Follow repeating motion from one oscillator into traveling waves, sound as a longitudinal wave, pitch-versus-loudness cues, beats from nearby frequencies, Doppler shifts from motion, superposition, standing patterns, and driven resonance.
Use this topic page when you want the wave story to stay tied to the oscillator underneath it. The grouped overview starts with one repeating system, expands into traveling and longitudinal sound waves, separates pitch from loudness on the same compact bench, adds beats as the nearby-frequency superposition bridge on that same sound branch, brings in the motion-caused Doppler shift, and then moves into combined waves, standing patterns, and the driven-response case that explains why resonance matters.
Best first concepts
The topic page keeps these starts in their own compact row so the first screen is about orientation and next action, not stacked feature cards.
See one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.
Foundations
Strong first stop for getting into this topic without scanning the whole library.
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.
Wave timing and spacing
Strong first stop for getting into this topic without scanning the whole library.
Specific learning goals
These goal cards stay authored and transparent. They reuse the current topic page, starter tracks, guided collections, concept bundles, and progress cues instead of adding a separate recommendation system on top of this branch.
Start on the topic route, keep the Waves Evidence Loop compact, and reuse the authored wave order before widening into the rest of the branch.
Primary move
Open topic route
No saved progress yet inside Oscillations and Waves.
Entry diagnostic
Start from the opening step
No saved diagnostic checks are available yet, so the opening step is still the best entry into the collection.
Reuses the guided collection entry for Waves Evidence Loop, with 0 of 2 probes already ready.
No saved progress yet inside Oscillations and Waves.
Orient with the oscillations and waves topic route is the next guided collection step.
Simple Harmonic Motion opens this track and sets up the rest of the path.
No saved progress yet for Wave Interference.
Grouped concept overview
Each group is authored in the topic catalog, but the actual concepts, progress badges, and track cues still come from the canonical concept metadata and shared progress model.
Group 01
Start with the repeating motion itself, then use energy and the circular-model projection to keep the same system readable from multiple angles.
在同一個反覆系統中，從位移到加速度再回到位移，直接看懂週期性運動。
Strong first stop for getting into this topic without scanning the whole library.
A strong first concept for opening the catalog without committing to a full track.
Open 簡諧追蹤粒子以恆定速率繞圓運動，並把半徑、角速度、切向速度、向心加速度與向內力需求連到同一個即時狀態。
Group 02
Move from one traveling wave into longitudinal sound in a medium, separate pitch from loudness, add beats as the nearby-frequency sound bridge, bring in the passing-source Doppler shift, and then move into superposition, standing-wave patterns, and the open-vs-closed tube resonances that grow out of them.
在同一介質中追蹤行進波，把波峰間距、傳播延遲、訊源節奏與 v = fλ 連到同一個即時實驗台。
Strong first stop for getting into this topic without scanning the whole library.
把聲音視為縱波，讓介質微粒運動、疏密變化、探針讀值與能量傳遞都留在同一個介質優先的實驗台上。
在同一個小型聲學實驗台上分清音高與頻率、響度與振幅／強度，以及探針延遲與訊源聲音本身。
看著移動聲源在前方壓縮、後方拉開波前，並理解聲源與觀察者運動如何共同改變聽到的音高。
在同一個空氣柱中比較開管與閉管邊界條件，讓駐波形狀、偶次諧波缺失、探針運動與壓力線索都綁在同一個共鳴狀態。
Group 03
Finish with the case where the oscillator is pushed from the outside and losses matter, so resonance becomes visible instead of abstract.