How this calculator works
The sine argument combines position, elapsed time and initial phase. The minus sign before the time term makes the wave travel in the positive position direction. The curve shows two wavelengths at the selected time. This model has constant amplitude and speed, with no damping or dispersion. Inverse modes use the principal sine branch, with phase between -pi/2 and pi/2 before subtracting initial phase. Other branches and whole cycles give additional solutions; a rejected positive-speed solution can indicate a different branch is needed.
Formula
y(x,t) = A sin(kx - omega t + phi); k = 2 pi/lambda; omega = k v; f = v/lambda.
Worked example
With A = 2 m, wavelength 4 m and speed 2 m/s, at x = 1 m and t = 0 the displacement is 2 m. With A = 3 m, wavelength 8 m and speed 4 m/s, x = 0 and t = 0.5 s give -3 m.
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Frequently asked questions
Is wave speed the particle speed?
No. Wave speed describes pattern propagation. Particle velocity is the time derivative of displacement.
Why is phase not unique?
Sine repeats every full turn and has two branches per cycle. A single measured displacement cannot identify a unique phase.
Can amplitude be inferred at a node?
A zero sine factor gives zero displacement for every amplitude, so amplitude cannot be inferred there.