Each lane is 100 m of material. The sound starts at the clap on the left. Real speeds; the picture is slowed down 20 times (slow motion makes it 80 times).
Waves that bounce back and make standing waves: Standing Waves. Pitch and loudness: Sound Waves.
A wave is a disturbance that carries energy from place to place without carrying the material along. On a rope, each bit only moves up and down while the wave travels on. Wave speed equals frequency × wavelength (v = fλ), and it depends on the medium: sound moves about 343 m/s in air at 20 °C.
| Frequency | Period | Wavelength | Speed (f × λ) |
|---|---|---|---|
| 0.50 Hz | 2.00 s | 8.00 m | 4.0 m/s |
| 1.00 Hz | 1.00 s | 4.00 m | 4.0 m/s |
| 2.00 Hz | 0.50 s | 2.00 m | 4.0 m/s |
Wave speed. v = fλ = λ / T, where T is the period. A crest moves one wavelength in one period. Example: a 2.0 Hz wave with λ = 1.5 m moves at 3.0 m/s.
The travelling wave. y(x, t) = A sin(kx − ωt), with angular frequency ω = 2πf and wave number k = 2π/λ, so v = ω/k = fλ. At the default settings (f = 1.00 Hz, λ = 4.00 m): ω = 6.28 rad/s and k = 1.57 rad/m.
Speed on a rope. v = √(FT/μ), where FT is the tension and μ the mass per meter. The simulator uses μ = 0.25 kg/m, so 1, 4, 9 and 16 N give 2, 4, 6 and 8 m/s. Four times the tension doubles the speed. (Newton’s second law on a short piece of rope gives μ ∂²y/∂t² = FT ∂²y/∂x², a wave with speed √(FT/μ).)
Wave speed vs particle speed. The pattern moves at v; each bit of rope moves up and down with a top speed of 2πfA (1.9 m/s at 1 Hz and 0.30 m), which has nothing to do with v.
Energy. The average power carried by a sine wave on a rope is P = ½μvω²A², so P grows with A² and f². At 0.30 m, 1 Hz and 4 m/s: P = 1.8 W; at 0.60 m it is 7.1 W (4 times). The Energy loss slider (More options) makes the amplitude shrink as e−γt, as in a real rope.
Superposition. When two pulses meet, the displacements add; afterwards each pulse goes on unchanged (try Pulse from each end). Two waves that run in opposite directions make standing waves; two close frequencies make beats.
Model limits. The rope here is ideal: no sag, no stiffness, and both ends soak up the wave (no echo). Real ropes lose some energy; real slinkies sag. In the Slinky lab the same slider stands for how stiff the slinky is (a slinky’s speed is set by its stiffness and mass); its energy numbers use the rope values and are illustrative. Very tall water waves are an exception to “amplitude does not change speed”: their speed depends a little on their height.
| Wave and medium | Speed | Time to travel 100 m |
|---|---|---|
| Wave on the simulator rope (4 N) | 4.0 m/s | 25 s |
| Tsunami over 4,600 m of ocean | about 212 m/s (765 km/h) | about 0.47 s |
| Sound in air, 20 °C | 343 m/s | 0.292 s |
| Sound in fresh water | 1,480 m/s | 0.0676 s |
| Sound in sea water | 1,540 m/s | 0.0649 s |
| Sound in steel | 5,960 m/s | 0.0168 s |
| Light in empty space | 300,000,000 m/s | 0.00000033 s |
Pick one answer for each question, then press Check my answers to see the explanations. New questions picks another set.
A 40–45 minute lesson for MS-PS4-1. Start on a projector (Full screen button): paint a bead red and ask the class to predict where it will be after the pulse. Then pairs work through the seven missions; each asks for a prediction before the simulator shows the result, and a certificate prints when all seven are done.
The rope is an illustrative ideal rope (0.25 kg/m, 1–16 N, no echo from the ends), so its speeds (2–8 m/s) are teaching values. The sound speeds in the Sound race are real (OpenStax College Physics 2e, Table 17.1); the race picture is slowed down 20 times. The energy meter shows the real power formula for that rope (P = ½μvω²A²).
Go deeper covers HS-PS4-1 (v = fλ with numbers, y = A sin(kx − ωt), v = √(FT/μ), power ∝ A²f², superposition). For bouncing waves and resonance use Standing Waves; for pitch, loudness and echoes use Sound Waves.
Standards: NGSS MS-PS4-1 (amplitude, wavelength, frequency, energy) · HS-PS4-1 in Go deeper (v = fλ)
| Time | Step | What students do | Go to |
|---|---|---|---|
| 5 min | Hook | Paint a bead, predict, send a pulse | Simulator |
| 10 min | Explore | Missions 2–3: frequency, pulse size | Simulator |
| 10 min | Energy | Missions 4–5: amplitude, tension | Simulator |
| 8 min | Sound | Missions 6–7: slinky, sound race | Simulator |
| 10 min | Check | Order game, then quiz or worksheet | Order game |
Worksheet: a print-out for students and a separate answer key page for the teacher (opens the print dialog; choose "Save as PDF" to keep a file).
In a transverse wave the material moves at right angles to the direction the wave travels, like a rope shaken up and down. In a longitudinal wave the material moves back and forth along the direction of travel, like a slinky pushed and pulled, or sound in air.
Key takeaway: transverse = across; longitudinal = along.Energy. Each bit of the medium is pushed or pulled by its neighbor and then returns to its own spot, so the material stays where it is. In the simulator, a pulse travels 12 m while the red bead moves 0 m along the rope.
Key takeaway: waves move energy, not matter.Multiply the frequency by the wavelength: v = f × λ. A wave with f = 2 Hz and λ = 3 m travels at 6 m/s. You can also time one crest: speed = distance ÷ time (the 12 m rope at 4 m/s takes 3 s).
Key takeaway: v = fλ.No. On a rope, or for sound in air, every wave travels at the same speed whatever its amplitude or frequency: the medium sets the speed. A bigger wave carries more energy (twice the amplitude, about 4 times the energy), but it is not faster. Water waves are a special case: on the ocean, longer waves travel faster.
Key takeaway: the medium sets the speed; amplitude sets the energy.Sound is passed on by particles pushing each other. In water and especially in steel the particles are linked much more stiffly, so a push is passed on faster: about 343 m/s in air, 1,480 m/s in water and 5,960 m/s in steel.
Key takeaway: stiffer medium, faster sound.Amplitude is how far the medium moves from its rest position (rest line to crest). A bigger amplitude means more energy: on the simulator rope, 0.30 m carries 1.8 W and 0.60 m carries 7.1 W, about 4 times as much.
Key takeaway: energy grows with amplitude squared.The tension and the mass per meter: v = √(FT/μ). A tighter rope is faster; a heavier rope is slower. With μ = 0.25 kg/m, 4 N gives 4 m/s and 16 N gives 8 m/s.
Key takeaway: four times the tension, twice the speed.This page keeps the ends of the rope from reflecting, so you see one traveling wave. For waves that bounce back and make standing waves, open Standing Waves & Resonance. For pitch, loudness and echoes, open Sound Waves.
Key takeaway: traveling waves here; standing waves and sound on their own pages.