow the authored sequence, or switch to recap mode for a faster review of the same path.

Full trackRecap mode
Starter track9 concepts2 checkpoints230 min

Waves

Not started

Use oscillation as the entry point, lock down wave speed and wavelength, carry that into longitudinal sound and pitch-versus-loudness cues, add beats as the nearby-frequency superposition bridge, then move into Doppler shifts, interference, standing-wave patterns, and open-vs-closed air-column resonance without losing the live connection between motion and graph.

This path uses one repeating motion as the anchor, then expands outward into traveling waves, longitudinal sound in a medium, pitch-versus-loudness reasoning on that same sound bench, beats from nearby frequencies on one bounded superposition bench, Doppler shifts from source and observer motion, standing patterns, and finally the tube-resonance branch where open and closed boundaries reshape the harmonic ladder. It works well if you want the wave ideas to stay visually tied to the oscillator that generates them.

Oscillation linkSpeed and wavelengthLongitudinal soundPitch vs loudnessBeatsDoppler shiftInterferenceStanding patternsOpen vs closed pipes

Entry diagnostic

Decide where to enter this path without opening a second testing system.

Reuse the SHM and wave-speed quick tests plus the dark-band interference challenge to see whether the oscillator-to-wave bridge is already solid enough to jump straight into standing patterns.

Start from beginning0 / 3 probes ready

Probe the wave bridge before you commit to the full path

Start from beginning

No saved diagnostic checks are available yet, so the opening concept is still the best place to start.

Uses the same local-first quick tests, checkpoint challenges, and track history already saved in this browser.

Begin with Simple Harmonic Motion
  1. Quick testNot started4 questions

    Oscillator quick test

    Check whether the repeated-motion story is still clear before it becomes a traveling wave.

    No saved quick-test result yet.

    SHM
    Open Simple Harmonic Motion quick test
  2. Quick testNot started4 questions

    Wave-speed quick test

    Check whether wavelength, period, and travel delay still read cleanly off the live wave system.

    No saved quick-test result yet.

    Wave speed
    Open Wave Speed and Wavelength quick test
  3. ChallengeNot started3 checks

    Dark-band checkpoint

    Use the existing interference challenge to see whether the wavelength and phase story is already robust enough for a later standing-wave entry.

    No saved checkpoint attempt yet.

    Interference
    Open Find a dark band

Why this order

The sequence is authored to keep the model honest.

Simple harmonic motion is first because every later wave idea depends on reading repeated motion cleanly. Wave speed and wavelength turns that repeated motion into a traveling pattern, sound waves and longitudinal motion keeps that same timing honest inside a real medium, pitch and loudness separates frequency from amplitude before the branch gets more crowded, beats shows how two nearby sound frequencies create a slow envelope from superposition, Doppler effect adds the motion-caused pitch shift on that same sound model, interference generalizes the superposition picture, standing waves stabilize the node-and-antinode pattern, and air-column resonance closes by changing the boundary conditions on that same standing-wave logic.

Shared concept pages

Each step opens the same simulation-first framework.

Compare mode, prediction mode, quick test, worked examples, guided overlays, challenge mode, and read-next cues stay on the concept pages. The track only decides the guided order and the next recommended stop.

Guided path

Follow the concepts and checkpoint moments in order.

Checkpoint cards reuse the authored challenge entries already living on the concept pages.

  1. 1Not startedMastery: NewStart here

    Simple Harmonic Motion

    See one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.

    Start here before moving into Wave Speed and Wavelength.

    OscillationsIntro25 min
    Start concept
  2. 2Not startedMastery: New

    Wave Speed and Wavelength

    Follow one traveling wave across the same medium and connect crest spacing, travel delay, source timing, and the relation v = f lambda on one honest live stage.

    Builds on Simple Harmonic Motion before setting up Sound Waves and Longitudinal Motion.

    OscillationsIntro25 min
    Open concept
  3. 3Not startedMastery: New

    Sound Waves and Longitudinal Motion

    See sound as a longitudinal wave by keeping parcel motion, compression and rarefaction, probe timing, and energy transfer tied to one compact medium-first bench.

    Builds on Wave Speed and Wavelength before setting up Pitch, Frequency, and Loudness / Intensity.

    OscillationsIntro25 min
    Open concept
  4. 4Not startedMastery: New

    Pitch, Frequency, and Loudness / Intensity

    Keep one compact sound bench while separating pitch from frequency, loudness from amplitude and an amplitude-squared intensity cue, and probe delay from the source sound itself.

    Builds on Sound Waves and Longitudinal Motion before setting up Beats.

    OscillationsIntro20 min
    Open concept
  5. 5Not startedMastery: New

    Beats

    Superpose two nearby sound frequencies, watch the fast carrier sit inside a slower envelope, and connect beat rate to the frequency difference on one compact bench.

    Builds on Pitch, Frequency, and Loudness / Intensity before setting up Doppler Effect.

    OscillationsIntro20 min
    Open concept
  6. 6Not startedMastery: New

    Doppler Effect

    Watch a moving sound source compress wavefronts ahead and stretch them behind, then see how source motion and observer motion combine to change the heard pitch on one bounded classical bench.

    Builds on Beats before setting up Wave Interference.

    OscillationsIntermediate25 min
    Open concept
  7. 7Not startedMastery: New

    Wave Interference

    Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.

    Builds on Doppler Effect before setting up Standing Waves.

    OscillationsIntermediate30 min
    Open concept
  8. Checkpoint 1LockedNot started

    Interference checkpoint

    Use the wavelength and timing story from the earlier wave steps to deliberately land on a dark interference band.

    Finish Wave Interference first. This checkpoint ties together SHM, Wave speed, Sound waves, Pitch and loudness, Beats, Doppler effect, and Interference through Find a dark band.

    Pause here after Wave Interference before moving into Standing Waves.

    SHMWave speedSound wavesPitch and loudnessBeatsDoppler effectInterference3 checksCoreGraph-linkedGuided start
    Return to InterferenceOpen concept
  9. 8Not startedMastery: New

    Standing Waves

    Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.

    Builds on Wave Interference before setting up Resonance in Air Columns / Open and Closed Pipes.

    OscillationsIntermediate30 min
    Open concept
  10. Checkpoint 2LockedNot started

    Standing-wave checkpoint

    Finish the wave path by using the interference picture to place the probe on a true node in a standing-wave pattern.

    Finish Standing Waves first. This checkpoint ties together Wave speed, Sound waves, Pitch and loudness, Beats, Doppler effect, Interference, and Standing waves through Probe on a node.

    Pause here after Standing Waves before moving into Resonance in Air Columns / Open and Closed Pipes.

    Wave speedSound wavesPitch and loudnessBeatsDoppler effectInterferenceStanding waves4 checksCoreGraph-linkedGuided start
    Return to Standing wavesOpen concept
  11. 9Not startedMastery: New

    Resonance in Air Columns / Open and Closed Pipes

    Compare open and closed pipe boundary conditions on one compact air column so standing-wave shapes, missing even harmonics, probe motion, and pressure cues stay tied to the same resonance state.

    Capstone step after Standing Waves.

    OscillationsIntermediate30 min
    Open concept