Physics · Grade 11

Active learning ideas

Wave Speed and the Wave Equation

Active learning works for wave speed because students often confuse frequency, wavelength, and speed as directly linked rather than inversely related. Concrete measurements in hands-on labs make the abstract equation v = λf visible and memorable, turning a formula into evidence they collect themselves.

• Ontario Curriculum Expectations
• HS-PS4-1

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 35 min · Pairs

Pairs Activity: Slinky Wave Lab

Pairs stretch a slinky across the floor to a fixed point. One student creates transverse waves by shaking one end at a steady rate; the other measures wavelength with a ruler, times 10 waves for speed, and counts cycles in 10 seconds for frequency. Groups calculate v = λf, then adjust shake rate and repeat to observe wavelength changes.

Explain how the wave equation relates the fundamental properties of a wave.

Facilitation Tip

During the Slinky Wave Lab, circulate to ensure pairs mark crests clearly and measure wavelengths at consistent tension to avoid amplitude confusion.

What to look for

Present students with three scenarios: 1) A wave with a frequency of 20 Hz and a wavelength of 5 m. Ask them to calculate the speed. 2) A wave traveling at 100 m/s with a frequency of 50 Hz. Ask them to calculate the wavelength. 3) A wave traveling at 300 m/s with a wavelength of 10 m. Ask them to calculate the frequency. Review answers as a class.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Small Groups: String Tension Experiment

Small groups tie a string to a fixed point and hang weights over a pulley to vary tension. They pluck the string, video-record waves, and use slow-motion playback to measure wavelength and frequency. Predict and test how speed changes with tension, graphing results to confirm patterns.

Predict how changing the frequency of a wave affects its wavelength, assuming constant speed.

Facilitation Tip

In the String Tension Experiment, have students weigh masses precisely and strike strings the same way each trial to isolate tension's effect on speed.

What to look for

On an index card, ask students to write the wave equation and define each variable. Then, pose this question: 'If a guitar string vibrates at a higher frequency, what happens to the wavelength of the sound wave it produces, assuming the speed of sound in air remains constant? Explain your reasoning using the wave equation.'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 25 min · Individual

Individual Practice: Wave Simulator Stations

Students rotate through computers with PhET or similar wave simulators. They input values for frequency and speed to observe wavelength changes, then solve inverse problems. Record five scenarios in a table and explain trends in exit tickets.

Analyze how the tension in a string affects the speed of a wave traveling along it.

Facilitation Tip

At Wave Simulator Stations, require students to record at least three trials for each setting and average results before calculating speed.

What to look for

Facilitate a brief class discussion using this prompt: 'Imagine you are playing a string instrument. How could you change the tension of a string to produce a sound wave with a higher speed? How would this affect the pitch (frequency) of the sound, if the wavelength were to remain constant?'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 30 min · Whole Class

Whole Class Demo: Melde's Experiment

Demonstrate standing waves on a string driven by a vibrator at fixed frequency. Vary tension with weights; class measures node distances for wavelength and calculates speed. Discuss predictions as a group before each change.

Explain how the wave equation relates the fundamental properties of a wave.

Facilitation Tip

For Melde's Experiment, run a practice trial to model precise measurement of nodes and antinodes before students attempt it themselves.

What to look for

Present students with three scenarios: 1) A wave with a frequency of 20 Hz and a wavelength of 5 m. Ask them to calculate the speed. 2) A wave traveling at 100 m/s with a frequency of 50 Hz. Ask them to calculate the wavelength. 3) A wave traveling at 300 m/s with a wavelength of 10 m. Ask them to calculate the frequency. Review answers as a class.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teachers approach this topic by first letting students experience the relationships physically before formalizing them with the equation. Avoid starting with the equation; instead, let students observe patterns in their data, then introduce v = λf as a summary tool. Research shows students retain the concept better when they derive the equation from their own measurements rather than receive it as given.

Successful learning looks like students fluently using v = λf to solve for any variable, explaining why changing one factor affects another, and connecting medium properties to wave speed. They should justify predictions with data from experiments and simulations.

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Watch Out for These Misconceptions

• During the Slinky Wave Lab, watch for students who believe increasing the frequency of shakes will increase wave speed along the slinky.

  Prompt students to measure the distance a crest travels in five shakes at 1 Hz and again at 3 Hz. Have them compare the crest's speed at both frequencies to see it remains constant, then discuss why wavelength must change instead.

• During the String Tension Experiment, watch for students who think adding more mass to the string will slow the wave down.

  Have students time how long it takes for a pulse to travel the string's length with no weight and with 500g. Guide them to observe that the pulse arrives sooner with more weight, then connect this to the equation v = sqrt(T/μ) using their data.

• During the Wave Simulator Stations, watch for students who measure amplitude instead of wavelength.

  Ask students to mark two consecutive crests on a printed wave image with a ruler, measure the horizontal distance, and compare it to the amplitude value they recorded. Repeat with a different wave to reinforce the difference.

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Methods used in this brief

• Problem-Based Learning