Electric field (E)
Magnetic field (B)
∇·E = 0 ∇·B = 0 ∇×E = −∂B/∂t ∇×B = μ₀ε₀ ∂E/∂t
← → adjust frequency · ↑ ↓ adjust amplitude · [ / ] adjust phase · Space toggle play · R reset

Wavelength, amplitude and the frame clock

Read the explanation

The actual tool draws a scalar sinusoid. Its spatial argument is two pi times frequency times x divided by ten. The slider therefore specifies cycles per ten source distance units, not a temporal frequency in hertz. At frequency one, spatial wavelength is ten source units. This graph isolates that wavelength relationship while holding source time at zero. Increase the spatial frequency parameter from one to five. Wavelength is ten divided by frequency, so the marker moves down the reciprocal curve. Five complete cycles fit in the ten-unit source interval. The fixed axes show exactly how increasing cycle count decreases spacing. The page’s temporal rate remains one half cycle per source time unit. At frequency five, wavelength is two source distance units. This is the source sinusoid arithmetic, not a calibrated electromagnetic material solver. The two traces labeled E and B in the page are identical scalar functions in the same plot; they do not form a perpendicular physical vector-field visualization. Now hold spatial frequency at one, source time zero, phase zero, and examine the point x equal to two point five. The sine argument there is pi over two, so the field equals amplitude. Start at amplitude zero point five. The source coordinates and units are illustrative. The graph plots the fixed crest value against the amplitude input. Increase amplitude from zero point five to one point five. The crest value rises along a straight line with exactly the same numeric value as amplitude. Frequency, wavelength, source time and phase remain fixed. This isolates vertical scaling; it does not claim changing amplitude alters the spatial period or creates a new physical propagation speed. At amplitude one point five the chosen crest is one point five source field units, three times the initial value. The same source value is used by both labeled scalar traces. No electric-to-magnetic physical unit conversion is modeled. These are teaching calculations for the actual plotted sinusoid. Keep amplitude one and spatial frequency one at the same point x equal to two point five. Freeze source time at zero. The field is sine of pi over two plus phase, equal to cosine of phase. Initially phase is zero, and the field value is positive one. The vertical axis is signed field value from minus one to plus one. Increase phase from zero to pi radians. The marker follows cosine of phase at the fixed spatial point. At pi over two the field passes through zero. At pi it becomes negative one. The sine wave’s amplitude and spatial period stay unchanged; changing phase relocates the pattern relative to the chosen coordinate. This sweep is a control comparison, not physical elapsed time. The final field is negative one at the same point where it began positive one. The source advances its internal time by a fixed increment per draw frame, so its animation is not calibrated to wall-clock seconds. This video deliberately freezes that time and explains the actual source spatial-frequency, amplitude and phase controls while preserving the original tool.

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