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CED objectives

Periodic Waves

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletPeriodic Wave Bench · measure the repeat on the position pane and on the time pane, then find which knob the wave speed listens to

A displacement-against-position graph is a snapshot of the whole wave, and its repeat distance is the wavelength; a displacement-against-time graph follows one particle, and its repeat interval is the period. In $v = f\lambda$ the medium fixes the speed and the source fixes the frequency, so on a given string raising the frequency shortens the wavelength and leaves the speed alone, while crossing into a new medium pins the frequency and lets both the speed and the wavelength change. Amplitude and frequency are independent properties read off different axes: loudness tracks amplitude and pitch tracks frequency.

Three errors dominate. Reading the repeat distance on a position graph as a period, or the repeat interval on a time graph as a wavelength, which makes everything computed afterwards wrong with mismatched units. Using $v = f\lambda$ to conclude that raising the source frequency raises the wave speed, which is holding the wrong quantity fixed. And treating amplitude and frequency as one knob, so a taller curve is read as a higher pitch or a shorter wavelength.

the same curve twice; the axis label is the whole difference x (metres) λ a SNAPSHOT of the whole wave repeat distance = wavelength t (seconds) T ONE PARTICLE, followed over time repeat interval = period
Nothing about the two curves distinguishes them except what runs along the bottom. That is why the label has to be read before the shape.
two independent knobs, read on two different axes reference TALLER, same repeat same note, LOUDER same height, HALF the repeat same loudness, HIGHER note the error reads the yellow curve as the green one: taller mistaken for higher-pitched
The yellow and green curves each change exactly one property. Neither one changed both, and neither one changed the wave speed.

The work

3 ways in · any order
Lesson
Periodic Waves ›

Separates the position graph from the time graph, names which quantity is pinned before applying v = f lambda, and keeps loudness and pitch on their own axes.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the failure modes of this topic: reading a wavelength as a period, raising the wave speed by raising the source frequency, and hearing a taller wave as a higher note. Take it cold to find which one is yours, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.

Take the diagnostic to identify your misconceptions
Diagnostic first