Phase & sign — quick reference

Oscillation: y = A·sin(ωt + φ) — φ sets the head start. +φ leads, −φ lags.

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.

Particle velocity ∂y/∂t ≠ wave velocity v. A crest is where phase = π/2.

Full walkthrough →

Waves Lab · all topics

Part II · Waves

Waves & Oscillations

Every oscillation is a live trace on the bench. Drag the amplitude, watch the phasor spin, pluck the string — and hear the physics.

          
          SIGNAL LAB · CH1
        
          2.00 V/div1.0 ms/divTRIG ●

f  = 2.00 Hz
A  = 2.00 V
φ  = 0.00 rad
t  = 0.00 s

6 modules/ 2D · phasor · 3D views/ 🔊 real audio/ exam-ready

The modules

six instruments · one bench

🔊

Turn your sound on

Beats, harmonics, resonance & Doppler play real, mutable tones — hear the pitch you're drawing.

signal A

signal B

resultant

envelope