MS-PS4-1Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy of the wave. MS-PS4-2Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials. SEP: Analyzing DataYou will collect trial data and look for patterns between amplitude and energy. SEP: Using MathYou will graph your data and decide which model — linear or squared — best fits. CCC: Energy & MatterWaves transfer energy without transferring matter. CCC: Scale & ProportionDoubling the amplitude does not simply double the energy.

Predict → TestYou commit to a prediction first, then test it against real data — a core scientific habit. Productive StruggleWrong predictions are not failures — they are data you can revise. Claim · Evidence · ReasoningYou will defend your model with your own collected evidence. Worked-Out DiscoveryYou uncover the amplitude–energy relationship from data, not from being told. Spaced RetrievalCheckpoint quizzes between phases reinforce learning by retrieval, not re-reading.

Investigation

Amplitude Challenge

How much energy does a wave actually carry? Predict, test, gather data, build a model — then figure out how much amplitude is enough to get real work done.

Amplitude · Energy · Waves

Before You Begin

Read this first, then investigate

This is a four-phase investigation into how a wave's amplitude affects the energy it delivers. Complete each phase in order — each one builds on the last.

What is this investigation about?

You will discover how a wave's amplitude — the height of its crest — controls the energy it delivers. Bigger amplitude = more energy, but the relationship is not what most people guess.

Why does this matter?

Amplitude is what makes a sound loud, an earthquake destructive, an ocean wave powerful, and a light bright. The same rule applies to every kind of wave.

What will I actually do?

You will explore a wave, run amplitude trials and record data, hit energy targets, and finally build a model that explains your data — using your own evidence.

How do I move through it?

Each phase unlocks automatically when you complete the one before it. You must answer a short checkpoint question to advance. Need a refresher? Revisit Nature of Waves first.

Phase 1

Wave Explorer

Get familiar with a wave. Drag the sliders to change its shape, then click on the wave to identify its parts. Finally, predict how amplitude affects energy — you will test your prediction with real data later.

Click all 3 wave parts on the canvas, then make a prediction. The checkpoint question will appear.

Amplitude 5

Frequency 3

Click on the part of the wave labeled in the prompt above the canvas to identify it. Find all 3 parts to unlock your prediction.

Crest Amplitude Wavelength

Checkpoint · Phase 1

Answer correctly to unlock Phase 2 — Amplitude Lab, where you'll collect real data.

Which measurement describes a wave's amplitude?

The distance from one crest to the next The height from the rest line up to a crest How fast the wave moves forward The number of waves per second

Phase 2

Amplitude Lab

Time to collect data. Choose an amplitude, then click Run Trial. The detector on the right will measure how much energy the wave delivered. Run at least 6 trials across different amplitudes.

Collect 6+ trials across 5+ different amplitudes. The checkpoint question will appear once your data is ready to analyze.

Amplitude 3

Trial Data

Trial	Amplitude (what you changed)	Energy Detected (what you measured)
No trials yet — choose an amplitude and click Run Trial.

Trials0 / 6

Distinct amplitudes0 / 5

Rangetest a low and a high

Ready to analyze

Observation Prompt

Start with an extreme — try amplitude 1 or 8 first. Extremes reveal patterns fastest.

Checkpoint · Phase 2

Answer correctly to unlock Phase 3 — Energy Targets, where you'll put your data to work.

Look at your data. As amplitude increases, what happens to the energy delivered?

Energy stays about the same Energy decreases Energy increases — and it grows faster than amplitude does Energy increases at exactly the same rate as amplitude

Phase 3

Energy Targets

Now apply what your data showed. Each target needs a minimum amount of energy to activate. Use your Phase 2 data as evidence — pick the smallest amplitude you think will do the job, then send the wave.

Activate all 3 targets. The checkpoint question will appear once each one has received enough energy.

♪

Ring a Bell

Needs ≥ 5 J

Inactive

✿

Spin a Wheel

Needs ≥ 20 J

Inactive

▲

Lift a Weight

Needs ≥ 45 J

Inactive

Checkpoint · Phase 3

Answer correctly to unlock Phase 4 — Wave Energy Model, where you'll build a model from your data.

Why does doubling the amplitude do more than double the work the wave can do?

Bigger waves travel faster, so they do more work Energy grows with the square of amplitude — so doubling amplitude means about four times the energy The detector becomes more sensitive at higher amplitudes It's actually a coincidence — there is no real pattern

Phase 4

Build the Wave Energy Model

Your data is now plotted below. Toggle the two model curves to see which one actually fits — then write a short Claim · Evidence · Reasoning explanation defending your choice.

Pick a model (Linear or Squared), then write your Claim, Evidence, and Reasoning. The final checkpoint will appear once all four are complete.

Click a point to see its trial details. Toggle Show as Ratios to compare every trial to your lowest-amplitude trial.

Analyze Your Data — Compare Trial Pairs

Which model fits your data?

Linear · E = k · A Squared · E = k · A²

Claim

In one sentence: which model describes the amplitude–energy relationship?

HintDid your data look like a straight line, or did it curve upward faster than amplitude grew?

0 / 25 minimum

Evidence

Point to specific numbers from your trial data that support your claim.

HintRun more trials in Phase 2 first — your evidence will be stronger with real numbers to cite.

0 / 30 minimum

Reasoning

Explain why this pattern makes sense — what does it tell you about how waves carry energy?

HintAmplitude is how far the wave displaces matter. A bigger wave has to push farther AND with more force. Connect those two ideas.

0 / 30 minimum

Your Phase 1 prediction:

Checkpoint · Phase 4

Last checkpoint — answer correctly to finish the investigation and choose how to wrap up.

Two waves are identical in every way except amplitude. Wave B has three times the amplitude of Wave A. About how much more energy does Wave B carry?

Three times as much About nine times as much The same amount — amplitude doesn't matter One-third as much

Next Step

Choose Your Mode

You've finished the investigation. Pick how you want to wrap up: Practice Mode if you're exploring on your own, or Classroom Mode if your teacher assigned this.

Practice Mode shows the quiz so you can self-check — nothing will be sent to your teacher. Classroom Mode adds a submission panel so your work is sent to your teacher.

Phase 5

Check Your Understanding

You explored a wave, ran amplitude trials, hit energy targets, and built a model. Answer these 5 questions, then click Score My Quiz. In Classroom Mode, fill in your name and teacher below to submit your work. In Practice Mode, scoring the quiz is the finish line — nothing is sent.

Amplitude Challenge

Your Prediction

Which model fits your data?