Vedatom Physics Waves / Wave Motion ◈ Sims ▤ Full book
Phase & sign — quick reference
Travelling wave: y = A·sin(kx − ωt) moves in +x; kx + ωt moves in −x.
Relations: ω = 2πf, k = 2π/λ, v = ω/k = fλ.
Two velocities: particle ∂y/∂t = −v·∂y/∂x ≠ wave speed v.
Path difference Δx maps to phase Δφ = (2π/λ)·Δx. A crest is where the phase = π/2.
Full walkthrough →
Waves Lab · all topics
01

Transverse vs longitudinal

particle lattice · wave travels →
→ rightward = wave velocity v ↕ red arrow = particle velocity vp
Watch a single tracked particle: in a transverse wave it moves perpendicular to the direction of travel (string, light, water ripples); in a longitudinal wave it moves parallel to it, bunching into compressions and spreading into rarefactions (sound). Either way, the particle never travels with the wave — only the disturbance propagates. Transverse waves need a medium that resists shear, so in a fluid mechanical waves are longitudinal.
02

The progressive wave

snapshot y vs x
→ rightward = wave velocity v ↕ red arrow = particle velocity vp (toggle above)
Wave no. k
{{ Ktxt }}
Angular ω
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Wave speed v=fλ
{{ Vtxt }}
Max particle Aω
{{ VpMaxTxt }}
Period T
{{ Ttxt }}
The snapshot above is y vs x frozen in time — its repeat length is the wavelength λ. The tracked particle stays at one x and its y vs t history is the small trace on the right; its repeat time is the period T. Same sine shape, completely different axes. The whole pattern shifts one λ every T, so v = λ/T = fλ.
tracked particle · y vs t