Starter track
Follow the authored sequence, or switch to recap mode for a faster review of the same path.
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.
Entry diagnostic
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.
Probe the wave bridge before you commit to the full path
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.
Check whether the repeated-motion story is still clear before it becomes a traveling wave.
No saved quick-test result yet.
Check whether wavelength, period, and travel delay still read cleanly off the live wave system.
No saved quick-test result yet.
Starting from Center bright, move the probe onto a dark region where the screen intensity almost vanishes.
No saved checkpoint attempt yet.
About this track
Keep the first scan focused on the next lesson. Open the authored rationale and shared-framework notes only when you need them.
Why this order
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
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
Checkpoint cards reuse the authored challenge entries already living on the concept pages.
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.
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.
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.
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.
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.
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.
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.
Starting from Center bright, move the probe onto a dark region where the screen intensity almost vanishes.
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.
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.
Starting from the third harmonic, move the probe onto a node so its local envelope becomes almost zero.
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.
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.
