Free · Rotational and periodic motion calculators 🌎

Traveling Sine-Wave Displacement & Phase

Evaluate a traveling sinusoidal wave from amplitude, wavelength, position, speed, time and phase, with retained inverse branches.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

With amplitude 2 cm, wavelength 4 cm, position 1 cm, zero time and zero phase, the displacement is 2 cm.

y = A sin[(2π/λ)(x − vt) + φ]

Enter these known values and leave the other values blank.

Amplitude is nonnegative and wavelength is positive. Displacement magnitude cannot exceed amplitude.
The model is a single ideal traveling sinusoid, without damping, dispersion or superposition. Positive speed propagates toward increasing position.
Inverse trigonometric calculations return one retained solution branch. Periodic waves have many equivalent phases, positions and times; this tool does not enumerate all roots.

The sine repeats, so a displacement may occur at multiple times. The inverse returns one branch consistent with the equation.

Yes. The phase selector converts degrees and radians; the calculation uses radians internally.

Bookify rejects displacement magnitudes greater than the amplitude before inverse trigonometric calculations.