What a wave is
A wave is a disturbance that carries energy from place to place without carrying the material itself along with it. Drop a pebble in a pond and the ripple races outward, but a floating leaf only bobs up and down; the water doesn’t travel to the shore. The animation above shows a single wave moving steadily to the right. Press Pause at any time to freeze a snapshot, and drag the sliders to reshape it.
Three numbers describe almost any repeating wave:
- Amplitude: how far each point swings from its rest position. Bigger amplitude means more energy (a louder sound, a brighter light).
- Wavelength (λ): the distance from one crest to the next identical point. The marked span beneath the curve shows exactly one wavelength.
- Frequency (f): how many full cycles pass a fixed point each second, measured in hertz (Hz). Higher frequency packs the wiggles closer together in time.
Transverse vs. longitudinal
Use the toggle to compare the two basic ways a wave can move:
- In a transverse wave, the medium vibrates perpendicular to the direction the wave travels, like the up-and-down sine curve, or a shaken rope. Light and other electromagnetic waves are transverse.
- In a longitudinal wave, the medium vibrates parallel to the travel direction, creating compressions (particles bunched together) and rarefactions (particles spread apart). Sound moving through air is the classic example.
Notice that both views respond to the same wavelength and frequency sliders: the physics is identical; only the direction of vibration differs.
The two key equations
The single most important wave relationship connects speed, frequency, and wavelength: v = f × λ. A wave that completes more cycles per second (higher f) or has longer crests (larger λ) travels faster. The period is just the time for one full cycle: T = 1 / f. Watch both values update as you move the sliders, and try to predict each before you let go.
Using this with a class
Project it and ask students to keep the speed constant: if you raise the frequency, what must happen to the wavelength? It’s free to embed on a class site or worksheet so learners can experiment on their own devices.