What does the Harmonic Wave Equation Calculator do?

It evaluates the displacement of a sinusoidal travelling wave using the equation y = A * sin(kx - ωt + φ), where A is amplitude, k is wave number, ω is angular frequency, x is position, t is time, and φ is phase.

What units should I use for the inputs?

Amplitude in meters (m), wave number in radians per meter (rad/m), angular frequency in radians per second (rad/s), position in meters (m), time in seconds (s), and phase in radians (rad).

Can this calculator handle negative values for position or time?

Yes, the calculator accepts negative values for position and time, which can represent waves traveling in the opposite direction or evaluating at earlier times.

Physics

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Harmonic Wave Equation Calculator.

Evaluate a sinusoidal travelling-wave equation.

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Set your values

Results update as you type.

02 / ANSWER

Amplitude

Wave number

Angular frequency

Position

Time

Phase

Displacement

Results update automatically as you type.

Use Cases

Physics Homework and Exam Preparation

Quickly verify manual calculations of wave displacement for textbook problems or practice exercises.

Example: Check the displacement of a wave with A=0.5 m, k=2 rad/m, ω=3 rad/s at x=1 m, t=2 s, φ=0.

Engineering Wave Analysis

Evaluate wave displacement at specific points and times for designing or analyzing systems like acoustic or electromagnetic waves.

Example: Determine the displacement of a sound wave in air at a given position and time.

Frequently Asked Questions

What does the Harmonic Wave Equation Calculator do?: It evaluates the displacement of a sinusoidal travelling wave using the equation y = A * sin(kx - ωt + φ), where A is amplitude, k is wave number, ω is angular frequency, x is position, t is time, and φ is phase.
What units should I use for the inputs?: Amplitude in meters (m), wave number in radians per meter (rad/m), angular frequency in radians per second (rad/s), position in meters (m), time in seconds (s), and phase in radians (rad).
Can this calculator handle negative values for position or time?: Yes, the calculator accepts negative values for position and time, which can represent waves traveling in the opposite direction or evaluating at earlier times.

Tips & Common Mistakes

Tips

Ensure all inputs are in the specified units (m, rad/m, rad/s, s, rad) to get correct results.
Remember that the phase φ shifts the wave horizontally; a positive phase shifts the wave to the left.
Use consistent sign conventions: the equation y = A sin(kx - ωt + φ) represents a wave traveling in the positive x-direction.
For a wave traveling in the negative x-direction, you can use a negative wave number or adjust the phase accordingly.

Common Mistakes to Avoid

Mixing up units, such as using degrees for phase instead of radians.
Forgetting to include the phase term, which can lead to incorrect displacement values.
Using the wrong sign for the angular frequency term (ωt) relative to the wave number term (kx).

Last updated: August 13, 2026