PhysicsLab

Waves · Progressive Transverse Wave

Wave Anatomy Lab

v = fλ · Δφ = 2πΔx/λ
λ = v/f = 2.00 mT = 1/f = 1.00 st/T = 0.000
click a bead → sets Q
Try first: Pause, then press Step +T/8 eight times.

Controls

λ = v/f = 2.0/1.00 = 2.00 m (derived — λ is not a free knob)

ⓘ more

8 steps = one period exactly — watch the crest marker land one λ to the right. Ghost = translucent profile T/8 ahead + each bead's velocity arrow. Sign toggle flips the plotted graphs only; the 3D motion is untouched.

Phase — pick two particles P and Q

Δφ = (Δx/λ)·2π = (1.00/2.00)·2π = 3.14 rad = 1.00π (reduced to 0–2π)

ANTIPHASE — Δφ = π

P is nearer the source — P leads Q on the y–t graph.

Live readouts

f / Hz

1.00

T / s

1.00

λ / m

2.00

fλ / m s⁻¹

2.00

particle P: v_y = −v·∂y/∂x (oscillates)

-1.88 m s⁻¹

y_P = -0.000 m

wave speed v (constant)

2.00 m s⁻¹

= λ/T = fλ

Graphs — snapshot above, biographies below

ⓘ more

Top: whole string at ONE instant — the ruler ticks are spaced λ; the dashed line tracks one crest. Bottom: TWO points over time — the gridlines are spaced T. Moving a probe restarts its trace.

What this confirms
  • “Progressive wave”. Every bead oscillates in y on its own faint equilibrium tick — no bead ever drifts along x. Only the shape (and the energy) travels; the matter does not.
  • “Snapshot vs biography”. The y–x graph is the whole string at one instant — read λ off it. The y–t graph is one particle's full history — read T off it. Same shape, different axes, different information.
  • “v = fλ — and its derivation”. Pause and press Step +T/8 eight times: the crest marker lands exactly one λ-ruler tick to the right. One λ per T ⇒ v = λ/T = fλ, and the fλ readout equals the v slider.
  • “Wave velocity ≠ particle velocity”. Side-by-side readout: wave v is constant while particle v_y oscillates — zero at crests/troughs, maximum (Aω) crossing equilibrium. They are different quantities with different values.
  • “Wave-shift trick”. The ghost profile is the wave T/8 later. Each bead moves toward the ghost: on a rising limb (y increasing with x) the arrow points DOWN, exactly v_y = −v·∂y/∂x for a rightward wave.
  • “The two phase formulas”. Δφ = 2πΔx/λ is computed live from P and Q's separation — and the same Δφ appears as the time offset 2πΔt/T between their two y–t traces.
  • “Who leads whom”. The particle nearer the source (smaller x) reaches each crest earlier on the y–t graph — it leads; the further one lags.
  • “In phase / antiphase”. Snap Q = P + λ: traces overlap exactly (Δφ ≡ 0). Q = P + λ/2: perfect mirror images (Δφ = π). Q = P + λ/4: quarter-period offset (Δφ = π/2).
  • “Sign conventions flip graphs”. Toggle “downward +”: both plotted graphs invert while the 3D motion is unchanged — the physics is identical, only the plotting convention flips.