Wave Equation Modelling

Overview

In this lesson, students use PhET’s Wave Interference simulation to model how wavelength, frequency, and wave velocity relate. They will collect measurements, build mathematical relationships from graphs, and test predictions across multiple simulation trials.

Learning intentions

• Students will explain measurable wave properties (wavelength, frequency, amplitude, velocity) and how changing parameters affects them.
• Students will use the wave equation relationship to predict how wave velocity changes with wavelength and frequency.
• Students will collect and process quantitative data from the simulation to identify patterns and relationships.
• Students will communicate a scientific explanation using evidence from graphs and measurements.

Success criteria

• I can measure wavelength and frequency from the simulation settings and graphs.
• I can calculate wave speed using collected data and justify my method.
• I can describe how changing one variable affects another (with evidence).
• I can present a clear conclusion linking data to the wave relationship.

Curriculum links

• PY-11-02: Students explain the properties and behaviours of waves, including measurable characteristics and relationships.
• PY-11WS-01: Students develop and evaluate question(s) and hypothesis(es) for a scientific investigation.
• PY-11WS-04: Students select and process qualitative and quantitative data and information (graph reading, calculations, uncertainties).
• PY-11WS-07: Students communicate scientific arguments using evidence and scientific language for a specific audience.

Lesson structure (45 minutes)

1. 0–5 min · Hook and goal setting. Teacher demonstrates a short change in wavelength and frequency in the simulation and asks: “What stays the same, what changes, and how would you test it?” Students record a one-sentence prediction in their groups.

2. 5–12 min · Direct teach: modelling workflow. Teacher models a workflow: set parameters → measure wavelength from distance between crests → measure frequency from the time axis/oscillation rate → calculate wave speed → graph relationships. Students annotate a class “data + reasoning” template (columns, units, one calculation line).

3. 12–29 min · Group investigation: Wave equation challenge. Students work in groups to complete two simulation trials (A and B) using assigned variables:

• Trial A: Keep frequency fixed; vary wavelength in set steps; record wavelength and corresponding wave speed (or compute speed if the simulation provides it).
• Trial B: Keep wavelength fixed; vary frequency in set steps; record frequency and wave speed. Teacher circulates with guiding prompts: “What is your hypothesis?” “What trend do you expect on a graph?” “How will you check your calculations?” Students produce:
• A table of measured/calculated values
• Two scatter/line graphs (e.g., wave speed vs frequency, wave speed vs wavelength)

4. 29–38 min · Analysis: identify the relationship. Teacher leads a brief whole-class compare: groups share which graph looks linear and what gradient meaning suggests. Students use graph evidence to state the relationship in words and then write the equation form that matches their observations (including rearrangement for predictions).

5. 38–45 min · Exit ticket: evidence-based scientific argument. Teacher prompts an individual response: “Using evidence from Trial A or B, explain how wave velocity depends on wavelength and frequency, and include one calculation or data point.” Students submit their exit ticket and one improvement suggestion for the next lesson.

Resources

• Devices with access to the Wave Interference simulation
• Student data sheet (table + graph prompts) with units and calculation space
• Graphing paper or digital graphing tool (if available)
• Calculator access for speed calculations
• Timer for trial steps
• Teacher observation checklist (measurement accuracy, data recording, use of scientific language)

Assessment

• Formative: teacher checks during circulation for correct measurement of wavelength/frequency and correct unit usage.
• Formative: students’ graphs and calculations are checked against success criteria (trend recognition, consistency).
• Summative-in-class (exit ticket): evidence-based explanation using at least one data point and one calculation or justified inference from graph shape.

Differentiation

• Support: provide sentence starters for hypotheses and conclusions (e.g., “If frequency increases while wavelength stays constant, then…”).
• Support: offer a partially completed data table format and unit reminders (m, s, Hz, m s⁻¹).
• Extension: challenge groups to estimate uncertainty by repeating one setting and comparing variation; or ask them to test a prediction for an untried parameter set.
• EAL/SEN: allow diagrams (e.g., labelled crest spacing and time intervals) alongside written explanations; provide a vocabulary bank for crest, wavelength, frequency, period, velocity, amplitude.