Vedatom Physics Waves / Phase convention

Phase & sign — quick reference

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

Travelling wave: kx − ωt moves +x; kx + ωt moves −x.

Path → phase: Δφ = (2π/λ)·Δx. A full λ of path is 2π of phase.

Constants: ω = 2πf, k = 2π/λ, v = ω/k.

Waves Lab · all topics

Reference · the one convention

Phase & sign convention

Every wave on this bench is written the same way — y = A·sin(kx − ωt + φ). Learn to read the sign of each term and you never again guess which way a wave moves or which source leads. Flip the signs below and watch the trace obey.

The sign in front of ωt sets the direction

Hold x fixed and let time run. If the wave is sin(kx − ωt), a point that was at phase θ must move to larger x to keep kx − ωt constant — so the whole profile marches in +x. Swap to sin(kx + ωt) and it runs the other way.

Wave speed v{{ vTxt }} Wavelength λ{{ lamTxt }}

y = A · sin(kx {{ signGlyph }} ωt)

travels in {{ dirTxt }}

k = 2π/λ

ω = vk

Read it as a race. The yellow marker is one fixed particle — it only bobs up and down. The crest it rides sweeps sideways at v = ω/k. The particle never travels with the wave; only the pattern does.

φ is a head start — lead and lag

The phase constant φ just rotates the phasor to its starting angle. A wave with +φ reaches every value earlier — it leads the reference; −φ lags behind. Spin the dial and compare the violet trace against the dim reference.

          phasor · trace
          
        

Phase constant φ{{ phiTxt }}

y = A · sin(ωt {{ phiGlyph }})

Special angles. φ = +90° turns a sine into a cosine (velocity leads position by exactly this). φ = 180° is a full inversion — crest becomes trough. Two waves φ apart interfere constructively at 0°, destructively at 180°.

A gap in path is a gap in phase

Two points on the same wave, or two waves that travelled different distances, differ in phase by Δφ = (2π/λ)·Δx. One whole wavelength of extra path is exactly 2π — right back in step. Slide the second marker and read the phase gap.

          two points · one wave
          Δx in units of λ
        

Path gap Δx{{ dxTxt }}

Phase gap Δφ

Interference

Δφ = 2πλ · Δx

Call the sign

{{ quizSolved }}/5 right · read, don't compute

Q{{ q.n }} {{ q.q }}

Recap — the convention

◦ y = A·sin(kx − ωt + φ) is the master form.

◦ kx − ωt → +x; kx + ωt → −x.

◦ +φ leads, −φ lags; φ = 180° inverts.

◦ Δφ = (2π/λ)·Δx — one λ of path = 2π.

◦ ω = 2πf, k = 2π/λ, v = ω/k = fλ.

◦ Particle velocity ∂y/∂t ≠ wave velocity v.

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