1.1 Press Play. Describe what happens to the wave shape as time passes — does the pattern move, or does the medium move? You can sketch arrows on the grid to show your answer if that's easier than words.

1.2 Slide f up and down. Describe (in words, no numbers) what happens to how "squeezed together" the wave looks as f increases.

1.3 Slide A up and down instead. What changes about the wave's shape — and what stays the same (hint: does the spacing between crests change)?

1.4 Click "Up first" / "Down first" and Reset between each click. Describe the difference in how the source (the wall-mounted vibrator) starts moving.

1.5 Turn on the path/phase difference tool (↔ button). Drag Q₁ and Q₂ close together, then far apart. What happens to the two phasor arrows in the small circle as you do this?

1.6 Toggle particles off. What does the wave look like now? Why might this view be useful for thinking about a string or rope, rather than a row of separate particles?

2.1 In the Simulation tab, open Worksheet mode. Set f = 1.5 Hz as instructed. Before revealing, predict λ using λ = c ÷ f, with c = 290 px/s. Then click "Reveal λ" to check.

2.2 Set f = 0.5 Hz. Predict λ, then check the live readout. Is λ bigger or smaller than at f = 1.5 Hz? Does this match what you'd expect from λ = c/f?

2.3 Set f = 3.0 Hz (the maximum). Predict T = 1/f in seconds, then compare with the T readout in the info box.

2.4 Set A to its maximum value (82), then to its minimum (20), keeping f fixed. Predict whether λ changes between these two settings, then check the λ readout to confirm.

2.5 Set the vibrator to "Up first" and note the source's displacement-vs-time pattern in your head. Now switch to "Down first". At the exact same moment in the cycle, predict whether the source's displacement is the same, opposite, or unrelated to the "Up first" case — then verify by toggling between the two and watching the source point.

2.6 Open the path/phase difference tool. Drag Q₁ and Q₂ until the panel reads "in phase". Predict what Δx should be in terms of λ before reading the Δx value, then check.

2.7 Now drag until the panel reads "antiphase". Predict Δx in terms of λ first, then check against the live readout.

2.8 With Q₁ and Q₂ set to any path difference Δx you like, predict Δφ using Δφ = (2π/λ)Δx, then compare with the live Δφ readout. This is the general rule that questions 2.6 and 2.7 were both special cases of.

3.1 A progressive wave has frequency 50 Hz and travels at 340 m/s (the approximate speed of sound in air). Calculate its wavelength. Show answer

3.2 A wave has a period of 0.02 s. What is its frequency, and if its speed is 320 m/s, what is its wavelength? Show answer

3.3 Two points on a wave are 0.6 m apart. The wave has λ = 0.8 m. Calculate the phase difference between them, in radians and as a fraction of π. Show answer

3.4 Two points on a wave are exactly in antiphase. If their path difference is 0.75 m, what is the wavelength? (Hint: antiphase means Δx is an odd multiple of λ/2.) Show answer

3.5 Explain why reversing the initial direction of the vibrator (up-first vs down-first) does not change the values of f, λ, A, or c — but does change the wave's phase. Show answer

3.6 Required practical context: A student measures the wavelength of a sound wave using a microphone and oscilloscope, finding λ = 1.65 m at f = 200 Hz. Calculate the speed of sound implied by this measurement, and suggest one source of experimental uncertainty. Show answer

3.7 Sketch one full wavelength of a progressive wave with amplitude 2 squares and wavelength 6 squares on the grid below. Mark one crest and one trough clearly. Show answer